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+    {
+        "type": "text",
+        "text": "Fully Convolutional One-Stage 3D Object Detection on LiDAR Range Images ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Zhi Tian1, Xiangxiang $\\mathbf { C h u ^ { 1 } }$ , Xiaoming Wang2∗, Xiaolin Wei1, Chunhua Shen3† ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Meituan Inc. 2 Northwestern Polytechnical University 3 Zhejiang University 1 {tianzhi02,chuxiangxiang,weixiaolin02}@meituan.com 2 chunhua@me.com 3 xiaomingwang80@163.com ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            332,
+            535,
+            348
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "We present a simple yet effective fully convolutional one-stage 3D object detector for LiDAR point clouds of autonomous driving scenes, termed FCOS-LiDAR. Unlike the dominant methods that use the bird-eye view (BEV), our proposed detector detects objects from the range view (RV, a.k.a. range image) of the LiDAR points. Due to the range view’s compactness and compatibility with the LiDAR sensors’ sampling process on self-driving cars, the range view-based object detector can be realized by solely exploiting the vanilla 2D convolutions, departing from the BEV-based methods which often involve complicated voxelization operations and sparse convolutions. ",
+        "bbox": [
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+            363,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "For the first time, we show that an RV-based 3D detector with standard 2D convolutions alone can achieve comparable performance to state-of-the-art BEV-based detectors while being significantly faster and simpler. More importantly, almost all previous range view-based detectors only focus on single-frame point clouds, since it is challenging to fuse multi-frame point clouds into a single range view. In this work, we tackle this challenging issue with a novel range view projection mechanism, and for the first time demonstrate the benefits of fusing multi-frame point clouds for a range-view based detector. Extensive experiments on nuScenes show the superiority of our proposed method and we believe that our work can be strong evidence that an RV-based 3D detector can compare favourably with the current mainstream BEV-based detectors. Code will be made publicly available. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            670,
+            310,
+            686
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "With the rise of autonomous driving, 3D object detection from the LiDAR point cloud has been recently drawing increasing attention. Similar to the 2D image object detection [RHGS15, TSCH19, $\\mathrm { L A E ^ { + } } \\dot { 1 } 6$ , RF17, RDGF16], 3D object detection requires the model to predict the (3D) locations of the objects of interest and the associated properties (e.g., categories, sizes, heading, and the state of motion). In spite of the unprecedented success that the computer vision community has attained on the 2D image object detection, it is still intractable to transfer the success to the 3D object detection task. ",
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+        "text": "Most previous 3D object detection methods consider that the point cloud is amorphous and consists of a set of unordered points. Thus, this task is considered significantly different from its 2D detection counterpart, which works on structured RGB images. Moreover, the cornerstones of modern computer vision—CNNs or CNN-like vision transformers (e.g., Swin Transformers $[ \\mathrm { L L C ^ { + } } 2 1 ]$ ) also assume that the inputs are well-organized as grids, which poses another difficulty of accurate 3D object detection in point clouds. As a result, in order to adopt these well-developed techniques, almost all top-performing point cloud object detection methods first partition the 3D space into structured voxels (or pillars) [ZT18, YZK21, YML18, $\\mathrm { L V C ^ { + } } 1 9$ , Li17] and then follow a paradigm similar to that of 2D object detectors [RHGS15, ZWK19]. Additionally, given the prior that it is very rare two objects being stacked along with the elevation axis in autonomous driving scenes, most methods only carry out the detection task on the bird-eye view (BEV) of the point cloud, which can reduce the exponentially increasing complexity resulted from the third dimension. However, owing to incompatibility with the LiDAR’s sampling process in the autonomous driving scenes, BEV-based solutions often suffer from the following shortcomings. 1) In fact, the points in autonomous driving are regularly sampled in the spherical coordinate system with the origin being the LiDAR sensor. The BEV disregards this regularity, and causes the issue that the voxels far away from the origin have much fewer points than the ones near the origin; and a large number of voxels are even empty. This results in the need for sparse convolutions [YML18, YZK21, Gra14], significantly complicating the system, particularly for on-device applications. 2) The points in a voxel have to be sampled or padded so that every voxel has the same number of points. The sampling decimates a large number of points, leading to the loss of information before the model see anything. 3) From the BEV, some objects such as “pedestrian” and “traffic cone” become very small. Accurately detecting these objects requires a fine-grained voxel size, dramatically increasing the price of computation. ",
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+            "Figure 1: The range image of the point cloud (right). The size of the range image is $m \\times n$ , where $m$ is the number of beams and $n$ is the number of measurements (i.e., sampling frequency) per scan cycle. A 3D point’s coordinates on the range image are computed by discretizing the azimuthal angle $\\theta$ and the inclination angle $\\phi$ in the spherical coordinate system (left). The $m , n$ , and $\\Delta \\phi$ depend on the LiDAR specifications. "
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+        "text": "In this work, we advocate a new solution for 3D object detection that works on the range view (RV). As noted by many previous works $[ \\mathrm { F X W ^ { + } } 2 1$ , $\\mathrm { S K D } ^ { + } 2 0$ , $\\mathbf { M } \\mathbf { L } \\mathbf { K } ^ { + } \\mathbf { 1 9 } ]$ , if we consider these points in the spherical coordinate system and project them in terms of their inclination and azimuth angles, they can form a compact 2D image with size being $m \\times n$ (shown in Fig. 1), where $m$ is the number of beams (i.e., channels) of the LiDAR sensor and $n$ is the sampling frequency per scan cycle. The resulting image is referred to as “range image” or “range view” of the point cloud. Compared to the aforementioned BEV, the range image is nearly dense and compatible with the LiDAR sampling process, eliminating the need for sparse convolutions and alleviating the loss of points. In addition, the range image closely resembles the common RGB image, minimizing the cost of transferring the 2D detection methods to 3D ones. In the literature, some works attempted to detect objects on the range view such as RangeDet $[ \\mathrm { F X W } ^ { + } 2 1 ]$ and LaserNet $[ \\mathrm { M L K ^ { + } } 1 9 ]$ . These works have shown that RV-based methods can also achieve decent detection performance, showing the promise. However, previous RV-based methods only focus on the single-frame point cloud as the aforementioned range view structure does not hold anymore if the ego (and the origin) moves between the multiple frames. Additionally, the range image of a single-frame point cloud is already nearly dense so that there are not many vacancies the points from other frames can populate. These issues make the range-view based detectors difficult to benefit from the multi-frame fusion. In sharp contrast, the multi-frame fusion can dramatically improve the performance in the BEV-based detectors, as shown in [YZK21, $\\mathrm { L V C ^ { + } } 1 9 ]$ . This makes the performance of RV-based detectors largely lag behind that of the BEV-based ones, hampering their development and application. In this work, we show this issue can be largely remedied with a well-designed Multi-round Range View (MRV) projection mechanism. The proposed MRV makes the RV-based detectors be able to enjoy the gain of multi-frame fusion and thus achieve competitive performance with multi-frame BEV-based detectors. ",
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+        "type": "text",
+        "text": "Here, we summarize our main contributions as follows. ",
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+        "text": "• We propose a fully convolutional one-stage 3D object detector, termed FCOS-LiDAR. FCOS-LiDAR works on the LiDAR range images and minimizes the gap between the 3D and 2D detectors, while being substantially simpler than current mainstream BEV-based 3D detectors [YZK21, ZT18].   \nCompared to previous BEV-based detectors [ZT18, YZK21], FCOS-LiDAR sidesteps the complicated voxelization process and eliminates the need for sparse convolutions due to the highly compact range view representation of the point cloud. In the setting of only using the single-frame point cloud as inputs, FCOS-LiDAR can outperform the state-of-the-art BEV-based detector CenterPoint [YZK21] while being faster.   \n• We also present a well-designed Multi-round Range View (MRV) projection mechanism, making RV-based detectors be able to benefit from the multi-frame fusion of point clouds as well, and achieve competitive performance compared to the multi-frame BEV-based detectors. To our knowledge, we are the first one approaching the challenge of the RV-based multi-frame point clouds fusion and showing that RV-based detectors can also be boosted by the multi-frame fusion of point clouds.   \n• We believe that our excellent performance of the RV-based detector can be a strong evidence that RV-based detectors compare favorably against the mainstream BEV-based detectors and encourage the community to pay attention to this promising solution. ",
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+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+        "text": "Bird-view based 3D Detection. Most top-performing LiDAR-based 3D detectors $[ \\mathrm { F P Z ^ { + } } 2 1$ , YML18, YZK21, $\\mathrm { L V C ^ { + } } 1 9$ , ZT18] fall into this category, which first convert the point cloud into BEV images. VoxelNet [ZT18] is the first end-to-end BEV-based detector, which employs PointNet [QSMG17] to handle the representation within a voxel and 3D convolutions to generate high-level features for the region proposal network (RPN). SECOND [YML18] proposes to use sparse convolutions, which can save the computing burden of 3D convolutions. Another popular approach is to eliminate the voxelization along the elevation axis and convert the point cloud into the pillars $[ \\mathrm { L V C ^ { + } } 1 9 ]$ . Based on the voxel-based or pillar-based BEV representation, CenterPoint [YZK21] achieves state-of-the-art performance by using the anchor-free pipelines. ",
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+        "type": "text",
+        "text": "Range-view based 3D Detection. Due to the compactness of the RV representation, some methods $[ \\bar { \\mathrm { S } } \\mathrm { W } \\mathrm { C } ^ { + } 2 1$ , $\\mathrm { B S M ^ { + } } 2 1$ , $\\mathrm { M L K ^ { + } } 1 9$ , $\\mathrm { M L K ^ { + } } 1 9 ]$ also attempt to perform detection based on the representation. VeloFCN [LZX16] is the pioneering work to perform 3D objection using the range view, which transforms point cloud to the range image and then applies 2D convolution to detect 3D objects. After that, some following works $[ \\mathrm { M L K ^ { + } } 1 9$ , $\\mathrm { F X W } ^ { + } \\bar { 2 } \\bar { 1 } ]$ are proposed to narrow the performance gap between RV-based and BEV-based detectors. LaserNet $[ \\mathrm { M L K ^ { + } } 1 9 ]$ models the distribution of 3D box corners to capture their uncertainty, resulting in more accurate defections. RCD $[ \\mathbf { B } \\mathbf { S } \\mathbf { M } ^ { + } 2 1 ]$ introduces the range-conditioned dilation mechanism to dynamically adjust the dilation rate in terms of the measured range, which can alleviate the scale-sensitivity issue of the RV-based detectors. RangeDet $[ \\mathrm { F X W } ^ { + } 2 1 ]$ further proposes the Range Conditioned Pyramid to mitigate the scale-variation issue and utilizes the Meta-Kernel convolution to better exploit the 3D geometric information of the points. To our knowledge, these existing RV-based detectors only take into consideration the single frame point cloud and neglect the substantial improvements brought by the multi-frame fusion as shown in BEV-based detectors. ",
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+        "type": "text",
+        "text": "3 Our Approach ",
+        "text_level": 1,
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+        "text": "3.1 Range View Representation ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Given a LiDAR point $( x , y , z )$ in the Cartesian coordinate system with the $z$ -axis pointing upward, it can be uniquely transformed to the spherical coordinates $( r , \\theta , \\phi )$ with ",
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+        "img_path": "images/f42dc75d358641288957e7ca3222d8a3afa92243280c3c9959c519cd0fbcdbf2.jpg",
+        "text": "$$\nr = \\sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } , \\theta = \\mathrm { a t a n 2 } ( y , x ) , \\phi = \\mathrm { a t a n 2 } ( z , \\sqrt { x ^ { 2 } + y ^ { 2 } } ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $r , \\theta$ , and $\\phi$ are the range, azimuthal angle, and inclination angle, respectively, as shown in Fig. 1(left). The LiDAR samples the points with a fixed number of beams (denoted by $m$ ), each of which has a fixed inclination angle. These LiDAR beams synchronously rotate around the $z$ -axis uniformly to obtain a $3 6 0 ^ { \\circ }$ horizontal field of view and the LiDAR measures a certain number of times (denoted by $n$ ) per scan cycle (i.e., per frame). Thus, the difference of adjacent measurements’ azimuthal angles is $3 6 0 / n ^ { \\circ }$ . For example, on the nuScenes dataset, the LiDAR measures $n = 1 0 8 6$ times per scan cycle and has $m = 3 2$ beams. The inclination angles of these beams are evenly spaced from $- 3 0 . 6 7 ^ { \\circ }$ to $1 0 . 6 7 ^ { \\circ }$ , inclusive. Note that the inclination angles are not always evenly spaced and subject to the specifications of the LiDAR. ",
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+    {
+        "type": "text",
+        "text": "Given the regularity of the azimuthal and inclination angles for a given LiDAR, we can discretize the azimuthal angles with $n$ bins, and inclination angles with $m$ bins, respectively. Let $( i , j )$ be the indices of the bins for azimuthal and inclination angles, respectively. By computing all the pairs of $( i , j )$ of the points in a single scan cycle, we can fill these points into a 2D image $\\bar { I } \\bar { \\in } \\mathbb { R } ^ { m \\times n \\bar { \\times } C }$ (i.e., the range image), where $C = 9$ consists of the original Cartesian coordinates $( x , y , z )$ , the spherical coordinates $( r , \\theta , \\phi )$ , the reflected intensity $i$ , the existence $e$ of the point, and a relative timestamp $t$ The existence denotes whether or not the location is filled by a point, and the relative timestamp is only valid in the multi-frame point cloud inputs and denotes the time difference between the frame containing this point and the current frame. In practice, the vehicle itself is often in motion, and this causes that some points might be projected to the same bins on the range image. In this case, we keep the one with the minimal distance to the vehicle. ",
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+        "type": "text",
+        "text": "3.2 Multi-round Range View Projection (MRV) ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The point cloud of a single frame is often sparse in the 3D space and of low resolutions. In order to improve the detection performance, the current frame is often combined with several previous frames as the network’s inputs [YZK21, ZT18]. Taking the nuScenes dataset as an example, the methods on this dataset often take as the inputs 10 frames, which is composed of the current frame and previous 9 frames, including ${ \\sim } 2 4 0 \\mathrm { K }$ points in total. The crucial issue of the range view representation is the collision that multiple points fall into the same bin happens much more frequently in the multi-frame case. For instance, on nuScenes, only ${ \\sim } 2 8 \\mathrm { K }$ points are finally kept in the range image and ${ \\sim } 9 0 \\%$ of the points are discarded due to the collision. The decimation makes the multi-frame point cloud have almost the same number of valid points with the single-frame version, which is the dominant reason that RV-based methods cannot enjoy the benefit of multi-frame inputs. ",
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+        "type": "text",
+        "text": "In order to cope with this crucial issue, we propose the Multi-round Range View (MRV) projection mechanism. To be specific, we first project the points with the method in Sec. 3.1. Then, instead of discarding the rejected points, we project them again with the same process and put them in another group of nine channels. This projection process is repeated until a sufficient number of points are kept. On the nuScenes dataset, this is repeated five times and the percentage of the retained points can be improved from ${ \\sim } 1 0 \\%$ to more than $50 \\%$ . In theory, as long as we continue the process, all points can be kept. However, we found that the performance is saturated after 5 repetitions on the nuScenes dataset. Finally, the resulting range images of the five rounds are concatenated along the channel dimension and used as the inputs. Additionally, one caveat is that the points of the current frame should have the highest priority wherever the collision happens because the points of previous frames are stale and might not reflect the current status of the world. Despite being a very simple treatment, it significantly affects the effectiveness of the multi-frame fusion as shown in our experiments. ",
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+        "type": "text",
+        "text": "3.3 Modality-wise Convolutions ",
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+        "type": "text",
+        "text": "As mentioned before, each pixel on the single-frame range image contains nine channels. Different the RGB image, whose three channels are of the same modality (i.e., in the color space) and correlated for the manifold of natural images, the nine channels of the range image are not like that and belong to five modalities, i.e., $[ x , y , z ]$ , $[ r , \\theta , \\phi ]$ , [i], $[ e ]$ and $[ t ]$ , respectively, where the channels in the one pair of square brackets are of the same modality. For example, the correlation between the reflected intensity $i$ and the coordinate $x$ does not make sense. Further, even the different channel types in the same modality are orthogonal and less correlated as well. For instance, it is difficult to say there is a relationship between the azimuthal angle $\\theta$ and the range $r$ of a point. As a result, one channel type should be viewed as an individual “modality”. By default, the conv. layer simultaneously computes spatial correlations and cross-channel correlations. However, as shown before, the channels of the range image are less correlated, and thus, it is not reasonable to use the default conv. layer here, and the channels of the range image should be processed separately. This can be easily implemented with the grouped convolutions. Here, we term it modality-wise convolution because it is based on the “modalities”. Once the high-level semantic features of these modalities are individually obtained, we can aggregate the features of these modalities with a $1 \\times 1$ conv. layer (i.e., point-wise convolution) for further abstract analysis. ",
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+        "img_path": "images/67aad4d18ca4e000364946778b787a418ea050c0876b322f7af004777961aeda.jpg",
+        "image_caption": [
+            "Figure 2: Modality-wise convolutions with a multi-frame range image. As we can see, we first rearrange the channels of the multi-frame range image so that the channels with the same type from different frames (e.g., $x _ { 0 }$ , $x _ { 1 }$ , ... $x _ { T - 1 } )$ are adjacent. Then, two successive 2D conv. layers with the number of groups being 9 (which is equal to the number of different channel types) are used to process these channels separately, mapping each channel type to a 32-channel features. Finally, the features of these channel types are merged by a $1 \\times 1$ conv. layer. "
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+        "text": "In this way, the modality-wise convolution is analogous to the widely-used depth-wise convolution, but we highlight that the underlying nature is distinct. Our modality-wise convolution instantiates a reasonable inductive bias based on the prior that different modalities are less relevant, and thus it is expected to simultaneously improve both the effectiveness and efficiency, as shown in our experiments. This also leads to the fact that the modality-wise convolution can only be placed at the beginning of the network, where the channels are interpretable and have an explicit modality. In contrast, the depth-wise convolution (together with the point-wise convolution) is often viewed as an efficient approximation of the full conv. layer and thus it does not usually yield improved performance and can appear anywhere. Lastly, when it comes to the multi-frame point clouds, the channels of the same type from different frames should be handled together because they are closely correlated. The whole procedure of the modality-wise convolution is illustrated in Fig. 2. ",
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+    {
+        "type": "text",
+        "text": "3.4 Overall Architecture ",
+        "text_level": 1,
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+        "text": "The overall architecture of FCOS-LiDAR is shown in Fig. 3. FCOS-LiDAR follows the spirit of the anchor-free detector FCOS [TSCH19] in the image-based object detection and is a standard fully convolutional network [LSD15]. ",
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+        "text": "Taking a (multi-frame) range image $I \\in \\mathbb { R } ^ { m \\times n \\times ( T \\times C ) }$ as an example, where $T$ is the number of the used frames, we first forward the range image through our backbone network, termed LiDAR-Net. LiDAR-Net is adapted from ResNet-50 [HZRS16]. Specifically, before the first conv. layer of ResNet50, we insert three branches of the modality-wise convolutions with three dilation rates being 1, 3, and 6, respectively. The branches with various dilation rates aim to capture the multi-scale context, whose outputs are summed up. Then, the first two $2 \\times$ downsamplings of ResNet-50 are removed, which is of great importance due to the low resolutions of the range images. Moreover, we change the numbers of blocks of ResNet-50’s four stages from $( 3 , 4 , 6 , 3 )$ to $( 4 , 4 , 1 , 1 )$ and stop doubling the number of channels in the third and fourth stages because we found that the final performance is not sensitive to the capacity of the later stages but quite sensitive to that of the early stages. This ravels one of the important difference between the LiDAR-based and image-based object detection tasks. For object detection in RGB images, more convolutions in the later stages are often required to transform the RGB pixels into the highly semantic and abstract features that can be used to obtain the geometries of the objects. However, the LiDAR points themselves are already geometric points and thus that many convolutions in the later stages are no longer needed. Thus, we can instead allocate the capacity in the later stages to the early stages (before any downsampling) to better incorporate the geometric information carried by the raw points. Finally, the four levels of feature maps from LiDAR-Net’s four stages are used, denoted by $C _ { 2 }$ , $C _ { 3 }$ , $C _ { 4 }$ , and $C _ { 5 }$ , respectively. ",
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+    {
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+        "img_path": "images/ccc7a5ad0561507b5fc76d7c684bc309f1ceec7dbcca626196036e4658e76911.jpg",
+        "image_caption": [
+            "Figure 3: Overall architecture. The overall architecture of FCOS-LiDAR resembles the 2D imagebased detector FCOS [TSCH19]. By taking as input an range image, the network obtains the multi-level FPN features, and then the classification and regression branches are attached to these feature levels to predict the final 3D boxes. Different from FCOS, the weights of the detection heads are not shared between the FPN levels as mentioned in Sec. 3.4. In addition, the class-specific regression heads are used instead of the class-agnostic ones in FCOS. "
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+        "text": "Next, following FCOS, the four levels of feature maps are sent into a feature pyramid network (FPN) $[ \\mathrm { L D G ^ { + } i } \\bar { 7 } ]$ to obtain six levels of pyramid feature maps denoted by $P _ { 2 }$ , $P _ { 3 }$ , $P _ { 4 }$ , $P _ { 5 }$ , $P _ { 6 }$ , and $P _ { 7 }$ . Their spatial downsampling ratios to the input are $1 / 1 , \\bar { 1 / 2 } , \\bar { 1 / 4 } , \\bar { 1 / 8 } , \\bar { 1 / } \\bar { 1 6 }$ , and $^ { 1 / 3 2 }$ , respectively. Then, similar to FCOS, the classification and regression heads, each with four $3 \\times 3$ conv. layers of channel 64 and a final prediction conv. layer (for the classification or regression), are attached to these feature levels. Unlike the heads in image-based detectors, whose weights are shared between these feature levels, it is important in the LiDAR-based detector to untie these weights. This is another important difference between image-based and LiDAR-based detectors. In image-based detectors, different sizes of objects can be normalized to similar sizes of objects by the downsampling the image with corresponding factors. That is what the “pyramid” means in the FPN. Thus, the image-based detectors can share the weights of the detection heads because the objects have been normalized to similar sizes after the FPN. However, in LiDAR-based detection, the objects’ sizes cannot be normalized in this way because the sizes of the objects are determined by the 3D points’ coordinate values in them and downsampling the range images cannot alter their real sizes in the 3D space. Therefore, it is no longer reasonable to share the detection heads between these FPN levels. This is also confirmed in our experiments. ",
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+    {
+        "type": "text",
+        "text": "Training Targets Computation. Similar to FCOS [TSCH19], we need to assign the training targets to each location of the feature maps computed with the range image. The training targets computation is described using the nuScenes dataset as an example. On nuScenes, an object’s ground-truth 3D box is parameterized by $( c _ { x } ^ { * } , c _ { y } ^ { * } , c _ { z } ^ { * } , w ^ { * } , h ^ { * } , l ^ { * } , \\alpha ^ { * } )$ , where $( c _ { x } ^ { * } , c _ { y } ^ { * } , c _ { z } ^ { * } )$ is the 3D center of the box, and $w , h , l$ , and respectively are the width, height, length, and the yaw angle around the axis. First, each location on the feature maps is mapped to the pixel location on the range image by multiplying them by the feature maps’ downsampling ratio. Next, we use the 3D LiDAR point projected by the first-round MRV projection as the 3D point of the pixel. If the pixel’s 3D point is contained in an object’s 3D box, the feature location is responsible for the object and predicts its category, 3D box and etc.. Here, the 3D box regression targets of the feature location are relative to the 3D point coordinates of the pixel and are defined as ",
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+    {
+        "type": "equation",
+        "img_path": "images/82528897c139459bcb53c50be8d93f9b0fa7e41ec523b340ee11bc394a50b6b0.jpg",
+        "text": "$$\n\\Delta c _ { x } = c _ { x } ^ { * } - x _ { 0 } , \\Delta c _ { y } = c _ { y } ^ { * } - y _ { 0 } , \\Delta c _ { z } = c _ { z } ^ { * } - z _ { 0 } , t _ { w } = \\log ( w ^ { * } ) , t _ { h } = \\log ( h ^ { * } ) , t _ { l } = \\log ( l ^ { * } ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            179,
+            155,
+            797,
+            174
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $( x _ { 0 } , y _ { 0 } , z _ { 0 } )$ are the 3D point coordinates of the range image pixel. Similarly, the regression targets of the yaw angle $\\alpha$ are also relative to the azimuthal angle of the pixel, and following the convention [YZK21], we decouple the relative azimuthal angle into $( \\sin \\Delta \\alpha , \\cos \\Delta \\alpha )$ . On nuScenes, we also need to predict the velocity vector $( v _ { x } ^ { * } , v _ { y } ^ { * } )$ of the object, which are used as the training targets as is. Other locations on the feature maps that correspond to 3D points not in any 3D box are used as the negative samples. Note that all the pixels within a object’s 3D box actually form a 2D mask on the range image. ",
+        "bbox": [
+            174,
+            181,
+            825,
+            280
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Network Outputs. The nuScenes dataset has $C = 1 0$ classes of interest, which is predicted by the classification head followed by a softmax layer (the upper head in Fig. 3). The other regression targets are predicted by four sibling output heads of the regression branch, respectively, as shown in Fig. 3. Here, we use the class-specific regression predictions and thus the number of the output channels is amplified by $C$ times. Moreover, following $[ \\mathrm { G L W ^ { + } } 2 1$ , RDGF16], each positive pixel also predicts the intersection-over-union (IoU) between the predicted 3D box and ground-truth one, which is multiplied to the classification score before the non-maximum suppression (NMS). ",
+        "bbox": [
+            174,
+            285,
+            825,
+            382
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Loss Functions. The classification predictions are supervised with the cross entropy (CE) loss. Following $[ \\mathrm { G L L ^ { + } } 2 1 ]$ , we dynamically reassign the classification labels during training. Specifically, for a ground-truth 3D box, only the top $K$ pixels whose predicted 3D boxes have the lowest costs with the ground-truth box are assigned with the positive labels and other pixels are considered negative, where the cost is defined as the summation of the classification loss and the opposite of the IoU between the predicted boxes and the ground-truth box, and $K$ is dynamically calculated, being the summation (rounded to an integer) of the highest $Q = 2 0$ IoUs between the predicted boxes and the ground-truth box. For the 3D box regression, we make use of both the IoU loss $[ \\mathrm { Y } \\mathrm { J } \\mathrm { W } ^ { + } 1 6 ]$ and $L _ { 1 }$ loss. Following [TSCH19], the IoU predictions are penalized with the binary cross entropy (BCE) loss since they are in the range $[ 0 , 1 ]$ . ",
+        "bbox": [
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+            388,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Inference. The inference is very similar to that of the 2D image-based detector FCOS. To be specific, the range images are forwarded through the network and the aforementioned predictions are obtained. The predictions are filtered in terms of the classification scores and only the predictions with the score greater than 0.01 are kept. The 3D boxes are restored by inverting the computation of the training targets. Then, the NMS on the 3D boxes is applied with threshold 0.2 to remove the duplications. Finally, the top 500 predictions with the highest scores are used as the final predictions. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            637,
+            312,
+            655
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We conduct experiments on the nuScenes dataset $[ \\mathrm { C B L ^ { + } } 2 0 ]$ , which contains 1000 scenes with 700, 150, and 150 scenes for training, validation, and testing, respectively. The training, validation, and testing sets have 28K, 6K, 6K keyframes annotated with 10 classes, respectively. For all ablation experiments, we train the models on the training set and report the performance on the validation set unless specified. The metrics of the 3D detection task are mean Average Precision (mAP) and the nuScenes detection score (NDS). The LiDAR sensor of the nuScenes dataset has $m = 3 2$ beams and $n = 1 0 8 6$ measurements per scan cycle. The mAP is based the center distances on the bird-eye view at thresholds $0 . 5 \\mathrm { m }$ , 1m, $2 \\mathrm { m }$ , $4 \\mathrm { m }$ in place of the box IoUs. NDS is a weighted average of mAP, the translation error, the scale error, the orientation error, the velocity error, and the box attributes error. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details. Unless specified, following [YZK21], FCOS-LiDAR is trained by 40 epochs with the AdamW [LH17] optimizer under the MMDetection3D framework [Con20], which takes ${ \\sim } 2 6$ hours on 8 A100 GPUs. The one-cycle learning rate policy [ST19] with initial learning rate $1 0 ^ { - 3 }$ is used. The learning rate gradually increases to 0.01 in the first $40 \\%$ epochs and then gradually decreases to $1 0 ^ { - 7 }$ in the rest of the training process. The weight decay is 0.01, and the momentum ranges from 0.85 to 0.95. In addition, due to the low vertical resolution of the range image on the nuScenes dataset, we upscale the range image in the vertical direction by 2 with the nearest interpolation. During training, the point cloud is randomly flipped along both the $x$ and $y$ axes and rotated in the range $[ - \\pi , \\pi ]$ , as well as globally scaled by a random factor from [0.95, 1.05]. The ground-truth copy-paste data augmentation from [YML18] is also used. For multi-frame point cloud, we use 10 sweeps in total, as in previous works [YZK21, $\\mathrm { L V C ^ { + } } 1 9 ]$ . The inference time is measured on a 3090Ti GPU with batch size 1. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/3558dc389ebe8aa1def32a69a011b3e56acf0f83a73003713e4a85d0423f27f0.jpg",
+        "table_caption": [
+            "Table 1: Multi-round range view (MRV) projection. Time: the elapsed time of MRV. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">Single-frame</td><td colspan=\"3\">Multi-frame</td></tr><tr><td>#Rounds</td><td>Time (ms)</td><td>mAP (%)</td><td>NDS (%)</td><td>mAP (%)</td><td>NDS (%)</td></tr><tr><td>1</td><td>0.66</td><td>53.14</td><td>51.52</td><td>55.02</td><td>61.27</td></tr><tr><td>3</td><td>0.72</td><td>53.76</td><td>53.62</td><td>56.01</td><td>62.82</td></tr><tr><td>5</td><td>0.76</td><td>53.42</td><td>53.40</td><td>57.08</td><td>63.15</td></tr><tr><td>7</td><td>0.76</td><td>53.06</td><td>53.10</td><td>56.99</td><td>63.47</td></tr></table>",
+        "bbox": [
+            174,
+            112,
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+            199
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e604e51cccb9e56093acc753e0caea81d738f0a54d662978b2e3bcee905610b5.jpg",
+        "table_caption": [
+            "Table 2: Whether to make the points of the current frame have the highest priority. The per-category mAP results are reported. “C.V.”, “Ped.” and “C.T.” indicate “construction vehicle”, “pedestrian” and “traffic cone”, respectively. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Prioritized? mAP(%) NDS(%)</td><td></td><td></td><td>Car</td><td>Truck</td><td>Bus</td><td>Trailer</td><td></td><td></td><td>C.V.Ped. Motor</td><td>Bicycle</td><td>T.C.</td><td>Barrier</td></tr><tr><td></td><td>54.29</td><td>62.31</td><td>76.8</td><td>47.3</td><td>62.0</td><td>32.0</td><td>16.5</td><td>80.3</td><td>53.8</td><td>38.2</td><td>70.1</td><td>65.9</td></tr><tr><td>√</td><td>57.08</td><td>63.15</td><td>82.1</td><td>52.3</td><td>65.2</td><td>33.6</td><td>18.3 84.1</td><td></td><td>58.5</td><td>35.3</td><td>73.4</td><td>67.9</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.1 Multi-round Range View Projection ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            402,
+            462,
+            419
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Here, we conduct experiments to demonstrate the effectiveness of the proposed multi-round range view (MRV) projection. As shown in Table 1, in the single-frame settings, MRV is also helpful, for example, by increasing the number of rounds from 1 to 3, the mAP can be boosted by $0 . 6 2 \\%$ . This is due to the fact that the vehicle is often in motion and the aforementioned collisions happen within a single frame as well. As you can see, if one round is used, the multi-frame fusion can improve the mAP by a substantial margin ${ \\sim } 1 . 9 \\%$ (from $5 3 . 1 4 \\%$ to $5 5 . 0 2 \\%$ ). The improvement can be dramatically increased to $3 . 9 \\%$ mAP if we use 5 rounds in MRV $( 5 7 . 8 \\%$ mAP), due to the fact that 5-round MRV can keep much more points in the multi-frame point clouds as mentioned in Sec. 3.2. This confirmed the effectiveness of MRV. Note that elapsed time of MRV is insensitive to the number of rounds as shown in Table 1. ",
+        "bbox": [
+            173,
+            429,
+            826,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "More importantly, in the RV-based multi-frame settings, it is crucial to assign the highest priority to the points from the current frame when the collision happens. As shown in Table 2, without this treatment, the performance of the multi-frame fusion is significantly dropped from $5 7 . 0 8 \\%$ to $5 4 . 2 9 \\%$ in mAP. Note that the single-frame counterpart can already achieve mAP $5 3 . 4 2 \\%$ . We argue that the neglect of this point in previous works is one of the main reasons that RV-based detectors can barely enjoy the benefit of multi-frame fusion. ",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.2 Modality-wise Convolutions ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            672,
+            406,
+            688
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/548b58822c6d06df6bd1c510cffbfa36fe97e44460f4aab2cb66d74907f6ae5c.jpg",
+        "table_caption": [
+            "Table 3: Modality-wise convolutions. “Multi-round”: whether to group together the channels with the same type from multiple projection rounds. Note that all the items here are with the multi-frame fusion and multi-round projections. The only difference is the way to group the channels. Time: the latency of this module. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Modality groups</td><td>Multi-round</td><td>Time (ms)</td><td>mAP (%)</td><td>NDS (%)</td></tr><tr><td>[x,y,z,r,0,Φ,i,t,e]</td><td>√</td><td>6.0</td><td>56.35</td><td>62.65</td></tr><tr><td>[x,y,z],[r，0,],[i],[t],[e]</td><td>√</td><td>4.2</td><td>56.34</td><td>63.07</td></tr><tr><td>[x],[y]，[2],[r],[0]，[]，[]，[，[e]</td><td>√</td><td>3.2</td><td>57.08</td><td>63.15</td></tr><tr><td>[x],[],[2],，[r],[0],，[],，[]，[],[e]</td><td></td><td>3.8</td><td>56.83</td><td>63.15</td></tr></table>",
+        "bbox": [
+            176,
+            767,
+            823,
+            842
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The experimental results of our modality-wise convolutions are shown in Table 3. If we use the full convolutions here, which compute the correlation between all the channels of the range image, FCOS-LiDAR can achieve $5 6 . 3 5 \\%$ in mAP. By splitting the channels into various modalities (2nd row), the performance can be slightly improved, i.e., from NDS $6 2 . 6 5 \\%$ to $6 3 . 0 7 \\%$ . Moreover, due to the fact that even the different channel types of the same modality are orthogonal and less correlated, we process each channel type individually. As shown in the table, the performance can be further boosted from mAP $5 6 . 3 4 \\%$ to $5 7 . 0 8 \\%$ (3rd row) while the lowest latency is achieved. Finally, the last row shows the results if we do not consider the channels with the same type from multiple rounds together, where the mAP is slightly worse. In Table 4, we vary the number of the conv. layers in the modality-wise convolutions. As we can see, using two conv. layers achieves the best performance here. ",
+        "bbox": [
+            174,
+            856,
+            825,
+            911
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/23aee155ae029f1c086c6594b3771c076217136b6285317aa613109f959879d9.jpg",
+        "table_caption": [
+            "Table 4: Varying the number of the conv. layers in the modality-wise convolutions. Time: the latency of the modality-wise convolutions. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>#Conv. Time (ms) mAP(%) NDS(%) Car Truck Bus Trailer C.V. Ped. Motor Bicycle T.C. Barrier</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1</td><td>2.0</td><td>55.81</td><td>61.98</td><td></td><td>81.8 51.4</td><td>65.2</td><td>30.7</td><td>16.9 83.4</td><td>56.0</td><td>32.8 71.9</td><td>68.1</td></tr><tr><td>2</td><td>3.2</td><td>57.08</td><td>63.15</td><td></td><td>82.1 52.3 65.2</td><td></td><td>33.6</td><td>18.3 84.1</td><td>58.5</td><td>35.3 73.4</td><td>67.9</td></tr><tr><td>3</td><td>4.3</td><td>56.71</td><td>63.25</td><td>82.6 51.4 65.3</td><td></td><td></td><td>31.9</td><td>18.5 83.9</td><td>57.3 34.9</td><td>72.9</td><td>68.4</td></tr></table>",
+        "bbox": [
+            174,
+            126,
+            823,
+            185
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/d6905667f45d5103c4858af51b650edb86dcc426e51ea4502b8bf408b4bc6cb8.jpg",
+        "table_caption": [
+            "Table 5: Multi-scale context aggregation. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dilations mAP(%)</td><td></td><td>NDS(%)</td><td>Car</td><td>Truck</td><td>Bus</td><td>Trailer</td><td>C.V.</td><td>Ped.</td><td>Motor</td><td>Bicycle</td><td>T.C.</td><td>Barrier</td></tr><tr><td>（1,）</td><td>55.87</td><td>62.68</td><td>81.8</td><td>51.0</td><td>64.1</td><td>32.6</td><td>16.9</td><td>83.8</td><td>56.3</td><td>31.2</td><td>72.7</td><td>68.3</td></tr><tr><td>(1,3)</td><td>56.39</td><td>62.96</td><td>82.3</td><td>52.1</td><td>65.3</td><td>32.8</td><td>17.1</td><td>83.7</td><td>58.2</td><td>32.5</td><td>72.0</td><td>67.8</td></tr><tr><td>(1,3,6)</td><td>57.08</td><td>63.15</td><td>82.1</td><td>52.3</td><td>65.2</td><td>33.6</td><td>18.3</td><td>84.1</td><td>58.5</td><td>35.3</td><td>73.4</td><td>67.9</td></tr><tr><td>(1,1,1)</td><td>56.63</td><td>63.12</td><td>82.1</td><td>51.5</td><td>65.2</td><td>32.9</td><td>17.1</td><td>83.7</td><td>58.8</td><td>33.7</td><td>73.1</td><td>68.0</td></tr></table>",
+        "bbox": [
+            176,
+            224,
+            821,
+            296
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            173,
+            325,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In addition, as mentioned before, we employ multiple modality-wise convolution branches with various dilation rates in parallel to capture the multi-scale context. The experiments are shown in Table 5. As we can see, compared with the one using only one dilation rate, using multiple dilation rates can improve the performance by more than $1 \\%$ in mAP (from $5 5 . 8 7 \\%$ to $5 7 . 0 8 \\%$ ). ",
+        "bbox": [
+            174,
+            429,
+            825,
+            486
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3 Untied Weights of Detection Heads ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            505,
+            455,
+            520
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/0e810db4a4aa0f70daf55cb9686f1950f8dcd7ea9a4d46c7e43fba22b5987d5d.jpg",
+        "table_caption": [
+            "Table 6: Whether to untie the weights of the detection heads. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Untied? mAP(%)</td><td></td><td>NDS(%)</td><td>Car</td><td>Truck</td><td>Bus</td><td>Trailer</td><td>C.V.</td><td>Ped.</td><td>Motor</td><td>Bicycle</td><td>T.C.</td><td>Barrier</td></tr><tr><td></td><td>56.44</td><td>63.09</td><td>82.0</td><td>51.1</td><td>64.3</td><td>31.1</td><td>18.3</td><td>83.8</td><td>57.9</td><td>34.7</td><td>72.9</td><td>68.4</td></tr><tr><td>√</td><td>57.08</td><td>63.15</td><td>82.1</td><td>52.3</td><td>65.2</td><td>33.6</td><td>18.3</td><td>84.1</td><td>58.5</td><td>35.3</td><td>73.4</td><td>67.9</td></tr></table>",
+        "bbox": [
+            176,
+            564,
+            823,
+            611
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "As mentioned before, it is better to untie the weights of the detection heads between the FPN levels in the LiDAR-based detector. This is confirmed in Table 6. As we can see, by untying the weights, the performance can be improved from mAP $5 6 . 4 4 \\%$ to $5 7 . 0 8 \\%$ . This ravels one of the interesting differences between image-based and LiDAR-based detectors because the shared detection heads between FPN levels often achieve better performance in image-based detectors [TSCH19, $\\mathrm { L D G ^ { + } } 1 7 ]$ . ",
+        "bbox": [
+            173,
+            627,
+            826,
+            698
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/5625127cd70aa78264e86dd5d09f44e98586e77a4f0eff9d85073bc0b1add537.jpg",
+        "table_caption": [
+            "Table 7: Inference time breakdowns. We compare against the state-of-the-art BEV-based CenterPoint [YZK21], which is trained with exactly the same strategies. We use the CenterPoint implementation in MMDetection3D [Con20] with sparse convolution version 1.2.1 [SPC21]. FCOS-LiDAR is faster as well as competitive in the multi-frame setting (and superior in the single-frame setting). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"7\">Method Voxel/MRV(ms) Backbone(ms) Heads(ms) Overall(ms) mAP(%) NDS(%)</td></tr><tr><td>single-frame point cloud</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CenterPoint [YZK21]</td><td>1.62</td><td>41</td><td>8</td><td>50.62</td><td>52.83</td><td>53.86</td></tr><tr><td>FCOS-LiDAR (Ours)</td><td>0.63</td><td>31</td><td>7</td><td>38.63</td><td>53.42</td><td>53.40</td></tr><tr><td>multi-frame point cloud</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>CenterPoint [YZK21]</td><td>1.95</td><td>63</td><td>9</td><td>73.95</td><td>60.40</td><td>67.25</td></tr><tr><td>FCOS-LiDAR(Ours)</td><td>0.76</td><td>31</td><td>7</td><td>38.76</td><td>57.08</td><td>63.15</td></tr></table>",
+        "bbox": [
+            174,
+            790,
+            823,
+            891
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/f7ccb3a912c1781f1795eb6f7a4bbd9f9f94cc578866dd2d77460643ba4154f2.jpg",
+        "table_caption": [
+            "Table 8: Comparisons with state-of-the-art methods on the nuScenes test set. The results are directly quoted from their original papers. All other methods on nuScenes rely on BEV or multiple views because previous RV-only methods are unable to handle the multi-frame fusion on this dataset. As you can see, our RV-based FCOS-LiDAR can achieve competitive performance with state-of-the-art BEV-based detectors. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method mAP(%)NDS(%) Car Truck Bus TrailerC.V.Ped.Motor Bicycle T.C.Barrier</td></tr><tr><td></td><td>45.3</td><td></td><td></td><td>68.4 23.0 28.2 23.4</td><td>4.1 59.7 27.4 1.1 30.8</td></tr><tr><td>PointPillars [LVC+ 19] SSN [ZMW+20]</td><td>30.5 46.3 56.9</td><td>80.7 37.5 39.9</td><td>43.9 14.672.3 43.7</td></tr><tr><td>CVCNet [CSCY20] 55.3 64.4</td><td>82.7 46.1 46.6 49.4 22.679.8 59.1</td></tr><tr><td>CBGS[YZK21] 52.8 63.3</td><td>31.4 81.1 48.5 54.9 42.9 10.580.1 51.5</td></tr><tr><td>CenterPoint [YZK21] 58.0</td><td>22.3 70.9</td></tr><tr><td>AFDetV2 [HDG+22] 62.4 68.5 S2M2-SSD [ZHJF22] 62.9 69.3 86.3 56.0</td><td>65.5 84.6 51.0 60.2 53.2 17.583.4 53.7 23.7 76.7 86.3 54.2 62.5 58.9 26.785.8 63.8 34.3 80.1</td></tr></table>",
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+        "text": "4.4 Inference Time Comparisons ",
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+        "text": "We compare the inference time of FCOS-LiDAR and the state-of-the-art BEV-based detector CenterPoint [YZK21]. As shown in Table 7, the proposed MRV is faster than the voxelization in CenterPoint. It is worth noting that the voxelization algorithm reported here is nondeterministic, which cannot yield stable results but being significantly faster. In the official code of MMDetection3D [Con20], the deterministic voxelization takes ${ \\sim } 1 0 0 \\mathrm { m s }$ for the multi-frame point clouds. In sharp contrast, the proposed MRV is always deterministic and highly efficient. Moreover, due to the compactness of the range image, our network can be implemented with the standard convolutions alone, thus being much more efficient than CenterPoint using the sparse convolutions as shown in the table. The elapsed time of the post-processing is omitted here as it is closely similar in both methods. ",
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+        "text": "4.5 Comparisons with State-of-the-art Methods ",
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+        "text": "We further compare FCOS-LiDAR with other state-of-the-art methods on the nuScenes test set. For the model on the test set, we increase the number of channels in the detection heads from 64 to 128, which improve the validation mAP by ${ \\sim } 0 . 6 \\%$ with slightly longer latency. Additionally, we remove the copy-paste data augmentation in the last 5 epochs during training as in [WMZY21] (termed as the “fade strategy” in [WMZY21]). This can improve the performance by about $2 \\%$ mAP. As shown in Table 8, FCOS-LiDAR achieves competitive performance with other state-of-the-art BEV-based methods. Note that in order to leverage the multi-frame fusion on nuScenes, all other methods on nuScenes rely on BEV (or the multi-view fusion). FCOS-LiDAR is the first RV-only method that is able to benefit from the multi-frame fusion. ",
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+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
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+        "text": "We have presented an efficient range-view-based 3D object detector FCOS-LiDAR. FCOS-LiDAR shows the challenging LiDAR-based object detection can also be solved with the standard convolutions alone, similar to what we have done in the image-based 2D object detection. We also for the first time show the RV-based 3D detector can also enjoy the benefit of the multi-frame fusion with the proposed MRV. We hope our strong results can encourage the community to pay more attention to this promising direction. ",
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+        "text": "Societal Impacts. This paper presents a method that can locate the 3D location of the objects of interest in LiDAR point clouds. This technique might be abused for military purposes, for example, on lethal autonomous weapons. ",
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+        "text": "Acknowledgments. C. Shen’s participation was in part supported by a major grant from Zhejiang Provincial Government. ",
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+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            90,
+            266,
+            106
+        ],
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+    },
+    {
+        "type": "text",
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Process. Syst., volume 33, pages 21224–21235, 2020.   \n[DLSJ22] Shengheng Deng, Zhihao Liang, Lin Sun, and Kui Jia. Vista: Boosting 3d object detection via dual cross-view spatial attention. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8448–8457, June 2022.   \n$[ \\mathrm { F P Z } ^ { + } 2 1 ]$ Lue Fan, Ziqi Pang, Tianyuan Zhang, Yu-Xiong Wang, Hang Zhao, Feng Wang, Naiyan Wang, and Zhaoxiang Zhang. Embracing single stride 3d object detector with sparse transformer. arXiv preprint arXiv:2112.06375, 2021.   \n$[ \\mathrm { F X W } ^ { + } 2 1 ]$ Lue Fan, Xuan Xiong, Feng Wang, Naiyan Wang, and Zhaoxiang Zhang. Rangedet: In defense of range view for lidar-based 3d object detection. In Proc. IEEE Int. Conf. Comp. Vis., pages 2918–2927, 2021.   \n$[ \\mathrm { G L L ^ { + } } 2 1 ]$ Zheng Ge, Songtao Liu, Zeming Li, Osamu Yoshie, and Jian Sun. OTA: Optimal transport assignment for object detection. In Proc. IEEE Conf. Comp. Vis. 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SSD: Single shot multibox detector. In Proc. Eur. Conf. Comp. Vis., pages 21–37. Springer, 2016.   \n$[ \\mathrm { L D G ^ { + } } 1 7 ]$ Tsung-Yi Lin, Piotr Dollár, Ross Girshick, Kaiming He, Bharath Hariharan, and Serge Belongie. Feature pyramid networks for object detection. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 2117–2125, 2017. [LH17] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017. [Li17] Bo Li. 3d fully convolutional network for vehicle detection in point cloud. In Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, pages 1513–1518, 2017.   \n$[ \\mathrm { L L C } ^ { + } 2 1 ]$ Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In Proc. IEEE Int. Conf. Comp. Vis., pages 10012–10022, 2021. [LSD15] Jonathan Long, Evan Shelhamer, and Trevor Darrell. Fully convolutional networks for semantic segmentation. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 3431–3440, 2015.   \n$[ \\mathrm { L V C ^ { + } } 1 9 ]$ Alex Lang, Sourabh Vora, Holger Caesar, Lubing Zhou, Jiong Yang, and Oscar Beijbom. Pointpillars: Fast encoders for object detection from point clouds. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 12697–12705, 2019. [LZX16] Bo Li, Tianlei Zhang, and Tian Xia. Vehicle detection from 3d lidar using fully convolutional network. arXiv preprint arXiv:1608.07916, 2016.   \n$[ \\mathrm { M L K ^ { + } } 1 9 ]$ Gregory P Meyer, Ankit Laddha, Eric Kee, Carlos Vallespi-Gonzalez, and Carl Wellington. Lasernet: An efficient probabilistic 3d object detector for autonomous driving. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 12677–12686, 2019.   \n[QSMG17] Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. Pointnet: Deep learning on point sets for 3d classification and segmentation. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 652–660, 2017.   \n[RDGF16] Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You only look once: Unified, real-time object detection. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 779–788, 2016. [RF17] Joseph Redmon and Ali Farhadi. Yolo9000: Better, faster, stronger. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 7263–7271, 2017.   \n[RHGS15] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster R-CNN: Towards real-time object detection with region proposal networks. In Proc. Advances in Neural Inf. Process. Syst., pages 91–99, 2015.   \n$[ \\mathrm { S K D } ^ { + } 2 0 ]$ Pei Sun, Henrik Kretzschmar, Xerxes Dotiwalla, Aurelien Chouard, Vijaysai Patnaik, Paul Tsui, James Guo, Yin Zhou, Yuning Chai, Benjamin Caine, et al. Scalability in perception for autonomous driving: Waymo open dataset. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 2446–2454, 2020. [SPC21] https://github.com/traveller59/spconv/tree/v1.2.1, 2021. [ST19] Leslie Smith and Nicholay Topin. Super-convergence: Very fast training of neural networks using large learning rates. In Artificial Intelligence and Machine Learning for Multi-domain Operations Applications, 2019.   \n$[ \\mathrm { S W C } ^ { + } 2 1 ]$ Pei Sun, Weiyue Wang, Yuning Chai, Gamaleldin Elsayed, Alex Bewley, Xiao Zhang, Cristian Sminchisescu, and Dragomir Anguelov. RSN: Range sparse net for efficient, accurate lidar 3d object detection. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 5725–5734, 2021.   \n[TSCH19] Zhi Tian, Chunhua Shen, Hao Chen, and Tong He. FCOS: Fully convolutional one-stage object detection. In Proc. IEEE Int. Conf. Comp. Vis., pages 9627–9636, 2019.   \n[WMZY21] Chunwei Wang, Chao Ma, Ming Zhu, and Xiaokang Yang. PointAugmenting: Cross-modal augmentation for 3d object detection. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 11794–11803, 2021. [XBT22] Xinge Zhu Qingqiu Huang Yilun Chen Hongbo Fu Xuyang Bai, Zeyu Hu and Chiew-Lan Tai. TransFusion: Robust Lidar-Camera Fusion for 3d Object Detection with Transformers. CVPR, 2022.   \n$[ \\mathrm { Y J W ^ { + } } 1 6 ]$ Jiahui Yu, Yuning Jiang, Zhangyang Wang, Zhimin Cao, and Thomas Huang. Unitbox: An advanced object detection network. In Proc. ACM Int. Conf. Multimedia, pages 516–520, 2016. [YML18] Yan Yan, Yuxing Mao, and Bo Li. Second: Sparsely embedded convolutional detection. Sensors, 18(10):3337, 2018. [YZK21] Tianwei Yin, Xingyi Zhou, and Philipp Krahenbuhl. Center-based 3d object detection and tracking. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 11784–11793, 2021. [ZHJF22] Wu Zheng, Mingxuan Hong, Li Jiang, and Chi-Wing Fu. Boosting 3d object detection by simulating multimodality on point clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13638–13647, 2022.   \n$[ Z \\mathrm { M W } ^ { + } 2 0 ]$ Xinge Zhu, Yuexin Ma, Tai Wang, Yan Xu, Jianping Shi, and Dahua Lin. SSN: shape signature networks for multi-class object detection from point clouds. In European Conference on Computer Vision, pages 581–597. Springer, 2020. [ZT18] Yin Zhou and Oncel Tuzel. Voxelnet: End-to-end learning for point cloud based 3d object detection. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., pages 4490–4499, 2018. [ZWK19] Xingyi Zhou, Dequan Wang, and Philipp Krähenbühl. Objects as points. arXiv: Comp. Res. Repository, 2019. ",
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+        "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   \n(b) Did you describe the limitations of your work? [Yes] ] In multi-frame settings, the RV-based detector still cannot outperform the BEV-based ones despite being faster.   \n(c) Did you discuss any potential negative societal impacts of your work? [Yes] See the conclusion section.   \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ",
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parse/dev/3s9IrEsjLyk/3s9IrEsjLyk.md

@@ -0,0 +1,358 @@
+# Diffusion-LM Improves Controllable Text Generation
+
+Xiang Lisa Li Stanford University xlisali@stanford.edu
+
+John Thickstun Stanford University jthickst@stanford.edu
+
+Ishaan Gulrajani Stanford Univeristy igul@stanford.edu
+
+Percy Liang Stanford Univeristy pliang@cs.stanford.edu
+
+Tatsunori B. Hashimoto Stanford Univeristy thashim@stanford.edu
+
+# Abstract
+
+Controlling the behavior of language models (LMs) without re-training is a major open problem in natural language generation. While recent works have demonstrated successes on controlling simple sentence attributes (e.g., sentiment), there has been little progress on complex, fine-grained controls (e.g., syntactic structure). To address this challenge, we develop a new non-autoregressive language model based on continuous diffusions that we call Diffusion-LM. Building upon the recent successes of diffusion models in continuous domains, Diffusion-LM iteratively denoises a sequence of Gaussian vectors into word vectors, yielding a sequence of intermediate latent variables. The continuous, hierarchical nature of these intermediate variables enables a simple gradient-based algorithm to perform complex, controllable generation tasks. We demonstrate successful control of Diffusion-LM for six challenging fine-grained control tasks, significantly outperforming prior work.1
+
+# 1 Introduction
+
+Large autoregressive language models (LMs) are capable of generating high quality text [39, 3, 5, 56], but in order to reliably deploy these LMs in real world applications, the text generation process needs to be controllable: we need to generate text that satisfies desired requirements (e.g. topic, syntactic structure). A natural approach for controlling a LM would be to fine-tune the LM using supervised data of the form (control, text) $\mathbb { \lVert 1 8 \rVert }$ . However, updating the LM parameters for each control task can be expensive and does not allow for compositions of multiple controls (e.g. generate text that is both positive sentiment and non-toxic). This motivates light-weight and modular plug-and-play approaches $\textcircled { 6 }$ that keep the LM frozen and steer the generation process using an external classifier that measures how well the generated text satisfies the control. But steering a frozen autoregressive LM has been shown to be difficult, and existing successes have been limited to simple, attribute-level controls (e.g., sentiment or topic) [6, 25, 55].
+
+In order to tackle more complex controls, we propose Diffusion-LM, a new language model based on continuous diffusions. Diffusion-LM starts with a sequence of Gaussian noise vectors and incrementally denoises them into vectors corresponding to words, as shown in Figure $\mathbb { L }$ These gradual denoising steps produce a hierarchy of continuous latent representations. We find that this hierarchical and continuous latent variable enables simple, gradient-based methods to perform complex control tasks such as constraining the parse tree of a generated sequence.
+
+Continuous diffusion models have been extremely successful in vision and audio domains [13, 24, 41, 8, 4], but they have not been applied to text because of the inherently discrete nature of text $\textcircled { \ S 3 }$ . Adapting this class of models to text requires several modifications to standard diffusions: we add an embedding step and a rounding step to the standard diffusion process, design a training objective to learn the embedding, and propose techniques to improve rounding (§4). We control Diffusion-LM using a gradient-based method, as shown in Figure $\bar { \bigtriangledown }$ This method enables us to steer the text generation process towards outputs that satisfy target structural and semantic controls. It iteratively performs gradient updates on the continuous latent variables of Diffusion-LM to balance fluency and control satisfaction $\textcircled { | \ S 5 . 1 \ r { } }$
+
+![](images/85abfe25ddc79937aadce69f04fece3bc4b636e9f25ab3c917f5d3b689d389c6.jpg)  
+Figure 1: Diffusion-LM iteratively denoises a sequence of Gaussian vectors into word vectors, yielding a intermediate latent variables of decreasing noise level $\mathbf { x } _ { T } \cdots \mathbf { x } _ { 0 }$ . For controllable generation, we iteratively perform gradient updates on these continuous latents to optimize for fluency (parametrized by Diffusion-LM) and satisfy control requirements (parametrized by a classifier).
+
+To demonstrate control of Diffusion-LM, we consider six control targets ranging from fine-grained attributes (e.g., semantic content) to complex structures (e.g., parse trees). Our method almost doubles the success rate of previous plug-and-play methods and matches or outperforms the fine-tuning oracle on all these classifier-guided control tasks $( \ S 7 . 1 )$ . In addition to these individual control tasks, we show that we can successfully compose multiple classifier-guided controls to generate sentences with both desired semantic content and syntactic structure $\textcircled { \lVert \mathbb { S } ^ { 7 . 2 } \rVert }$ . Finally, we consider span-anchored controls, such as length control and infilling. Diffusion-LM allows us to perform these control tasks without a classifier, and our Diffusion-LM significantly outperforms prior plug-and-play methods and is on-par with an autoregressive LM trained from scratch for the infilling task $( \ S 7 . \bar { 3 } )$ .
+
+# 2 Related Work
+
+Diffusion Models for Text. Diffusion models $ { \mathbb { B } } 7  { \mathbb { I } }$ have demonstrated great success in continuous data domains [13, 33, 24, 31], producing images and audio that have state-of-the-art sample quality. To handle discrete data, past works have studied text diffusion models on discrete state spaces, which defines a corruption process on discrete data (e.g., each token has some probability to be corrupted to an absorbing or random token) [1, 15, 16]. In this paper, we focus on continuous diffusion models for text and to the best of our knowledge, our work is the first to explore this setting. In contrast to discrete diffusion LMs, our continuous diffusion LMs induce continuous latent representations, which enables efficient gradient-based methods for controllable generation.
+
+Autoregressive and Non-autoregressive LMs. Most large pre-trained LMs are left-to-right autoregressive (e.g., GPT-3 [3], PaLM [5]). The fixed generation order limits the models’ flexibility in many controllable generation settings, especially those that impose controls globally on both left and right contexts. One example is infilling, which imposes lexical control on the right contexts; another example is syntactic structure control, which controls global properties involving both left and right contexts. Since autoregressive LMs cannot directly condition on right contexts, prior works have developed specialized training and decoding techniques for these tasks [46, 9, 36]. For example, Qin et al. [37] proposed a decoding method that relaxes the discrete LM outputs to continuous variables and backpropagates gradient information from the right context. Diffusion-LM can condition on arbitrary classifiers that look at complex, global properties of the sentence. There are other non-autoregressive LMs that have been developed for machine translation and speech-to-text tasks [12, 43]. However these methods are specialized for speech and translation settings, where the entropy over valid outputs is low, and whether they work for language modeling remains an open problem. We leave detailed discussions to Appendix H.
+
+Plug-and-Play Controllable Generation. Plug-and-play controllable generation aims to keep the LM frozen and steer its output using potential functions (e.g., classifiers). Given a probabilistic potential function that measures how well the generated text satisfies the desired control, the generated text should be optimized for both control satisfaction (measured by the potential function) and fluency (measured by LM probabilities) . There are several plug-and-play approaches based on autoregressive LMs: FUDGE $\bar { \| 5 5 \| }$ reweights the LM prediction at each token with an estimate of control satisfaction for the partial sequence; GeDi $\mathbb { \left[ \left[ 2 5 \right] \right] }$ and DExperts $\pmb { \left. \widetilde { 2 8 } \right. }$ reweight the LM prediction at each token with a smaller LM finetuned/trained for the control task.
+
+The closest work to ours is PPLM $\pmb { \Vert 6 \Vert }$ , which runs gradient ascent on an autoregressive LM’s hidden activations to steer the next token to satisfy the control and maintain fluency. Because PPLM is based on autoregressive LMs, it can only generate left-to-right. This prevents PPLM from repairing and recovering errors made in previous generation steps. Despite their success on attribute (e.g., topic) controls, we will show these plug-and-play methods for autoregressive LMs fail on more complex control tasks such as controlling syntactic structure and semantic content in $\ S 7 . 1 .$ We demonstrate that Diffusion-LM is capable of plug-and-play controllable generation by applying classifier-guided gradient updates to the continuous sequence of latent variables induced by the Diffusion-LM.
+
+# 3 Problem Statement and Background
+
+We first define controllable generation $( \sqrt { \ S 3 . 1 } )$ and then review continuous diffusion models $\textcircled { | \ S 3 . 3 ) }$
+
+# 3.1 Generative Models and Controllable Generation for Text
+
+Text generation is the task of sampling w from a trained language model $p _ { \mathrm { l m } } ( \mathbf { w } )$ , where $\mathbf { w } =$ $[ w _ { 1 } \cdots w _ { n } ]$ is a sequence of discrete words and $p _ { \mathrm { l m } } ( \mathbf { w } )$ is a probability distribution over sequences of words. Controllable text generation is the task of sampling w from a conditional distribution $p ( \mathbf { w } \mid \mathbf { c } )$ , where c denotes a control variable. For syntactic control, c can be a target syntax tree (Figure $\bigstar \bigstar \bigstar \bigstar$ , while for sentiment control, c could be a desired sentiment label. The goal of controllable generation is to generate w that satisfies the control target c.
+
+Consider the plug-and-play controllable generation setting: we are given a language model $p _ { \mathrm { l m } } ( \mathbf { w } )$ trained from a large amount of unlabeled text data, and for each control task, we are given a classifier $p ( \mathbf { c } \mid \mathbf { w } )$ trained from smaller amount of labeled text data (e.g., for syntactic control, the classifier is a probabilistic parser). The goal is to utilize these two models to approximately sample from the posterior $p ( \mathbf { w } \mid \mathbf { c } )$ via Bayes rule $p ( \mathbf { w } \mid \mathbf { c } ) \propto p _ { \mathrm { l m } } ( \mathbf { w } ) \cdot p ( \mathbf { c } \mid \mathbf { w } )$ . Here, $p _ { \mathrm { l m } } ( \mathbf { w } )$ encourages w to be fluent, and the $p ( \mathbf { c } \mid \mathbf { w } )$ encourages w to fulfill the control.
+
+# 3.2 Autoregressive Language Models
+
+The canonical approach to language modeling factors $p _ { \mathrm { l m } }$ in an autoregressive left-to-right mannar, $\begin{array} { r } { p _ { \mathrm { l m } } ( \mathbf { w } ) \ = \ p _ { \mathrm { l m } } ( \mathbf { \bar { \boldsymbol { w } } } _ { 1 } ) \prod _ { i = 2 } ^ { n } p _ { \mathrm { l m } } ( \mathbf { \bar { \boldsymbol { x } } } _ { i } \ \mathbf { \bar { \boldsymbol { \lfloor } } } \ x _ { < i } ) } \end{array}$ . In this case, text generation is reduced to the task of repeatedly predicting the next token conditioned on the partial sequence generated so far. The next token prediction $p _ { \operatorname { l m } } ( x _ { i } \mid x _ { < i } )$ is often parametrized by Transformer architecture $\lVert \boldsymbol { 5 2 } \rVert$ .
+
+# 3.3 Diffusion Models for Continuous Domains
+
+A diffusion model $\textcircled { 1 3 } \textcircled { 3 3 } \textcircled { }$ is a latent variable model that models the data $\mathbf { x } _ { 0 } \in \mathbb { R } ^ { d }$ as a Markov chain $\mathbf { x } _ { T } \ldots \mathbf { x } _ { 0 }$ with each variable in $\mathbb { R } ^ { d }$ , and $\mathbf { x } _ { T }$ is a Gaussian. The diffusion model incrementally denoises the sequence of latent variables $\mathbf { x } _ { T : 1 }$ to approximate samples from the target data distribution (Figure $\boxed { 2 }$ . The initial state $p _ { \theta } ( \mathbf { x } _ { T } ) \approx \mathcal { N } ( 0 , \mathbf { I } )$ , and each denoising transition ${ \bf x } _ { t }  { \bf x } _ { t - 1 }$ is parametrized by the model $p _ { \theta } ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } ) = \mathcal { N } ( \mathbf { x } _ { t - 1 } ; \mu _ { \theta } ( \mathbf { x } _ { t } , t ) , \Sigma _ { \theta } ( \mathbf { x } _ { t } , t ) )$ . For example, $\mu _ { \theta }$ and $\Sigma _ { \theta }$ may be computed by a U-Net or a Tranformer.
+
+To train the diffusion model, we define a forward process that constructs the intermediate latent variables $\mathbf { x } _ { 1 : T }$ . The forward process incrementally adds Gaussian noise to data $\mathbf { x } _ { \mathrm { 0 } }$ until, at diffusion step $T$ , samples $\mathbf { x } _ { T }$ are approximately Gaussian. Each transition $\mathbf { x } _ { t - 1 }  \mathbf { x } _ { t }$ is parametrized by $q ( \bar { \mathbf { x } } _ { t } \mid \mathbf { x } _ { t - 1 } ) = \mathcal { N } ( \mathbf { x } _ { t } ; \sqrt { 1 - \beta _ { t } } \mathbf { x } _ { t - 1 } , \bar { \beta } _ { t } \mathbf { I } )$ , where the hyperparameter $\beta _ { t }$ is the amount of noise added at diffusion step $t$ . This parametrization of the forward process $q$ contains no trainable parameters and allows us to define a training objective that involves generating noisy data according to a pre-defined forward process $q$ and training a model to reverse the process and reconstruct the data.
+
+![](images/1946d9d19dfde1075af467cf5c5709359b2cd6b243909836ee2ca4584222e44f.jpg)  
+Figure 2: A graphical model representing the forward and reverse diffusion processes. In addition to the original diffusion models $\bar { \mathbb { 1 } } \bar { 1 } \bar { 3 } \mathbb { I }$ , we add a Markov transition between $\mathbf { x } _ { \mathrm { 0 } }$ and $\mathbf { w }$ , and propose the embedding §4.1 and rounding $\ S 4 . 2$ techniques.
+
+The diffusion model is trained to maximize the marginal likelihood of the data $\mathbb { E } _ { \mathbf { x } _ { 0 } \sim p _ { \mathrm { d a t a } } } [ \log p _ { \theta } ( \mathbf { x } _ { 0 } ) ]$ , and the canonical objective is the variational lower bound of $\log p _ { \theta } ( \mathbf { x } _ { 0 } )$ [47],
+
+$$
+\mathcal { L } _ { \mathrm { v l b } } ( \mathbf { x } _ { 0 } ) = \underset { q ( \mathbf { x } _ { 1 : T } | \mathbf { x } _ { 0 } ) } { \mathbb { E } } \left[ \log \frac { q ( \mathbf { x } _ { T } | \mathbf { x } _ { 0 } ) } { p _ { \theta } ( \mathbf { x } _ { T } ) } + \sum _ { t = 2 } ^ { T } \log \frac { q ( \mathbf { x } _ { t - 1 } | \mathbf { x } _ { 0 } , \mathbf { x } _ { t } ) } { p _ { \theta } ( \mathbf { x } _ { t - 1 } | \mathbf { x } _ { t } ) } - \log p _ { \theta } ( \mathbf { x } _ { 0 } | \mathbf { x } _ { 1 } ) \right] .
+$$
+
+However, this objective can be unstable and require many optimization tricks to stabilize $\pmb { \mathbb { B 3 } }$ . To circumvent this issue, Ho et al. $\mathbb { \lVert \lambda \rVert }$ devised a simple surrogate objective that expands and reweights each KL-divergence term in ${ \mathcal { L } } _ { \mathrm { v l b } }$ to obtain a mean-squared error loss (derivation in Appendix $\mathrm { J } )$ which we will refer to as
+
+$$
+\mathcal { L } _ { \mathrm { s i m p l e } } ( \mathbf { x } _ { 0 } ) = \sum _ { t = 1 } ^ { T } \underset { q ( \mathbf { x } _ { t } | \mathbf { x } _ { 0 } ) } { \mathbb { E } } | | \mu _ { \boldsymbol { \theta } } ( \mathbf { x } _ { t } , t ) - \hat { \mu } ( \mathbf { x } _ { t } , \mathbf { x } _ { 0 } ) | | ^ { 2 } ,
+$$
+
+where $\hat { \mu } ( \mathbf { x } _ { t } , \mathbf { x } _ { 0 } )$ is the mean of the posterior $q ( \mathbf { x } _ { t - 1 } | \mathbf { x } _ { 0 } , \mathbf { x } _ { t } )$ which is a closed from Gaussian, and $\mu _ { \theta } ( \mathbf { x } _ { t } , t )$ is the predicted mean of $p _ { \theta } ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } )$ computed by a neural network. While $\mathcal { L } _ { \mathrm { s i m p l e } }$ is no longer a valid lower bound, prior work has found that it empirically made training more stable and improved sample qualit $^ { , 2 } .$ We will make use of similar simplifications in Diffusion-LM to stabilize training and improve sample quality $( | \ S 4 . 1 )$ .
+
+# 4 Diffusion-LM: Continuous Diffusion Language Modeling
+
+Constructing Diffusion-LM requires several modifications to the standard diffusion model. First, we must define an embedding function that maps discrete text into a continuous space. To address this, we propose an end-to-end training objective for learning embeddings $( \ S 4 . 1 )$ . Second, we require a rounding method to map vectors in embedding space back to words. To address this, we propose training and decoding time methods to facilitate rounding $( \ S 4 . 2 )$ .
+
+# 4.1 End-to-end Training
+
+To apply a continuous diffusion model to discrete text, we define an embedding function $\operatorname { E M B } ( w _ { i } )$ that maps each word to a vector in $\mathbb { R } ^ { d }$ . We define the embedding of a sequence w of length $n$ to be: $\mathbf { E M B } ( \bar { \mathbf { w } _ { n } } ) = [ \mathbf { E M B } ( w _ { 1 } ) , \dots , \mathbf { E M B } ( w _ { n } ) ] \in \mathbb { R } ^ { n d }$ .
+
+We propose a modification of the diffusion model training objective (Equation $\bigstar \bigstar \bigstar \bigstar$ that jointly learns the diffusion model’s parameters and word embeddings. In preliminary experiments, we explored random Gaussian embeddings, as well as pre-trained word embeddings $[ \bar { 1 } 5 , \bar { 1 } \bar { 3 } 9 ]$ . We found that these fixed embeddings are suboptimal for Diffusion-LM compared to end-to-end training3.
+
+As shown in Figure $\bigstar$ our approach adds a Markov transition from discrete words w to $\mathbf { x } _ { \mathrm { 0 } }$ in the forward process, parametrized by $q _ { \phi } ( \mathbf { x } _ { 0 } | \mathbf { w } ) = \mathcal { N } ( \mathrm { E M B } ( \mathbf { w } ) , \sigma _ { 0 } I )$ . In the reverse process, we add a |trainable rounding step, parametrized by $p _ { \theta } ( \mathbf { w } \mid \mathbf { x } _ { 0 } ) = \prod _ { i = 1 } ^ { n } p _ { \theta } ( w _ { i } \mid x _ { i } )$ , where $p _ { \theta } ( w _ { i } \mid x _ { i } )$ is a softmax distribution. The training objectives introduced in §3 now becomes
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \mathrm { v l b } } ^ { \mathrm { e 2 e } } ( \mathbf { w } ) = \underset { q _ { \phi } ( \mathbf { x } _ { 0 } | \mathbf { w } ) } { \mathbb { E } } [ \mathcal { L } _ { \mathrm { v l b } } ( \mathbf { x } _ { 0 } ) + \log q _ { \phi } ( \mathbf { x } _ { 0 } | \mathbf { w } ) - \log p _ { \theta } ( \mathbf { w } | \mathbf { x } _ { 0 } ) ] ] , } \\ & { \mathcal { L } _ { \mathrm { s i m p l e } } ^ { \mathrm { e 2 e } } ( \mathbf { w } ) = \underset { q _ { \phi } ( \mathbf { x } _ { 0 : T } | \mathbf { w } ) } { \mathbb { E } } [ \mathcal { L } _ { \mathrm { s i m p l e } } ( \mathbf { x } _ { 0 } ) + | | \mathrm { E M B } ( \mathbf { w } ) - \mu _ { \theta } ( \mathbf { x } _ { 1 } , 1 ) | | ^ { 2 } - \log p _ { \theta } ( \mathbf { w } | \mathbf { x } _ { 0 } ) ] . } \end{array}
+$$
+
+We derive the simplifi $\mathcal { L } _ { \mathrm { s i m p l e } } ^ { \mathrm { e 2 e } } ( \mathbf { w } )$ m an $\mathcal { L } _ { \mathrm { v l b } } ^ { \mathrm { e 2 e } } ( \mathbf { w } )$ followingrivation de$\boxed { \ S 3 . 3 }$ tails are in Appendix J. Since we are training the embedding function, $q _ { \phi }$ now contains trainable parameters and we use the reparametrization trick [42, 20] to backpropagate through this sampling step. Empirically, we find the learned embeddings cluster meaningfully: words with the same part-of-speech tags (syntactic role) tend to be clustered, as shown in Figure 3.
+
+![](images/fdd8dd625de4da7094d9257338732ff9b4bdeb41d92145faac400af29970f0ad.jpg)  
+Figure 3: A t-SNE [51] plot of the learned word embeddings. Each word is colored by its POS.
+
+# 4.2 Reducing Rounding Errors
+
+The learned embeddings define a mapping from discrete text to the continuous $\mathbf { x } _ { \mathrm { 0 } }$ . We now describe the inverse process of rounding a predicted $\mathbf { x } _ { \mathrm { 0 } }$ back to discrete text. Rounding is achieved by choosing the most probable word for each position, according to argmax $\begin{array} { r } { p _ { \theta } ( \mathbf { w } \mid \mathbf { \bar { x } } _ { 0 } ) = \prod _ { i = 1 } ^ { n } \bar { p _ { \theta } } ( w _ { i } \mid x _ { i } ) } \end{array}$ Ideally, this argmax-rounding would be sufficient to map back to discrete text, as the denoising steps should ensure that $\mathbf { x } _ { \mathrm { 0 } }$ lies exactly on the embedding of some word. However, empirically, the model fails to generate $\mathbf { x } _ { \mathrm { 0 } }$ that commits to a single word.
+
+One explanation for this phenomenon is that the $\mathcal { L } _ { \mathrm { s i m p l e } } ( \mathbf { x } _ { 0 } )$ term in our objective $2$ puts insufficient emphasis on modeling the structure of $\mathbf { x } _ { \mathrm { 0 } }$ . Recall that we defined $L _ { \mathrm { s i m p l e } } ( \mathbf { x } _ { 0 } ) \ =$ $\begin{array} { r } { \sum _ { t = 1 } ^ { T } \mathbb { E } _ { \mathbf { x } _ { t } } | | \mu _ { \theta } ( \mathbf { x } _ { t } , t ) - \hat { \mu } ( \mathbf { x } _ { t } , \mathbf { x } _ { 0 } ) | | ^ { 2 } } \end{array}$ , where our model $\mu _ { \theta } ( \mathbf { x } _ { t } , t )$ directly predicts the mean of $p _ { \theta } ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } )$ for each denoising step $t$ . In this objective, the constraint that $\mathbf { x } _ { \mathrm { 0 } }$ has to commit to a single word embedding will only appear in the terms with $t$ near 0, and we found that this parametrization required careful tuning to force the objective to emphasize those terms (see Appendix $\boxed { \mathbf { M } }$ .
+
+Our approach re-parametrizes $\mathcal { L } _ { \mathrm { s i m p l e } }$ to force Diffusion-LM to explicitly model $\mathbf { x } _ { \mathrm { 0 } }$ in every term of the objective. Specifically, we derive an analogue to $\mathcal { L } _ { \mathrm { s i m p l e } }$ which is parametrized via $\mathbf { x } _ { \mathrm { 0 } }$ $\begin{array} { r } { \mathcal { L } _ { \mathbf { x } _ { 0 } - \mathrm { s i m p l e } } ^ { \mathrm { e 2 e } } ( \mathbf { x } _ { 0 } ) = \sum _ { t = 1 } ^ { T } \mathbb { E } _ { \mathbf { x } _ { t } } | | f _ { \theta } ( \mathbf { x } _ { t } , t ) - \mathbf { x } _ { 0 } | | ^ { 2 } } \end{array}$ , where our model $f _ { \theta } ( \mathbf { x } _ { t } , t )$ predicts $\mathbf { x } _ { \mathrm { 0 } }$ directly 4. This forces the neural network to predict $\mathbf { x } _ { \mathrm { 0 } }$ in every term and we found that models trained with this objective quickly learn that $\mathbf { x } _ { \mathrm { 0 } }$ should precisely centered at a word embedding.
+
+We described how re-parametrization can be helpful for model training, but we also found that the same intuition could be used at decoding time in a technique that we call the clamping trick. In the standard generation approach for a $\mathbf { x } _ { \mathrm { 0 } }$ -parametrized model, the model denoises $\mathbf { x } _ { t }$ to $\mathbf { x } _ { t - 1 }$ by first computing an estimate of $\mathbf { x } _ { \mathrm { 0 } }$ via $f _ { \theta } ( \mathbf { x } _ { t } , t )$ and then sampling $\mathbf { x } _ { t - 1 }$ conditioned on this estimate: $\mathbf { x } _ { t - 1 } = \sqrt { \bar { \alpha } } f _ { \theta } ( \mathbf { x } _ { t } , t ) + \sqrt { 1 - \bar { \alpha } } \epsilon$ , where $\begin{array} { r } { \bar { \alpha } _ { t } = \prod _ { s = 0 } ^ { t } ( 1 - \beta _ { s } ) } \end{array}$ and $\overline { { \epsilon } } \sim \bar { \mathcal { N } } ( 0 , I ) \big \lbrack \bar { \mathfrak { z } } \big \rbrack$ In the clamping trick, the model additionally maps the predicted vector $f _ { \theta } ( \mathbf { x } _ { t } , t )$ to its nearest word embedding sequence. Now, the sampling step becomes $\mathbf { x } _ { t - 1 } = \sqrt { \bar { \alpha } } \cdot \mathrm { C l a m p } ( f _ { \theta } ( \mathbf { x } _ { t } , t ) ) + \sqrt { 1 - \bar { \alpha } } \epsilon$ . The clamping trick forces the predicted vector to commit to a word for intermediate diffusion steps, making the vector predictions more precise and reducing rounding errors.6
+
+# 5 Decoding and Controllable Generation with Diffusion-LM
+
+Having described the Diffusion-LM, we now consider the problem of controllable text generation $\underline { { ( \ S ^ { 5 . 1 ) } } }$ and decoding $( \ S 5 . 2 )$ .
+
+# 5.1 Controllable Text Generation
+
+We now describe a procedure that enables plug-and-play control on Diffusion-LM. Our approach to control is inspired by the Bayesian formulation in $\underline { { \vec { \ S } \vec { 3 . 1 } } } ,$ but instead of performing control directly on the discrete text, we perform control on the sequence of continuous latent variables $\mathbf { x } _ { \mathrm { 0 : } T }$ defined by Diffusion-LM, and apply the rounding step to convert these latents into text.
+
+Controlling $\mathbf { x } _ { \mathrm { 0 : } T }$ is equivalent to decoding from the posterior $\begin{array} { r } { p ( \mathbf { x } _ { 0 : T } | \mathbf { c } ) = \prod _ { t = 1 } ^ { T } p ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } , \mathbf { c } ) } \end{array}$ , and we decompose this joint inference problem to a sequence of control problems at each diffusion step: $p ( \mathbf { x } _ { t - 1 } \mid \mathbf { \bar { x } } _ { t } , \mathbf { c } ) \propto \bar { p } ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } ) \cdot \bar { p } ( \mathbf { c } \mid \mathbf { x } _ { t - 1 } , \mathbf { x } _ { t } )$ . We further simplify $p ( \mathbf { c } \mid \mathbf { x } _ { t - 1 } , \mathbf { x } _ { t } ) = p ( \mathbf { c } \mid$ $\mathbf { x } _ { t - 1 } )$ via conditional independence assumptions from prior work on controlling diffusions $[ | \overline { { 4 9 } } | |$ . Consequently, for the $t$ -th step, we run gradient update on $\mathbf { x } _ { t - 1 }$ :
+
+$$
+\nabla _ { \mathbf x _ { t - 1 } } \log p ( \mathbf x _ { t - 1 } \mid \mathbf x _ { t } , \mathbf c ) = \nabla _ { \mathbf x _ { t - 1 } } \log p ( \mathbf x _ { t - 1 } \mid \mathbf x _ { t } ) + \nabla _ { \mathbf x _ { t - 1 } } \log p ( \mathbf c \mid \mathbf x _ { t - 1 } ) ,
+$$
+
+where both $\log p ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } )$ and $\log p ( \mathbf { c } \mid \mathbf { x } _ { t - 1 } )$ are differentiable: the first term is parametrized by Diffusion-LM, and the second term is parametrized by a neural network classifier.
+
+Similar to work in the image setting $ { \mathbb { B } } ,  { \mathbb { H } } 9  { \mathbb { I } }$ , we train the classifier on the diffusion latent variables and run gradient updates on the latent space $\mathbf { x } _ { t - 1 }$ to steer it towards fulfilling the control. These image diffusion works take one gradient step towards $\nabla _ { \mathbf { x } _ { t - 1 } } \log p ( \mathbf { c } \mid \mathbf { x } _ { t - 1 } )$ per diffusion steps. To improve performance on text and speed up decoding, we introduce two key modifications: fluency regularization and multiple gradient steps.
+
+To generate fluent text, we run gradient updates on a control objective with fluency regularization: $\lambda \log p ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } ) + \log p ( \mathbf { c } \mid \bar { \mathbf { x } _ { t - 1 } } )$ , where $\lambda$ is a hyperparameter that trades off fluency (the first term) and control (the second term). While existing controllable generation methods for diffusions do not include the $\lambda \log p ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } )$ term in the objective, we found this term to be instrumental for generating fluent text. The resulting controllable generation process can be viewed as a stochastic decoding method that balances maximizing and sampling $p ( \mathbf { x } _ { t - 1 } \mid \mathbf { x } _ { t } , \mathbf { c } )$ , much like popular text generation techniques such as nucleus sampling $\textcircled { 1 1 4 } \textcircled { 1 }$ or sampling with low temperature. In order to improve the control quality, we take multiple gradient steps for each diffusion step: we run 3 steps of the Adagrad $^ 7 \mathbb { \equiv } { \frac { } { \mathbb { I } \mathbb { 0 } } } \mathbb { I }$ update for each diffusion steps. To mitigate for the increased computation cost, we downsample the diffusion steps from 2000 to 200, which speeds up our controllable generation algorithm without hurting sample quality much.
+
+# 5.2 Minimum Bayes Risk Decoding
+
+Many conditional text generation tasks require a single high-quality output sequence, such as machine translation or sentence infilling. In these settings, we apply Minimum Bayes Risk (MBR) decoding $\left[ \left[ 2 6 \right] \right]$ to aggregate a set of samples $s$ drawn from the Diffusion-LM , and select the sample that achieves the minimum expected risk under a loss function $\mathcal { L }$ (e.g., negative BLEU score): $\hat { \textbf { w } } =$ $\begin{array} { r } { \operatorname * { a r g m i n } _ { \mathbf { w } \in S } \sum _ { \mathbf { w } ^ { \prime } \in S } \frac { 1 } { | S | } \mathcal { L } ( \mathbf { \dot { w } } , \mathbf { w } ^ { \prime } ) } \end{array}$ . We found that MBR decoding often returned high quality outputs, since a low quality sample would be dissimilar from the remaining samples and penalized by the loss function.
+
+# 6 Experimental Setup
+
+With the above improvements on training $\textcircled{8 4 }$ and decoding $( \ S 5 )$ , we train Diffusion-LM for two language modeling tasks. We then apply the controllable generation method to 5 classifier-guided control tasks, and apply MBR decoding to a classifier-free control task (i.e. infilling).
+
+# 6.1 Datasets and Hyperparameters
+
+We train Diffusion-LM on two datasets: E2E $\pmb { \Vert 3 4 \Vert }$ and ROCStories $\left[ \left| 3 2 \right| \right]$ . The E2E dataset consists of 50K restaurant reviews labeled by 8 fields including food type, price, and customer rating. The ROCStories dataset consists of 98K five-sentence stories, capturing a rich set of causal and temporal commonsense relations between daily events. This dataset is more challenging to model than E2E, because the stories contain a larger vocabulary of 11K words and more diverse semantic content.
+
+Table 1: Example input control and output text for each control tasks.   
+
+<table><tr><td>input (Semantic Content) output text</td><td>food : Japanese Browns Cambridge is good for Japanese food and also children friendly near The Sorrento.</td></tr><tr><td>input (Parts-of-speech) output text</td><td>PROPN AUX DET ADJ NOUN NOUN VERB ADP DET NOUN ADP DET NOUN PUNCT Zizzi is a local coffee shop located on the outskirts of the city .</td></tr><tr><td>input (Syntax Tree) output text</td><td>(TOP (S (NP(*) (*) (*)) (VP(*) (NP (NP(*) (*))) The Twenty Two has great food</td></tr><tr><td>input (Syntax Spans) output text</td><td>(7,10,VP) Wildwood pub serves multicultural dishes and is ranked 3 stars</td></tr><tr><td>input (Length) output text</td><td>14 Browns Cambridge offers Japanese food located near The Sorrento in the city centre .</td></tr><tr><td>input (left context) input (right context) output text</td><td>My dog loved tennis balls. My dog had stolen every one and put it under there. One day,I found all of my lost tennis balls underneath the bed.</td></tr></table>
+
+Our Diffusion-LM is based on Transformer $\pmb { \Vert 5 2 } \Vert$ architecture with 80M parameters, with a sequence length $n = 6 4$ , diffusion steps $T = 2 0 0 0$ and a square-root noise schedule (see Appendix $\boxed { \mathrm { A } }$ for details). We treat the embedding dimension as a hyperparameter, setting $d = 1 6$ for E2E and $d = 1 2 8$ for ROCStories. See Appendix $\mathbf { B }$ for hyperparameter details. At decoding time, we downsample to 200 diffusion steps for E2E and maintain 2000 steps for ROCStories. Decoding Diffusion-LM for 200 steps is still $7 \mathbf { x }$ slower than decoding autoregressive LMs. For controllable generation, our method based on Diffusion-LM is $1 . 5 \mathrm { x }$ slower than FUDGE but $6 0 \mathrm { x }$ faster than PPLM.
+
+# 6.2 Control tasks
+
+We consider 6 control tasks shown in Table 1: the first 4 tasks rely on a classifier, and the last 2 tasks are classifier free8. For each control task (e.g. semantic content), we sample 200 control targets c (e.g., rating ${ = } 5$ star) from the validation splits, and we generate 50 samples for each control target. To evaluate the fluency of the generated text, we follow the prior works [55, 6] and feed the generated text to a teacher LM (i.e., a carefully fine-tuned GPT-2 model) and report the perplexity of generated text under the teacher LM. We call this metric lm-score (denoted as lm): a lower lm-score indicates better sample quality. 9 We define success metrics for each control task as follows:
+
+Semantic Content. Given a field (e.g., rating) and value (e.g., 5 star), generate a sentence that covers field $\equiv$ value, and report the success rate by exact match of ‘value’.
+
+Parts-of-speech. Given a sequence of parts-of-speech (POS) tags (e.g., Pronoun Verb Determiner Noun), generate a sequence of words of the same length whose POS tags (under an oracle POS tagger) match the target (e.g., I ate an apple). We quantify success via word-level exact match.
+
+Syntax Tree. Given a target syntactic parse tree (see Figure 1), generate text whose syntactic parse matches the given parse. To evaluate the success, we parse the generated text by an off-the-shelf parser $\pmb { \left. \left[ 2 2 \right] \right. }$ , and report F1 scores.
+
+Syntax Spans. Given a target (span, syntactic category) pair, generate text whose parse tree over span $[ i , j ]$ matches the target syntactic category (e.g. prepositional phrase).We quantify success via the fraction of spans that match exactly.
+
+Length. Given a target length $1 0 , \ldots , 4 0$ , generate a sequence with a length within $\pm 2$ of the target.   
+In the case of Diffusion-LM, we treat this as a classifier-free control task.
+
+Infilling. Given a left context $( O _ { 1 } )$ and a right context $( O _ { 2 } )$ from the aNLG dataset $\pmb { \mathbb { D } } \mathbf { l }$ , and the goal is to generate a sentence that logically connects $O _ { 1 }$ and $O _ { 2 }$ (algorithm details in Appendix $\mathbf { G } )$ . For evaluation, we report both automatic and human evaluation from the Genie leaderboard $\mathbb { 1 1 9 } \mathrm { j }$
+
+<table><tr><td></td><td colspan="2">Semantic Content</td><td colspan="2">Parts-of-speech</td><td colspan="2">Syntax Tree</td><td colspan="2">Syntax Spans</td><td colspan="2">Length</td></tr><tr><td></td><td>ctrl 个</td><td>lm↓</td><td>ctrl个</td><td>im↓</td><td>ctrl个</td><td>lm↓</td><td>ctrl个</td><td>im↓</td><td>ctrl个</td><td>lm↓</td></tr><tr><td>PPLM FUDGE</td><td>9.9 69.9</td><td>5.32 2.83</td><td>1</td><td>1 7.96</td><td>1</td><td>-</td><td>1</td><td>1</td><td>1</td><td>-</td></tr><tr><td>Diffusion-LM</td><td></td><td></td><td>27.0</td><td></td><td>17.9</td><td>3.39</td><td>54.2</td><td>4.03</td><td>46.9</td><td>3.11</td></tr><tr><td></td><td>81.2</td><td>2.55</td><td>90.0</td><td>5.16</td><td>86.0</td><td>3.71</td><td>93.8</td><td>2.53</td><td>99.9</td><td>2.16</td></tr><tr><td>FT-sample</td><td>72.5</td><td>2.87</td><td>89.5</td><td>4.72</td><td>64.8</td><td>5.72</td><td>26.3</td><td>2.88</td><td>98.1</td><td>3.84</td></tr><tr><td>FT-search</td><td>89.9</td><td>1.78</td><td>93.0</td><td>3.31</td><td>76.4</td><td>3.24</td><td>54.4</td><td>2.19</td><td>100.0</td><td>1.83</td></tr></table>
+
+Table 2: Diffusion-LM achieves high success rate (ctrl ") and good fluency $( \ln \downarrow )$ across all 5 control tasks, outperforming the PPLM and FUDGE baselines. Our method even outperforms the fine-tuning oracle (FT) on controlling syntactic parse trees and spans.
+
+# 6.3 Classifier-Guided Control Baselines
+
+For the first 5 control tasks, we compare our method with PPLM, FUDGE, and a fine-tuning oracle. Both PPLM and FUDGE are plug-and-play controllable generation approaches based on an autoregressive LM, which we train from scratch using the GPT-2 small architecture $\pmb { \mathbb { B } } \pmb { \mathrm { 9 } } \|$
+
+PPLM[6]. This method runs gradient ascent on the LM activations to increase the classifier probabilities and language model probabilities, and has been successful on simple attribute control. We apply PPLM to control semantic content, but not the remaining 4 tasks which require positional information, as PPLM’s classifier lacks positional information.
+
+FUDGE[55]. For each control task, FUDGE requires a future discriminator that takes in a prefix sequence and predicts whether the complete sequence would satisfy the constraint. At decoding time, FUDGE reweights the LM prediction by the discriminator scores.
+
+FT. For each control task, we fine-tune GPT-2 on (control, text) pair, yielding an oracle conditional language model that’s not plug-and-play. We report both the sampling (with temperature 1.0) and beam search (with beam size 4) outputs of the fine-tuned models, denoted as FT-sample and FT-search.
+
+# 6.4 Infilling Baselines
+
+We compare to 3 specialized baseline methods developed in past work for the infilling task.
+
+DELOREAN [36]. This method continuously relaxes the output space of a left-to-right autoregressive LM, and iteratively performs gradient updates on the continuous space to enforce fluent connection to the right contexts. This yields a continuous vector which is rounded back to text.
+
+COLD[37]. COLD specifies an energy-based model that includes fluency (from left-to-right and right-to-left LM) and coherence constraints (from lexical overlap). It samples continuous vectors from this energy-based model and round them to text.
+
+AR-infilling. We train an autoregressive LM from scratch to do sentence infilling task $\pmb { \Vert }$ . Similar to training Diffusion-LM, we train on the ROCStories dataset, but pre-process it by reordering sentences from $( O _ { 1 } , O _ { \mathrm { m i d d l e } , } O _ { 2 } )$ to $( O _ { 1 } , O _ { 2 } , O _ { \mathrm { m i d d l e } } )$ . At evaluation time, we feed in $O _ { 1 } , O _ { 2 }$ , and the model generates the middle sentence.
+
+# 7 Main Results
+
+We train Diffusion-LMs on the E2E and ROCStories datasets. In terms of negative log-likelihood (NLL, lower is better), we find that the variational upper bound of Diffusion-LM NLL 10 underperforms the equivalent autoregressive Transformer model (2.28 vs. 1.77 for E2E, 3.88 vs 3.05 for ROCStories) although scaling up model and dataset size partially bridges the gap $3 . 8 8  3 . 1 0$ on ROCStories). Our best log-likelihoods required several modifications from $\ S 4 ;$ we explain these and give detailed log-likelihood results in Appendix $\boxed { \mathrm { K } }$ Despite worse likelihoods, controllable generation based on our Diffusion-LM results in significantly better outputs than systems based on autoregressive LMs, as we will show in §7.1,§7.2, and §7.3
+
+# 7.1 Classifier-Guided Controllable Text Generation Results
+
+As shown in Table 2, Diffusion-LM achieves high success and fluency across all classifier-guided control tasks. It significantly outperforms the PPLM and FUDGE baselines across all 5 tasks.
+
+Table 3: Qualitative examples from the Syntax Tree control. The syntactic parse tree is linearized by nested brackets representing the constituents, and we use the standard PTB syntactic categories. Tokens within each span are represented as \* . We color failing spans red and bold the spans of interest that we discuss in $\ S 7 . 1 .$   
+
+<table><tr><td>Syntactic Parse</td><td>（S(S(NP*)（VP*（NP(NP**)（VP*（NP(ADJP**)*)))))*（S（NP***)（VP*（ ADJP（ADJP *)））））</td></tr><tr><td>FUDGE</td><td>Zizzi is a cheap restaurant . [incomplete]</td></tr><tr><td>Diffusion-LM FT</td><td>Zizzi is a pub providing family friendly Indian food Its customer rating is low Cocum is a Pub serving moderately priced meals and the customer rating is high</td></tr><tr><td>Syntactic Parse</td><td>（S(S(VP*（PP*（NP**)))) *（NP***)（VP*（NP(NP**)（SBAR(WHNP*)（S（ VP*(NP**))))))*)</td></tr><tr><td>FUDGE</td><td>In the city near The Portland Arms is a coffee and fast food place named The Cricketers which is not family - friendly with a customer rating of 5 out of 5 .</td></tr><tr><td>Diffusion-LM FT</td><td>Located on the riverside,The Rice Boat is a restaurant that serves Indian food . Located near The Sorrento, The Millis a pub that serves Indian cuisine.</td></tr></table>
+
+<table><tr><td colspan="4">Semantic Content + Syntax Tree</td><td colspan="3">Semantic Content + Parts-of-speech</td></tr><tr><td></td><td>semantic ctrl ↑</td><td>syntax ctrl ↑</td><td>lm↓</td><td>semantic ctrl ↑</td><td>POS ctrl ↑</td><td>lm↓</td></tr><tr><td>FUDGE</td><td>61.7</td><td>15.4</td><td>3.52</td><td>64.5</td><td>24.1</td><td>3.52</td></tr><tr><td>Diffusion-LM</td><td>69.8</td><td>74.8</td><td>5.92</td><td>63.7</td><td>69.1</td><td>3.46</td></tr><tr><td>FT-PoE</td><td>61.7</td><td>29.2</td><td>2.77</td><td>29.4</td><td>10.5</td><td>2.97</td></tr></table>
+
+Table 4: In this experiment, we compose semantic control and syntactic control: Diffusion-LM achieves higher success rate (ctrl $\uparrow ,$ ) at some cost of fluency $( \ln \downarrow )$ . Our method outperforms both FUDGE and FT-PoE (product of experts of two fine-tuned models) on control success rate, especially for the structured syntactic controls (i.e. syntactic parse tree and POS).
+
+Surprisingly, our method outperforms the fine-tuning oracle on controlling syntactic parse trees and spans, while achieving similar performance on the remaining 3 tasks.
+
+Controlling syntactic parse trees and spans are challenging tasks for fine-tuning, because conditioning on the parse tree requires reasoning about the nested structure of the parse tree, and conditioning on spans requires lookahead planning to ensure the right constituent appears at the target position.
+
+We observe that PPLM fails in semantic content controls and conjecture that this is because PPLM is designed to control coarse-grained attributes, and may not be useful for more targeted tasks such as enforcing that a restaurant review contains a reference to Starbucks.
+
+FUDGE performs well on semantic content control but does not perform well on the remaining four tasks. Controlling a structured output (Parts-of-speech and Syntax Tree) is hard for FUDGE because making one mistake anywhere in the prefix makes the discriminator assign low probabilities to all continuations. In other control tasks that require planning (Length and Syntax Spans), the future discriminator is difficult to train, as it must implicitly perform lookahead planning.
+
+The non-autoregressive nature of our Diffusion-LM allows it to easily solve all the tasks that require precise future planning (Syntax Spans and Length). We believe that it works well for complex controls that involve global structures (Parts-of-speech, Syntax Tree) because the coarse-to-fine representations allow the classifier to exert control on the entire sequence (near $t = T$ ) as well as on individual tokens (near $t = 0$ ).
+
+Qualitative Results. Table $\textcircled { 3 }$ shows samples of Syntax Tree control. Our method and fine-tuning both provide fluent sentences that mostly satisfy controls, whereas FUDGE deviates from the constraints after the first few words. One key difference between our method and fine-tuning is that Diffusion-LM is able to correct for a failed span and have suffix spans match the target. In the first example, the generated span (“Family friendly Indian food”) is wrong because it contains 1 more word than the target. Fortunately, this error doesn’t propagate to later spans, since Diffusion-LM adjusts by dropping the conjunction.
+
+# 7.2 Composition of Controls
+
+One unique capability of plug-and-play controllable generation is its modularity. Given classifiers for multiple independent tasks, gradient guided control makes it simple to generate from the intersection of multiple controls by taking gradients on the sum of the classifier log-probabilities.
+
+Table 5: For sentence infilling, Diffusion-LM significantly outperforms prior work COLD $\pmb { \Vert 3 7 \Vert }$ and Delorean $\pmb { \mathbb { B } } 6 \|$ (numbers taken from paper), and matches the performance of an autoregressive LM (AR) trained from scratch to do infilling.   
+
+<table><tr><td rowspan="2"></td><td colspan="4">Automatic Eval</td><td rowspan="2">Human Eval</td></tr><tr><td>BLEU-4个</td><td>ROUGE-L↑</td><td>CIDEr↑</td><td>BERTScore↑</td></tr><tr><td>Left-only</td><td>0.9</td><td>16.3</td><td>3.5</td><td>38.5</td><td>n/a</td></tr><tr><td>DELOREAN</td><td>1.6</td><td>19.1</td><td>7.9</td><td>41.7</td><td>n/a</td></tr><tr><td>COLD</td><td>1.8</td><td>19.5</td><td>10.7</td><td>42.7</td><td>n/a</td></tr><tr><td>Diffusion</td><td>7.1</td><td>28.3</td><td>30.7</td><td>89.0</td><td>0.37+0.03 -0.02</td></tr><tr><td>AR</td><td>6.7</td><td>27.0</td><td>26.9</td><td>89.0</td><td>0.39±0.02 -0.03</td></tr></table>
+
+We evaluate this setting on the combination of Semantic Content $^ +$ Syntax Tree control and Semantic Content $^ +$ Parts-of-speech control. As shown in Table $^ { 4 , }$ our Diffusion-LM achieves a high success rate for both of the two components, whereas FUDGE gives up on the more global syntactic control. This is expected because FUDGE fails to control syntax on its own.
+
+Fine-tuned models are good at POS and semantic content control individually but do not compose these two controls well by product of experts (PoE), leading to a large drop in success rates for both constraints.
+
+# 7.3 Infilling Results
+
+As shown in Table $5 ,$ our diffusion LM significantly outperforms continuous relaxation based methods for infilling (COLD and DELOREAN). Moreover, our method achieves comparable performance to fine-tuning a specialized model for this task. Our method has slightly better automatic evaluation scores and the human evaluation found no statistically significant improvement for either method. These results suggest that Diffusion LM can solve many types of controllable generation tasks that depend on generation order or lexical constraints (such as infilling) without specialized training.
+
+# 7.4 Ablation Studies
+
+We verify the importance of our proposed design choices in $\ S \dot { 4 }$ through two ablation studies. We measure the sample quality of DiffusionLM using the lm-score on 500 samples $\ S 6 . 2 .$
+
+Learned v.s. Random Embeddings (§4.1) Learned embeddings outperform random embeddings on the ROCStories, which is a harder language modeling task. The same trend holds for the E2E dataset but with a smaller margin.
+
+Objective Parametrization $\textcircled { \ S 4 . 2 }$ . We propose to let the diffusion model predict $\mathbf { x } _ { \mathrm { 0 } }$ directly. Here, we compare this with standard
+
+![](images/bf134d627ad1c396765036f971cdd59bda1220a6ed8e17b0a956d4be0e69a6df.jpg)  
+Figure 4: We measure the impact of our proposed design choices through lm-score. We find both learned embeddings and reparametrization substantially improves sample quality.
+
+parametrization in image generation which parametrizes by the noise term ✏. Figure $\boxed { 4 }$ (right) shows that parametrizing by $\mathbf { x } _ { \mathrm { 0 } }$ consistently attains good performance across dimensions, whereas parametrizing by $\epsilon$ works fine for small dimensions, but quickly collapses for larger dimensions.
+
+# 8 Conclusion and Limitations
+
+We proposed Diffusion-LM, a novel and controllable language model based on continuous diffusions, which enables new forms of complex fine-grained control tasks. We demonstrate Diffusion-LM’s success in 6 fine-grained control tasks: our method almost doubles the control success rate of prior methods and is competitive with baseline fine-tuning methods that require additional training.
+
+We find the complex controls enabled by Diffusion-LM to be compelling, and we are excited by how Diffusion-LM is a substantial departure from the current paradigm of discrete autoregressive generation. As with any new technologies, there are drawbacks to the Diffusion-LMs that we constructed: (1) it has higher perplexity; (2) decoding is substantially slower; and (3) training converges more slowly. We believe that with more follow-up work and optimization, many of these issues can be addressed, and this approach will turn out to be a compelling way to do controllable generation at scale.
+
+# Acknowledgments and Disclosure of Funding
+
+We thank Yang Song, Jason Eisner, Tianyi Zhang, Rohan Taori, Xuechen Li, Niladri Chatterji, and the members of p-lambda group for early discussions and feedbacks. We gratefully acknowledge the support of a PECASE award. Xiang Lisa Li is supported by a Stanford Graduate Fellowship.
+
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parse/dev/BryMFPQ4L6/BryMFPQ4L6.md

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+# Augmenting Language Models with Long-Term Memory
+
+Weizhi Wang†, Li Dong‡, Hao Cheng‡, Xiaodong Liu‡, Xifeng $\mathbf { Y a n } ^ { \dagger }$ , Jianfeng Gao‡, Furu Wei‡ †University of California, Santa Barbara ‡Microsoft Research weizhiwang@ucsb.edu, {lidong1, chehao, xiaodl}@microsoft.com
+
+# Abstract
+
+Existing large language models (LLMs) can only afford fix-sized inputs due to the input length limit, preventing them from utilizing rich long-context information from past inputs. To address this, we propose a framework, Language Models Augmented with Long-Term Memory (LONGMEM), which enables LLMs to memorize long history. We design a novel decoupled network architecture with the original backbone LLM frozen as a memory encoder and an adaptive residual side-network as a memory retriever and reader. Such a decoupled memory design can easily cache and update long-term past contexts for memory retrieval without suffering from memory staleness. Enhanced with memory-augmented adaptation training, LONGMEM can thus memorize long past context and use long-term memory for language modeling. The proposed memory retrieval module can handle unlimited-length context in its memory bank to benefit various downstream tasks. Typically, LONGMEM can enlarge the long-form memory to $6 5 \mathrm { k }$ tokens and thus cache many-shot extra demonstration examples as long-form memory for in-context learning. Experiments show that our method outperforms strong longcontext models on ChapterBreak, a challenging long-context modeling benchmark, and achieves remarkable improvements on memory-augmented in-context learning over LLMs. The results demonstrate that the proposed method is effective in helping language models to memorize and utilize long-form contents. Our code is open-sourced at https://aka.ms/LongMem.
+
+# 1 Introduction
+
+Large language models (LLMs) have revolutionized natural language processing with great successes in advancing the state-of-the-art on various understanding and generation tasks [DCLT19, $\mathrm { R W C ^ { + } } 1 9$ , $\mathrm { L O G ^ { + } } 1 9$ , $\bar { \mathrm { Y } } \mathrm { { D Y } ^ { + } 1 9 }$ , $\mathrm { B M R } ^ { + } 2 0$ , $\mathrm { R S R } ^ { + } 2 0 ]$ . Most LLMs benefit from self-supervised training over large corpora via harvesting knowledge from fix-sized local context, showing emergent abilities, e.g., zero-shot prompting $[ \mathrm { R W C ^ { + } } 1 9 ]$ , in-context learning $[ \mathrm { B M R } ^ { + } 2 0 ]$ , and Chain-of-Thought (CoT) reasoning $[ \mathrm { W } \bar { \mathrm { W } } \mathrm { S } ^ { + } \bar { 2 } 2 ]$ . Nevertheless, the input length limit of existing LLMs prevents them from generalizing to real-world scenarios where the capability of processing long-form information beyond a fix-sized session is critical, e.g., long horizontal planning.
+
+To address the length limit issue, the most straightforward method is to simply scale up the input context length. For instance, GPT-3 $[ \mathrm { B M R } ^ { + } 2 0 ]$ increases the input length from 1k tokens in GPT-2 $[ \mathrm { R W C ^ { + } } 1 9 ]$ to $2 \mathrm { k }$ tokens, thereby allowing for better capture of long-range dependencies. However, this approach typically incurs computation-intensive training from scratch and the in-context dense attention is still heavily constrained by the quadratic computation complexity of Transformer self-attention $[ \mathrm { V S P ^ { + } 1 7 } ]$ . Another recent line of work [BPC20, $\mathrm { Z G D ^ { + } } 2 0 ]$ instead focuses on developing in-context sparse attention to avoid the quadratic cost of self-attention, which still largely requires training from scratch. In contrast, the prominent work, Memorizing Transformer (MemTRM) [WRHS22], approximates in-context sparse attention via dense attention over both incontext tokens and memorized tokens retrieved from a non-differentiable memory for Transformers. Thus, MemTRM scales up the resulting language model to handle up to 65k tokens and achieves substantial perplexity gains in modeling full-length books or long papers. However, MemTRM faces the memory staleness challenge during training due to its coupled memory design, which uses a single model for encoding memory and fusing memory for language modeling. In other words, as the model parameters are updated, cached older representations in memory may have distributional shifts from those from the latest model, thereby limiting the effectiveness of the memory augmentation.
+
+![](images/519066b13ea667f961d700ed9c3ecfb54d07e061e20fe2698ba0a94c8f74e2a8.jpg)  
+Figure 1: Overview of the memory caching and retrieval flow of LONGMEM. The long text sequence is divided into fix-length segments with each previous segment processed through a frozen backbone LLM and the corresponding attention key and value vectors of $m$ -th layer are cached into the memory bank. Given current inputs, the corresponding attention query vectors are used to retrieve the top- $K$ attention key-value pairs from previous segments stored in the memory bank, which will be then fused with local context for language modeling.
+
+In this paper, we present a framework for Language Models Augmented with Long-Term Memory (LONGMEM). This framework enables language models to cache lengthy previous context or knowledge into a non-differentiable memory bank, and then utilize them via a decoupled memory module to mitigate the issue of memory staleness. To achieve decoupled memory, we design a novel residual side-network (SideNet) in conjunction with a frozen backbone LLM. Paired attention keys and values of the previous context are extracted using the frozen backbone LLM, which are subsequently stored in the memory bank. In the memory-augmented layer of SideNet, the generated attention query of the current input is used to retrieve cached key-value pairs of previous contexts from the memory, and the corresponding memory augmentations are then fused into adaptable hidden states via a joint-attention mechanism. Furthermore, newly designed cross-network residual connections between the SideNet and the frozen backbone LLM facilitate better knowledge transfer from the pretrained backbone LLM. Through continuous training of the residual SideNet to retrieve and fuse memory augmentations, the pre-trained LLM can be adapted to effectively leverage longcontextual memory for enhanced modeling. The detailed memory cache, retrieval and fusion process is illustrated in Figure 1.
+
+Our decoupled memory design offers two key advantages. First, our proposed architecture effectively separates the process of encoding previous inputs into memory and the process of memory retrieval and fusion, thanks to the decoupled frozen backbone LLM and SideNet. In this way, the backbone LLM only works as the long-context knowledge encoder, while the residual SideNet works as the memory retriever and reader, which effectively resolves the issue of memory staleness. Second, directly adapting the entire LLM with memory augmentations is computationally inefficient and also prone to catastrophic forgetting. As the backbone LLM is frozen during the efficient memoryaugmented adaptation stage, LONGMEM can not only tap into the pretrained knowledge but also avoid catastrophic forgetting.
+
+LONGMEM is capable of taking various types of long-form text and knowledge into the memory bank based on downstream tasks. Here, we consider two representative cases, language modeling with full-length book contexts, and memory-augmented in-context learning with thousands of task-relevant demonstration examples. Specifically, we evaluate the effectiveness of the proposed LONGMEM on various long-text language modeling, and memory-augmented in-context learning for natural language understanding (NLU) tasks. Experimental results demonstrate that our model consistently outperforms the strong baselines in terms of long-text modeling and in-context learning abilities. Our method substantially improves LLM’s long-context language modeling capabilities, with a reduction in perplexity of $1 . 3 8 { \sim } 1 . 6 2$ over different length splits of Gutenberg-2022 corpus. Notably, our model achieves state-of-the-art performance of $4 0 . 5 \%$ identification accuracy on ChapterBreak, a challenging long-context modeling benchmark, significantly surpassing existing strong $\mathbf { X }$ -former baselines. Finally, with 2k demonstration examples in memory, LONGMEM shows pronounced improvements in in-context learning on popular NLU tasks, compared with prominent memoryaugmented and non-memory-augmented baselines.
+
+![](images/d5df7c5e3ae9fa9662e6eb6a4ae1aa993ad2d4d732eab292a975c3119339853b.jpg)  
+Figure 2: Overview of LONGMEM architecture. “MemAug” represents Memory-Augmented Layer.
+
+# 2 Methods
+
+To enable LLMs to harvest relevant information from the past long context in memory, we propose to augment the frozen backbone LLM with a decoupled memory module. To fuse the memory context information, we design a novel lightweight residual SideNet, which can be continually trained in an efficient way. In the following, we first discuss the problem formulation of language modeling with memory augmentations. Then, we formally introduce our efficient residual SideNet for adapting the frozen pretrained LLM to jointly attend over local input context and retrieved memory context. Lastly, we provide our designed processes of how past memory is encoded, stored, recalled and fused for language modeling.
+
+# 2.1 Language Models Augmented with Long-Term Memory
+
+Here, we focus on the high-level problem setup and defer more component details to later sections. Given its wide adoption for pretrained LLMs, our LONGMEM model is built on the Transformer architecture $[ \mathrm { V S P ^ { + } \bar { 1 } 7 } ]$ . For LONGMEM, there are three key components: the frozen backbone LLM, SideNet, and Cache Memory Bank. As most existing pretrained LLMs can only take a fix-sized input, only the input segment of a long sequence (e.g., a book) that can fit in the length limit is denoted as the current input as done for most existing autoregressive language models. Those previous segments that can not fit are denoted as previous inputs, which are used for memory augmentations. To tap into the learned knowledge of the pretrained LLM, both previous and current inputs are encoded using the frozen backbone LLM but different representations are extracted. For previous inputs, the key-value pairs from the Transformer self-attention at $m$ -th layer are stored in Cache Memory Bank, whereas the hidden states from each LLM decoder layer for the current inputs are retained and transferred to SideNet. For each current input token, top relevant key-value vector pairs are retrieved as memory augmentations for language modeling. The SideNet module can be viewed as an efficient adaption model that is trained to fuse the current input context and relevant cached previous contexts in the decoupled memory.
+
+Formally, for a fix-sized input text sequence $\{ { \bf x } _ { i } \} _ { i = 1 } ^ { | x | }$ (the current input), LONGMEM first performs a forward pass using the backbone LLM (indicated in blue in Figure 2) without any gradient calculation. The embedding layer of the backbone LLM first encodes the input $\{ \mathbf { x } _ { i } \} _ { i = 1 } ^ { | x | }$ into embedding space and outputs the initial hidden states, $\mathbf { H } _ { \mathrm { L L M } } ^ { 0 } \in \mathbb { R } ^ { | x | \times E }$ , where $E$ is the hidden dimension. Then each successive Transformer decoder layer of the frozen backbone LLM computes the new hidden states using the hidden states from the previous layer, Hl′LLM = fθl′LLM ( $\mathbf { H } _ { \mathrm { L L M } } ^ { l ^ { \prime } } = f _ { \theta _ { \mathrm { L L M } } ^ { l ^ { \prime } } } ( \mathbf { H } _ { \mathrm { L L M } } ^ { l ^ { \prime } - 1 } ) , \forall l ^ { \prime } \in$ $[ 1 , L ^ { \prime } ]$ and $L ^ { \prime }$ is the total # layers for the backbone LLM. During the forward pass with the backbone LLM for all previous inputs, the key-value pairs used for self-attention at the $m$ -th Transformer decoder layer are stored in Cached Memory Bank (highlighted in orange in upper-left of Figure 2). These pairs are subsequently recalled as memory augmentations for future inputs.
+
+Cached Memory Bank is a head-wise vector queue $\mathcal { Z } _ { k } , \mathcal { Z } _ { v } \in \mathbb { R } ^ { H \times M \times d }$ , which maintains attention key-value pairs of latest $M$ previous inputs $\widetilde { \mathbf { K } } , \widetilde { \mathbf { V } } \in \mathbb { R } ^ { H \times | x | \times d }$ , where $H , d$ denotes the number of attention heads and per-head dimension respectively. After memory retrieval and fusion (§2.3), the memory bank removes the key-value pairs of the oldest sequences and appends the current sequences to the cached vector bank. This update mechanism ensures the language modeling causality at the sequences level and enables the memory bank to consistently maintain records of the most recent previous context for the current inputs.
+
+After the forward pass with the backbone LLM, the SideNet module then takes all current input hidden states from the backbone LLM {Hl′LLM}L′l′=1 and the past key-value pairs in the Cached Memory Bank for computing memory-augmented representations. Specifically, our SideNet of LONGMEM consists of $( L - 1 )$ normal Transformer decoder layers and one special memory-augmented decoder layer. For efficient purposes, we mainly consider the case where #layers $L$ of the SideNet is smaller than that of the backbone LLM, i.e., $L < L ^ { \prime }$ . Our SideNet encodes $\mathbf { H } ^ { 0 }$ into memory-augmented contextual representation via $( L - 1 )$ normal Transformer decoder layers and a special memory-augmented layer.
+
+The memory-augmented layer is an extension of the vanilla Transformer decoder layer that takes a memory-augmented input, including both top relevant key-value pairs in memory and the hidden states from the current input. Here, the cached key-value pairs are recalled using a token-based memory retrieval module $( \ S 2 . 3 )$ . For each current input token, the memory retrieval module $s _ { r t } ( : )$ retrieves top- $K$ relevant key-value pairs in the memory bank $\{ \widetilde { \pmb { k } } _ { i j } , \widetilde { \pmb { v } } _ { i j } \} _ { j = 1 } ^ { K } = s _ { r t } ( \mathbf { x } _ { i } ) .$ . Then SideNet computes the output using the memory-augmented input, $\mathbf { H } _ { \mathrm { S i d e } } ^ { m _ { s } } = f _ { \theta _ { \mathrm { M e m } } } ( \mathbf { H } _ { \mathrm { S i d e } } ^ { m _ { s } - 1 } , \{ \{ \widetilde { \mathbf { k } } _ { i j } , \widetilde { \mathbf { v } } _ { i j } \} _ { j = 1 } ^ { K } \} _ { i = 1 } ^ { | x | } )$ , where is the layer index where we inject the memory-augmentation layer.
+
+Finally, the token probability is computed using the last SideNet hidden states $P ( \mathbf { x } _ { i } | \mathbf { x } _ { 1 } , \cdot \cdot \cdot , \mathbf { x } _ { i - 1 } ) =$ softmax $( W \mathbf { H } ^ { L } )$ , where $W$ is the frozen output embedding weight shared by both the backbone LLM and SideNet. We perform a memory-augmented adaptation training for LONGMEM to utilize the decoupled memory. Following the generative unsupervised pre-training [RNSS18], the training objective of LONGMEM is the standard left-to-right language modeling objective, which maximizes the likelihood of the next token based on the left context: max $\begin{array} { r } { \sum _ { x \in \mathcal { D } } \sum _ { i = 1 } ^ { | \mathbf { x } | } \log P ( \mathbf { x } _ { i } | \mathbf { x } _ { 1 } , \cdots , \mathbf { x } _ { i - 1 } ) } \end{array}$ , where $x$ is a randomly sampled sentence from the pre-training text corpus $\mathcal { D }$ .
+
+# 2.2 Residual SideNet
+
+SideNet Architecture and Initialization. Here, we implement SideNet based on Transformer $[ \mathrm { V S P ^ { + } 1 7 } ]$ . Specifically, the number of decoder layers $L$ in SideNet is equal to the number of layers $L ^ { \prime }$ in the backbone LLM divided by a reduction factor (a layer reduction factor of 2 is used throughout this work, i.e., $L ^ { \prime } = 2 L$ ). The weights of each decoder layer in SideNet are initialized from the corresponding pre-trained decoder layer of the backbone LLM at the same depth: $\Theta _ { \mathrm { S i d e } } ^ { l } = \Theta _ { \mathrm { L L M } } ^ { 2 l }$ . As illustrated in Figure 2, the SideNet model takes the output of backbone LLM’ser and reuses the language modeling head of the backbone LLM, which remains frozen during the continual adaption stage. Throughout the memory-augmented adaptation stage, all other parameters of SideNet are updated based on the training signal. In this way, the lightweight SideNet adaptation achieves fast convergence with knowledge transferred from pre-trained parameters.
+
+Cross-Network Residual Connections. To tap into knowledge from the pretrained backbone LLM, we utilize our proposed cross-network residual connections to fuse representations from the backbone
+
+LLM into SideNet. Specifically, we add the difference between output hidden states at $2 l$ -th and $( 2 l - 2 )$ -th layers of the backbone LLM as the residual connections to the output hidden states at $l$ -th layer of SideNet. Then, the input to the next $( l + 1 )$ -th layer of SideNet is the sum of the original hidden state forwarded through the previous layer $f _ { \Theta _ { \mathrm { S i d e } } ^ { l } } ( \mathbf { H } _ { \mathrm { S i d e } } ^ { l - 1 } )$ and the cross-network residual connection of the hidden state difference from the backbone LLM
+
+$$
+\mathbf { H } _ { \mathrm { S i d e } } ^ { l } = f _ { \ominus _ { \mathrm { S i d e } } ^ { l } } ( \mathbf { H } _ { \mathrm { S i d e } } ^ { l - 1 } ) + ( \mathbf { H } _ { \mathrm { L L M } } ^ { 2 l } - \mathbf { H } _ { \mathrm { L L M } } ^ { 2 l - 2 } ) , \forall l \in [ 1 , L ] ,
+$$
+
+where $\mathbf { H } ^ { 0 }$ is the output of embedding layer. It is worth noting that the residual connections after the self-attention and feed-forward network of a decoder layer $[ \mathrm { V S P ^ { + } 1 7 } ]$ will be performed as normal in $f _ { \Theta _ { \mathrm { S i d e } } ^ { l } } ( \mathbf { H } _ { \mathrm { S i d e } } ^ { l - 1 } )$ and parallel to the proposed cross-network residual connections.
+
+# 2.3 Memory Retrieval and Fusion
+
+The long-term memory capability of LONGMEM is achieved via a memory-augmentation module for retrieval and fusion.
+
+Token-to-Chunk Memory Retrieval. Instead of performing token-to-token retrieval, we focus on token-to-chunk retrieval for acceleration and integrity. A text-chunk refers to an n-gram structure of chunk-size $c s z$ number of contiguous tokens. The memory bank stores cached key-value pairs at the level of token chunks. We divide the memory bank into $M / c s z$ attention key-value paired chunks and use the mean-pooled vector on the chunk-size dimension to get the key vector for retrieval. Then we retrieve the top- $\left( K / c s z \right)$ attention key-value chunks w.r.t the dot product between the attention query of the current input token and the mean-pooled attention key of a candidate chunk. Finally, we squeeze the chunk-size dimension for retrieved key-value paired chunks and flatten them into $K$ key-value pairs at token-level  the retrieval index and acceler $\{ \widetilde { \mathbf { K } } _ { j } , \widetilde { \mathbf { V } } _ { j } \} _ { j = 1 } ^ { K }$ . Adopting token-to-chunk retrieval reduces the sizess. Meanwhile, the retrieval accuracy can be further improved, which is also observed in $[ \mathrm { L G W } ^ { + } 2 3 ]$ and $[ \mathrm { B M H ^ { + } } 2 1 ]$ . The hyperparameter chunk-size $c s z$ controls the granularity of retrieved contexts, which can be empirically adjusted based on downstream tasks. For instance, in-context learning requires more fine-grained label tokens from demonstration examples cached in memory, where a smaller $c s z$ is helpful.
+
+Memory Fusion. The memory fusion is performed within a special memory-augmented layer. As the conventional Transformer decoder layer uses the multi-head self-attention $[ \bar { \mathrm { V } } \mathrm { S P ^ { + } 1 7 } ]$ , we follow [WRHS22] to extend it to a joint-attention mechanism and propose a long-term memory fusion process to enable each token to attend on both local contexts and retrieved memory contexts. With the head-wise hidden state output from previous layer $\mathbf { H } ^ { l - 1 } \in \mathbb { R } ^ { | x | \times d }$ and the corresponding retrieved attention key-value pairs are $\{ \widetilde { \mathbf { K } } _ { i } , \widetilde { \mathbf { V } } _ { i } \} _ { i = 1 } ^ { | x | } \in \mathbb { R } ^ { | x | \times \mathrm { K } \times \mathrm { d } }$ , the output hidden state for the $l$ -th memory-augmented layer $\mathbf { H } ^ { l }$ is computed as:
+
+$$
+\begin{array} { r l } & { \mathbf { A } = \mathrm { s o f t m a x } ( \frac { \mathbf { Q } \mathbf { K } ^ { T } } { \sqrt { d } } ) \mathbf { V } , \mathbf { M } = \mathrm { C o n c a t } \{ \mathrm { s o f t m a x } ( \frac { \mathbf { Q } _ { i } \widetilde { \mathbf { K } } _ { i } ^ { T } } { \sqrt { d } } ) \widetilde { \mathbf { V } } _ { i } \} _ { i = 1 } ^ { | x | } , } \\ & { \mathbf { H } ^ { l } = \mathrm { s i g m o i d } ( g ) \cdot \mathbf { A } + ( 1 - \mathrm { s i g m o i d } ( g ) ) \cdot \mathbf { M } , } \end{array}
+$$
+
+where $\mathbf { Q } , \mathbf { K } , \mathbf { V } , \mathbf { A } , \mathbf { M } \in \mathbb { R } ^ { | x | \times \mathrm { d } }$ , $\mathrm { K }$ is the number of retrieved attention key-value pairs in cached memory for each token, and $g$ is a trainable head-wise gating vector. The hidden state output from previous layer $\mathbf { H } ^ { ( l - 1 ) }$ is linearly projected into attention queries, keys, and values $\mathbf { Q } , \mathbf { K } , \mathbf { V }$ separately via three matrices $W ^ { Q } , W ^ { K } , \bar { W } ^ { V } \in \mathbb { R } ^ { \mathrm { d } \times \mathrm { d } }$ . It is worth noting that the retrieved attention key-value pairs in cached memory are distinct to each token.
+
+# 3 Experiments
+
+We evaluate our proposed LONGMEM model on different tasks that require long-context modeling: a) long-text language modeling and language understanding when loading the past long-context into cached memory; b) infinite-length in-context learning when loading a large number of demonstration examples into cached memory.
+
+![](images/14da8024824c325b74cd1423e98cb487ba217111ca406b50973d6930b171469c.jpg)  
+Figure 3: Batchfying the large text corpora into batches to ensure that each consecutive segments within each document is distributed in consecutive batches.
+
+# 3.1 Training Setup
+
+Batchfying the training corpora. The conventional batchyfing process for large corpora truncates the whole corpora into consecutive fix-length text segments without padding and shuffles all segments to construct mini-batches $[ \mathrm { R W C ^ { + } } 1 9 ]$ . In contrast, LONGMEM must disable global shuffling and ensure the global causality at the segment level. Firstly, we divide all long documents in training corpora into batch-size number of document groups with equivalent length and then perform a document-level shuffling within each group. Then, we concatenate shuffled documents within one group and truncate them into ordered segments. In order to ensure that two consecutive segments of one long document are distributed in two consecutive input batches after batchfying, we select one segment from batch-size number of document groups with the same inner-group index. Thus a mini-batch with batch-size number of segments are constructed from exactly the batch-size number of document groups. In this way, as the training iteration steps, the cached attention key-value pairs in the memory bank are previous context of current inputs within the same document. The batchfying process is illustrated in Figure 3.
+
+Training Corpus, Backbone LLM and Hyperparameter. We sample a subset of the Pile $[ \mathrm { G B B ^ { + } } 2 0 ]$ as the training corpus, including BookCorpus2, Books3, OpenWebText2, Stack Exchange, Wikipedia, Gutenberg (PG-19), NIH ExPorter, and Pile-CC datasets. We reproduce GPT- $^ { . 2 ^ { * } }$ (407M-params) as the pre-trained backbone LLM with Alibi [PSL21] position embedding because original GPT$2 \left[ \mathrm { R W } \bar { \mathrm { C } } ^ { + } 1 9 \right]$ adopts absolute position embedding, which is found to perform poorly to enable LLM to learn long-distance dependencies $\mathrm { [ D Y Y ^ { + } 1 9 ] }$ . The backbone LLM holds a $L ^ { \prime } = 2 4 , H = 1 6 , d = 6 4$ architecture. The SideNet holds a $L = 1 2 , H = 1 6 , d = 6 4$ architecture. The training for memoryaugmented adaptation iterates on 26B tokens, with a global 256 batch-size and 1024 sequence length. The chunk-size $c s z$ is 4 tokens and the memory size $M$ is $6 5 \mathrm { k }$ key-value pairs of tokens. For each token, we retrieve $K { = } 6 4$ attention key-value pairs for augmentation, which are $K / c s z { = } 1 6$ text chunks. The memory-augmentation layer is the 9-th layer of SideNet. The attention keys and values from 18-th layer of backbone LLM is cached into memory and used for future retrieval. Other training details are presented in Appendix C.
+
+Memory Retrieval Module. The fixed memory-size of cached memory bank in one GPU is 65536 key-value pairs of tokens. We enable each GPU to construct and update their own memory retrieval module for efficiency. For the implementation of the efficient token-to-chunk retrieval, we use the faiss [JDJ21] toolkit to construct an exact-search index on GPU to store the mean-pooled attention keys of text chunks and perform efficient retrieval. The faiss index maintains a fixed $M / c s z$ keys and provides the efficient exact search w.r.t. inner product. The retrieval takes about 15ms per 1k tokens, which is $55 \%$ timecost of backbone LLM forwarding pass. We can easily adapt the exact search index to approximate search index to gain more retrieval efficiency.
+
+Baselines. In addition to the baseline of our pre-trained GPT- $^ { 2 ^ { * } }$ variant, we consider Memorizing Transformer (MemTRM) [WRHS22] and TRIME [ZLC22] as two memory-augmented baselines. The MemTRM model can be easily adapted to tune a pre-trained LLM to use external memory. We insert the KNN-augmented layer proposed by MemTRM as the same 18-th layer in the LLM decoder.
+
+<table><tr><td>Dataset Splits</td><td>S2</td><td></td><td>PG-22 S3</td><td>S4</td><td>S5</td><td>ArXiv</td></tr><tr><td>Len. Range</td><td>5K-10K</td><td>10K-100K</td><td>100K-500K</td><td>500K-1M</td><td>&gt;1M</td><td>&lt;60K</td></tr><tr><td>#Documents</td><td>500</td><td>100</td><td>30</td><td>8</td><td>1</td><td>100</td></tr><tr><td>Avg. #tokens</td><td>7.6K</td><td>47.6K</td><td>140K</td><td>640K</td><td>1.2M</td><td>15.4K</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 1: Dataset Statistics of five splits of PG-22 based on length range and ArXiv.
+
+To adapt TRIME for our experiments, we replace the batchfying function and loss function of training GPT- $^ { 2 ^ { * } }$ with those proposed by TRIME, which enables a memory-augmented adaptation tuning method for LLMs. The two reproduced baselines are trained for the same number of tokens under the same hyperparameter setting as LONGMEM.
+
+# 3.2 Long-Context Language Modeling
+
+The long-context language modeling can potentially benefit from the augmented memory of past longcontexts. The knowledge stored in retrieved attention key-values can provide valuable background and contextual information, helping models perform better in long-context language modeling. For instance, when trying to model a long-text book, acquiring knowledge from previous background and character relationships can be helpful in modeling the subsequent stories.
+
+Evaluation Setting. We first compare LONGMEM and baselines on three long-context modeling datasets, Project Gutenberg 2020-2022, ArXiv, and ChapterBreak. The majority of included books or papers in these datasets have the length of at least 16k tokens. All listed datasets are evaluated in a zero-shot manner without any task-specific tuning. The detailed evaluation settings on the three datasets are as follows:
+
+• Project Gutenberg 2020-2022 Language Modeling Dataset. We crawled and cleaned the books published between 2020 and 2022 under Project Gutenberg Library1 to build up a completely new long-text modeling dataset, named PG-22. It is significantly different from our training subset PG-19 in terms of domains and writing styles, because books in PG-19 [RPJL19] are published before 1919. We provide different validation splits of PG-22 based on length range, and the data statistics are presented in Table 1.
+
+• ArXiv Dataset. The ArXiv dataset includes papers in the areas of Math, Computer Science, and Physics. We select a validation split of ArXiv paper subset in the Pile corpus $[ \mathrm { G B B ^ { + } } 2 0 ]$ . The ArXiv subset of Pile is excluded from our training and serves an out-of-distribution dataset. We report the token-level language modeling perplexity on the long-context language modeling benchmarks of PG-22 and ArXiv.
+
+• ChapterBreak Benchmark. ChapterBreak [STI22] is a challenging suffix identification dataset that requires LLMs to distinguish the beginning of the ground-truth next chapter from a set of hard negative segments sampled from the same book, given the long context of previous chapters. ChapterBreak requires processing global long-context to comprehend and identify the correct suffix. [STI22] demonstrated that even state-of-the-art $\mathbf { X }$ -formers for long-text processing fail to effectively leverage long-range context to perform well on ChapterBreak. ChapterBreak has two subsets, the PG-19 subset and the Archive of Our Own (AO3) subset. As the PG-19 corpus has been included in the pre-training corpus of LONGMEM, it cannot be further used for evaluation. Thus, we select AO3 subset, which contains fan-fictions extracted from AO3. ChapterBreak provides 8 splits based on the prefix length from $0 . 5 \mathrm { k }$ to $^ \mathrm { 8 k }$ tokens to fit the length limit of different models. The splits of 4k, 6k, and $^ \mathrm { 8 k }$ prefix are selected for evaluation. For LLMs that cannot process over 4k tokens, we abandon the front prefix to fulfill the maximum input length of LLMs. For memory-augmented models (MemTRM and LONGMEM), we load the given $4 \mathrm { k } / 6 \mathrm { k } / 8 \mathrm { k }$ prefix contexts into the cached memory and then do the scoring. we use the perplexity as the scorer for each candidate suffix segment in a zero-shot manner. Then the suffix segment with lower perplexity is selected as the label. The suffix identification accuracy is used as the evaluation metric.
+
+Results. The main results on evaluated long-context datasets are summarized in Table 2. The proposed LONGMEM model significantly outperforms all considered baselines on long-text language modeling datasets, with improvements of 1.38 to 1.62 perplexity on different length splits of $P G \mathrm { - } 2 2$ , and 1.0 on ARXIV datasets. Surprisingly, the proposed method achieves the state-of-the-art performance of $40 . 5 \%$ accuracy on ChapterBreakAO3 suffix identification benchmark and outperforms both the strong long-context transformers and GPT-3 with $3 1 3 \mathrm { x }$ larger parameters. The substantial improvements on these datasets demonstrate that LONGMEM can comprehend past long-context in cached memory well for predicting future inputs.
+
+Table 2: Evaluation results on long-context language modeling datasets. We report token-level perplexity (PPL) (lower the better) on all datasets.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">In-Context Len.</td><td rowspan="2">In-Memory Len.</td><td colspan="5">PG-22</td><td rowspan="2">ArXiv</td></tr><tr><td>5K-10K</td><td>10K-100K</td><td>100K-500K</td><td>500K-1M</td><td>&gt;1M</td></tr><tr><td>GPT-2*</td><td>1k</td><td>N/A</td><td>22.78</td><td>24.39</td><td>24.12</td><td>24.97</td><td>18.07</td><td>11.05</td></tr><tr><td>MemTRM</td><td>1k</td><td>65K</td><td>21.77</td><td>23.56</td><td>23.23</td><td>24.16</td><td>17.39</td><td>10.81</td></tr><tr><td>TRIME</td><td>1k</td><td>65K</td><td>22.21</td><td>23.50</td><td>23.74</td><td>24.32</td><td>17.80</td><td>10.95</td></tr><tr><td>LONGMEM</td><td>1k</td><td>65K</td><td>21.29</td><td>23.01</td><td>22.55</td><td>23.35</td><td>16.71</td><td>10.05</td></tr></table>
+
+Table 3: Zero-shot Suffix Identification Accuracy on AO3 subset of ChapterBreak. Baselines marked with † are directly cited from [STI22]. The MemTRM and LONGMEM loads the given $4 \mathrm { k } / 6 \mathrm { k } / 8 \mathrm { k }$ prefix contexts into cached memory, while the input length to local context is still 1k tokens.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">#Params</td><td rowspan="2">In-Context Len.</td><td rowspan="2">In-Memory Len.</td><td colspan="3">ChapterBreakao3</td></tr><tr><td>ctx-4k</td><td>ctx-6k</td><td>ctx-8k</td></tr><tr><td>GPT-2-XLt [RWC+19]</td><td>1.5B</td><td>1K</td><td>N/A</td><td>24%</td><td>24%</td><td>24%</td></tr><tr><td>GPT-3† [BMR+20]</td><td>175B</td><td>2K</td><td>N/A</td><td>28%</td><td>28%</td><td>28%</td></tr><tr><td>LocalTRM+ [RSVG21]</td><td>516M</td><td>8K</td><td>N/A</td><td>24%</td><td>24%</td><td>24%</td></tr><tr><td>RoutTRM+ [RSVG21]</td><td>490M</td><td>8K</td><td>N/A</td><td>25%</td><td>24%</td><td>24%</td></tr><tr><td>Bigbirdt [ZGD+20]</td><td>128M</td><td>4K</td><td>N/A</td><td>26%</td><td>26%</td><td>26%</td></tr><tr><td>GPT-2*</td><td>407M</td><td>1K</td><td>N/A</td><td>18.4%</td><td>18.4%</td><td>18.4%</td></tr><tr><td>MemTRM</td><td>407M</td><td>1K</td><td>8</td><td>28.3%</td><td>28.7%</td><td>28.7%</td></tr><tr><td>LONGMEM</td><td>558M</td><td>1K</td><td>8</td><td>37.7%</td><td>39.4%</td><td>40.5%</td></tr></table>
+
+# 3.3 Memory-Augmented In-Context Learning
+
+LLMs have the emerging capability of in-context learning (ICL) via learning knowledge nonparametrically from few-shot demonstration examples in the local context. However, conventional in-context learning is heavily restricted by input context length, rendering it ineffective to absorb supervision from sufficient demonstration examples in the training set. With the proposed unlimited-length memory augmentation, LONGMEM can overcome the limitation of the number of demonstration examples in the local context and even attend on the whole training set by loading it into the cached memory. In this way, LONGMEM generalizes the conventional few-shot in-context learning to memory-augmented in-context learning with thousands of auxiliary demonstration examples.
+
+Evaluation Setting. Here, we evaluate the in-context learning capability of baselines and the proposed LONGMEM model on five NLU datasets, SST-2 $[ \mathrm { S P W ^ { + } } 1 \bar { 3 } ]$ , MPQA [WWC05], MR $[ \mathrm { A } \mathrm { \bar { B } } \mathrm { K } ^ { + } 0 7 ]$ , Subj [PL04] and SST-5 $[ \mathrm { S P W ^ { + } } 1 3 ]$ . We evaluate models on two few-shot settings, 4-shot and 20- shot. The 4-shot case is the data-insufficient scenario, while the 20-shot demonstrations can almost fulfill the 1k input length and provide sufficient contextual self-supervisions. We transform the $\mathbf { k }$ -shot examples to semantically meaningful demonstration examples via fixed text template, i.e., $d _ { i } = "$ "Review: $x _ { i }$ Sentiment: $y _ { i } " , \forall \{ ( x _ { i } , y _ { i } ) \} _ { i = 1 } ^ { k } \in { \mathcal { D } } _ { \operatorname { t r a i n } }$ for sentiment analysis tasks. Additionally, we evaluate the 3-shot ICL on question-answering using SQuAD [RZLL16] under an open-ended generation setting. The details of all prompt templates are presented in Appendix D. Then we concatenate the demonstration examples with newlines to delimit them. The prediction label is directly generated using greedy decoding given the demonstration examples and test cases in context. The prediction accuracy is used as the evaluation metric. We report the mean and standard deviation of 6 runs with different random seeds to assess the randomness in selecting $\mathbf { k }$ -shot demonstration examples. As mentioned previously, the chunk size controls the granularity of retrieved text chunks. Since the considered NLU datasets require more fine-grained labels from cached memory, we perform a hyperparameter selection on the validation set of SST-2, and the best chunk-size 2 is used to report the results for MemTRM, TRIME and our model.
+
+Table 5: Accuracy $[ \% ]$ of 4-shot and 20-shot ICL on 5 NLU tasks (SST-2, mr, subj, SST-5, mpqa). We sample 2000 extra demonstration examples and load them into cached memory. The subscript is the standard deviation across 6 runs. Avg. refers to the average accuracy on 5 datasets.   
+
+<table><tr><td>Model</td><td>In-Context #Demons.</td><td>In-Memory #Demons.</td><td>SST-2 ACC↑</td><td>MR ACC↑</td><td>Subj ACC↑</td><td>SST-5 ACC↑</td><td>MPQA ACC↑</td><td>Avg.</td></tr><tr><td>Majority</td><td>N/A</td><td>N/A</td><td>50.9</td><td>50.0</td><td>50.0</td><td>20.0</td><td>50.0</td><td>44.2</td></tr><tr><td>GPT-2*</td><td>4</td><td>N/A</td><td>68.311.6</td><td>64.712.5</td><td>51.94.2</td><td>31.44.4</td><td>61.511.8</td><td>55.6</td></tr><tr><td>MemTRM</td><td>4</td><td>2000</td><td>67.512.4</td><td>64.611.3</td><td>53.26.0</td><td>29.64.4</td><td>63.012.1</td><td>55.6</td></tr><tr><td>TRIME</td><td>4</td><td>2000</td><td>69.514.5</td><td>63.89.8</td><td>51.51.5</td><td>31.86.7</td><td>63.612.9</td><td>56.0</td></tr><tr><td>LONGMEM</td><td>4</td><td>2000</td><td>71.814.0</td><td>65.111.0</td><td>53.83.7</td><td>36.06.8</td><td>65.412.8</td><td>58.4</td></tr><tr><td>GPT-2*</td><td>20</td><td>N/A</td><td>68.211.5</td><td>63.45.2</td><td>57.610.2</td><td>33.66.0</td><td>70.87.6</td><td>58.7</td></tr><tr><td>MemTRM</td><td>20</td><td>2000</td><td>65.19.6</td><td>65.19.3</td><td>58.210.6</td><td>31.96.3</td><td>72.77.4</td><td>58.6</td></tr><tr><td>TRIME</td><td>20</td><td>2000</td><td>74.313.9</td><td>71.52.5</td><td>57.511.4</td><td>33.04.6</td><td>69.87.8</td><td>61.1</td></tr><tr><td>LONGMEM</td><td>20</td><td>2000</td><td>78.014.1</td><td>78.63.3</td><td>65.68.5</td><td>36.57.5</td><td>74.67.3</td><td>66.7</td></tr></table>
+
+Results. The results on in-context learning are summarized in Table 5 and Table 4. LONGMEM achieves remarkable improvements on all NLU tasks under the 20-shot sufficient in-context setting, with $+ 5 . 6$ average scores increase over pretrained GPT- $^ { 2 ^ { * } }$ , MemTRM, and TRIME.
+
+Meanwhile, LONGMEM also brings performance improvements on the 4-shot case. Additionally, LONGMEM improves the in-context learning capabilities of LLMs on open-ended generation tasks, with $+ 4 . 5$ EM score increase on SQuAD. The results indicate that having more demonstration examples loaded in cached memory can provide additional contextual cues to assist in-context learning. LONGMEM can utilize task-relevant knowledge from both local contextual demonstrations and in-memory augmented demonstrations, thereby achieving superior incontext learning capabilities.
+
+<table><tr><td>Model</td><td>EM</td><td>F1</td></tr><tr><td>GPT-2*</td><td>22.282.3</td><td>30.782.0</td></tr><tr><td>MemTRM</td><td>22.843.5</td><td>32.652.8</td></tr><tr><td>LONGMEM</td><td>26.772.3</td><td>35.702.0</td></tr></table>
+
+Table 4: Exact match (EM) and F1 scores of 3-shot (about 1k tokens) in-context learning on SQuAD. LONGMEM loads 200 extra demonstration examples into cached memory.
+
+# 3.4 Ablation Studies
+
+So far, we empirically verify the effectiveness and superiority of LONGMEM in utilizing cached memory for long-context modeling, long-context understanding, and many-shot in-context learning. Furthermore, we would like to investigate the extend to which the cached memory contributes to the long-context understanding capability of LONGMEM through an ablation study of removing memory augmentations. Besides, since the design of the cached memory bank involves several hyperparameters, such as memory size $m s z$ and chunk-size $c s z$ , we conduct a series of ablation studies to evaluate the effects of those choices.
+
+Effects of Long-Term Memory Augmentation. To evaluate the effects and contributions of memory augmentations, we set the memory-size to 0 and maintain the SideNet parameters during inference. The results of LONGMEM without memory augmentation are shown in Table 6 of Appendix. As expected, without augmented long-term memory, the vanilla model with only backbone LLM and SideNet only gains 59.4 average scores on ICL NLU tasks, which is a 7.3 average accuracy decrease due to the removal of memory augmentation.
+
+Effects of Chunk-Size. As analyzed before, the chunk-size $c s z$ controls the granularity of retrieval and thus it may make a difference to tasks with requirements of fine-grained retrieval. We perform an ablation study on the effects of various chunk-size choices $c s z \in \bar { \{ 2 , 4 , 8 \} }$ for in-context learning and the results are presented in 4(a). The chunk size of 2 yields the best performance on in-context learning tasks on five NLU datasets, which is consistent with the property of NLU tasks with the requirement of fine-grained retrieval and fusion towards classification label tokens.
+
+Effects of Memory Size. The memory size (msz) controls the capacity of the memory bank. In general, the memory size should be compatible with the average length of documents or contexts, i.e., a set of books with average 16k tokens should deploy the memory size of 16k tokens in cached memory. The training $m s z$ of 65 tokens is excessive for downstream tasks such as ChapterBreak as the whole prefix context length does not exceed $6 5 \mathrm { k }$ tokens. Thus, we perform an ablation study on the effects of memory size $m s z \in \{ 8 k , 1 6 k , 3 2 k , 6 5 k \}$ during the inference stage on the PG-22 language modeling datasets and the results are shown in 4(b). To model the books with lengths of $8 \mathrm { k } { - } 5 0 \mathrm { k }$ , the smaller memory size $1 6 k$ which is consistent with the average length of target books yields the best perplexity.
+
+![](images/de4bcd827ba3f0d14048dea90d518ae335fe99f3a1ab8e426f36f59efb7a7395.jpg)  
+Figure 4: (a) Accuracy on 5 NLU datasets given different chunk size during inference; (b) ∆Perplexity on 4 splits of PG-22 given different memory size during inference, in which the perplexity when $\scriptstyle { m s z = 6 5 \mathrm { k } }$ is used as baseline.
+
+# 4 Related Work
+
+Large Language Models. Large Language Models, i.e., GPT-3 $[ \mathrm { B M R } ^ { + } 2 0 ]$ , LLAMA $[ \mathrm { T M S ^ { + } } 2 3 ]$ , GPT-4 [Ope23], significantly revolutionized NLP research and promoted the state-of-the-art of various language understanding, language generation $[ \mathrm { W } Z \mathrm { G } ^ { + } 2 2 ]$ , and even vision-language tasks $[ \mathrm { W D C ^ { + } } 2 2 ]$ . Additionally, enabled by multi-task instruction tuning $[ \mathrm { W B } Z ^ { + } 2 1$ , $\mathrm { O W J ^ { + } } 2 2 ]$ , LLMs exhibit “emergent abilities“ $[ \dot { \mathrm { W } } \mathrm { T B } ^ { + } 2 2 ]$ like mathematical reasoning $[ \mathrm { W } \mathrm { W } \mathrm { S } ^ { + } 2 2 ]$ , code completion $[ \mathbf { C } \mathbf { T } \mathbf { J } ^ { + } 2 1 ]$ , etc.
+
+$\mathbf { X }$ -formers. To enable transformers to attend on longer context, many variants of “ $\mathbf { \dot { x } }$ -formers“ are proposed. Transformer-XL $\mathrm { [ D Y Y ^ { + } 1 9 ] }$ proposes to cache attention keys and values of past segment and reuse them in recurrent manner. Recent seminal works of $\mathbf { X }$ -formers, including LinFormer $[ \bar { \mathrm { W } } \mathrm { L K } ^ { + } 2 0 ]$ , LongFormer [BPC20], Routing Transformer [RSVG21], proposed various sparse attention mechanisms for decreasing $O ( n ^ { 2 } )$ complexity to $O ( n \log n )$ or even $O ( n )$ . BigBird $[ Z \mathrm { G D } ^ { + } 2 0 ]$ achieves a $4 \mathrm { k }$ sequence length via attending on a subset of context tokens. Although these $\mathbf { X }$ -formers achieve substantial efficiency improvements, such efficiency gains are not remarkable when modeling sequences that spans book-level length. Moreover, the largest sequence length of these methods is still upper-bounded by 16k tokens, making them invalid in modeling long-sequences at the book or wikipedia-page level (i.e., average 70k tokens for full-length books in PG19 dataset [RPJL19]).
+
+Side-Tuning. The method of Side-Tuning $[ Z \mathrm { S } Z ^ { + } 2 0$ , SCB22] is a task-specific tuning method for pre-trained models via training a lightweight side-network that is fused with the fixed pre-trained network via summation. Our method inherits the idea of adopting a side-network but distinguishes the side-tuning method in terms of learning objective and cross-network fusion ways. LONGMEM proposes to augment LLMs with decoupled memory to retrain information from long past inputs without any task-specific tuning. The cross-network residual connections introduced here are novel and distinct from the vanilla summation used in Side-Tuning.
+
+# 5 Conclusion
+
+In this paper, we propose to augment LLMs with long-term memory for enabling them to memorize long-form context and gain long-form memory. The designed decoupled memory module can cache attention key and value pairs of past inputs for future retrieval and fusion. A decoupled residual SideNet is introduced as the memory retriever and reader, meanwhile the LLM itself is frozen and works as knowledge and memory encoder. Experiments on various long-contextual language modeling datasets demonstrate the effectiveness of our model over other memory-augmentation baselines. The proposed method can also enable in-context learning of LLMs to overcome the limited number of demonstration examples in context, which is constrained by the contextual length, via caching thousands of auxiliary demonstration examples in memory.
+
+# Acknowledgement
+
+This work is done during the first author’s internship at Microsoft Research. We would like to thank the anonymous reviewers for the helpful comments. We appreciate Yutao Sun and Yaru Hao for helpful suggestions on implementation and evaluation benchmarks. The first author was partly sponsored by the DARPA PTG program (HR001122C0009). Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of funding agencies.
+
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+$[ \mathrm { L O G ^ { + } } 1 9 ]$ Yinhan Liu, Myle Ott, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. RoBERTa: A robustly optimized bert pretraining approach. ArXiv, abs/1907.11692, 2019. [Ope23] OpenAI. Gpt-4. https://openai.com/research/gpt-4, 2023. Accessed on March 14, 2023.   
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+$\mathrm { [ T M S ^ { + } } 2 3 $ ] Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov, Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288, 2023.   
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+
+A Ablation Study on the Effect of Memory Augmentation   
+
+<table><tr><td>Model</td><td>In-Context #Demons.</td><td>In-Memory #Demons.</td><td>SST-2 ACC↑</td><td>MR ACC↑</td><td>Subj ACC↑</td><td>SST-5 ACC↑</td><td>MPQA ACC↑</td><td>Avg.</td></tr><tr><td>Majority</td><td>N/A</td><td>N/A</td><td>50.9</td><td>50.0</td><td>50.0</td><td>20.0</td><td>50.0</td><td>44.2</td></tr><tr><td>GPT-2*</td><td>4</td><td>N/A</td><td>68.311.6</td><td>64.712.5</td><td>51.94.2</td><td>31.44.4</td><td>61.511.8</td><td>55.6</td></tr><tr><td>MemTRM</td><td>4</td><td>2000</td><td>67.512.4</td><td>64.611.3</td><td>53.26.0</td><td>29.64.4</td><td>63.012.1</td><td>55.6</td></tr><tr><td>TRIME</td><td>4</td><td>2000</td><td>69.514.5</td><td>63.89.8</td><td>51.51.5</td><td>31.86.7</td><td>63.612.9</td><td>56.0</td></tr><tr><td>LONGMEM</td><td>4</td><td>2000</td><td>71.814.0</td><td>65.111.0</td><td>53.83.7</td><td>36.06.8</td><td>65.412.8</td><td>58.4</td></tr><tr><td>w/o Memory</td><td>4</td><td>0</td><td>69.412.4</td><td>64.312.1</td><td>53.47.7</td><td>29.05.2</td><td>62.512.3</td><td>55.7</td></tr><tr><td>GPT-2*</td><td>20</td><td>N/A</td><td>68.211.5</td><td>63.45.2</td><td>57.610.2</td><td>33.66.0</td><td>70.87.6</td><td>58.7</td></tr><tr><td>MemTRM</td><td>20</td><td>2000</td><td>65.19.6</td><td>65.19.3</td><td>58.210.6</td><td>31.96.3</td><td>72.77.4</td><td>58.6</td></tr><tr><td>TRIME</td><td>20</td><td>2000</td><td>74.313.9</td><td>71.52.5</td><td>57.511.4</td><td>33.04.6</td><td>69.87.8</td><td>61.1</td></tr><tr><td>LONGMEM</td><td>20</td><td>2000</td><td>78.014.1</td><td>78.63.3</td><td>65.68.5</td><td>36.57.5</td><td>74.67.3</td><td>66.7</td></tr><tr><td>w/o Memory</td><td>20</td><td>0</td><td>70.012.8</td><td>70.86.2</td><td>52.94.6</td><td>30.96.4</td><td>72.57.5</td><td>59.4</td></tr></table>
+
+Table 6: Ablation study results on the effect of memory augmentation of 4-shot and 20-shot ICL on 5 NLU tasks (SST-2, mr, subj, SST-5, mpqa). We sample 2000 extra demonstration examples and load them into cached memory. The subscript is the standard deviation across 6 runs. Avg. refers to the average accuracy on 5 datasets. "w/o" is short for "without".
+
+# B Inference Efficiency and GPU-Memory Efficiency
+
+When the model is required to comprehend long sequences, the proposed method LONGMEM can load the out-of-boundary inputs into the cached memory as previous context. Thus, the memory usage and inference speed can be significantly improved compared with vanilla self-attention-based models. The detailed statistics in terms of the efficiency is presented in Table 7.
+
+<table><tr><td>Model</td><td>In-Context Len.</td><td>In-Memory Len.</td><td>Inference Speed (tokens/s)↑</td><td>GPU-Memory Usage (MBs)↓</td></tr><tr><td>GPT-2*</td><td>4k</td><td>N/A</td><td>14666</td><td>20671</td></tr><tr><td>LONGMEM</td><td>1k</td><td>3k</td><td>22638</td><td>13335</td></tr><tr><td>GPT-2*</td><td>8k</td><td>N/A</td><td>8417</td><td>54195</td></tr><tr><td>LONGMEM</td><td>1k</td><td>7k</td><td>21343</td><td>13437</td></tr></table>
+
+Table 7: The superiority of our method over fully dense self-attention (GPT- $2 ^ { * }$ ) in terms of inference speed and GPU-memory utilization.
+
+# C Training Details
+
+The pre-training of reproduced GPT- $^ { 2 ^ { * } }$ iterates on 117B tokens in total, with 512 batch-size and 1024-token fixed segment-length. The Adam optimizer [KB15] is adopted in memory-augmented adaptation training. The pre-training and adaptation are trained on 16 32GB-Tesla-V100 GPUs. Other detailed training hypperparamters and settings are presented in Table 8.
+
+<table><tr><td>Hyperparameter</td><td>LONGMEM</td></tr><tr><td colspan="2">Reproduced GPT-2* Backbone LLMHyperparameters</td></tr><tr><td>Parameters</td><td>407M</td></tr><tr><td>Precision</td><td>float16</td></tr><tr><td>Layers Hidden dim.</td><td>24</td></tr><tr><td>Attention heads</td><td>1024</td></tr><tr><td></td><td>16</td></tr><tr><td>Head Dim</td><td>64</td></tr><tr><td>Vocab size</td><td>52k</td></tr><tr><td>Sequence length</td><td>1024</td></tr><tr><td>Position emb.</td><td>Alibi</td></tr><tr><td>Tied embedding</td><td>False</td></tr><tr><td colspan="2">SideNetHyperparameters</td></tr><tr><td>Parameters</td><td>151M</td></tr><tr><td>Precision</td><td>float16</td></tr><tr><td>Layers</td><td>12</td></tr><tr><td>Hidden dim.</td><td>1024</td></tr><tr><td>Attention heads</td><td>16</td></tr><tr><td>Head Dim</td><td>64</td></tr><tr><td>Sequence length</td><td>1024</td></tr><tr><td colspan="2">Memory-Augmented Adaptation Hyperparameters</td></tr><tr><td>Global Batch Size</td><td>256</td></tr><tr><td>Learning rate</td><td>2.0e-4</td></tr><tr><td>Total tokens</td><td>26B</td></tr><tr><td>Warmup tokens</td><td>0</td></tr><tr><td>LR Decay style</td><td>polynomial</td></tr><tr><td>Adam(β1,β2)</td><td>(0.9, 0.98)</td></tr><tr><td>Adam eps</td><td>1e-06</td></tr><tr><td>Weight decay</td><td>0.01</td></tr><tr><td></td><td></td></tr><tr><td>Gradient clipping</td><td>2.0</td></tr></table>
+
+Table 8: Memory-Augmented Adaptation and Architectural Hyperparameters.
+
+# D Prompting Templates
+
+We present all hand-crafted in-context learning prompting templates and labels for 5 NLU datasets and Squad QA dataset in Tabel 9.
+
+<table><tr><td>Task</td><td>Prompt</td><td>Labels</td></tr><tr><td>SST-2</td><td>Review: [Sentence] Sentiment: [Label]</td><td>{positive, negative}</td></tr><tr><td>MR</td><td>Review: [Sentence] Sentiment: [Label]</td><td>{positive, negative}</td></tr><tr><td>MPQA</td><td>Review: [Sentence] Sentiment: [Label]</td><td>{positive, negative}</td></tr><tr><td>SST-5</td><td>input: [Sentence] type: [Label]</td><td>{terrible,bad,okay,good,great}</td></tr><tr><td>Subj</td><td>input: [Sentence] type: [Label]</td><td>{objective, subjective}</td></tr><tr><td> Squad</td><td colspan="2">Passage: [Passage]\n Question: [Question] Answer: [Answer]</td></tr></table>
+
+Table 9: The hand-crafted prompts used to query the model predictions on the zero-shot evaluation of 5 NLU datasets and one question-answering dataset Squad.

parse/dev/BryMFPQ4L6/BryMFPQ4L6_content_list.json

@@ -0,0 +1,1100 @@
+[
+    {
+        "type": "text",
+        "text": "Augmenting Language Models with Long-Term Memory ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Weizhi Wang†, Li Dong‡, Hao Cheng‡, Xiaodong Liu‡, Xifeng $\\mathbf { Y a n } ^ { \\dagger }$ , Jianfeng Gao‡, Furu Wei‡ †University of California, Santa Barbara ‡Microsoft Research weizhiwang@ucsb.edu, {lidong1, chehao, xiaodl}@microsoft.com ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
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+            319,
+            535,
+            335
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Existing large language models (LLMs) can only afford fix-sized inputs due to the input length limit, preventing them from utilizing rich long-context information from past inputs. To address this, we propose a framework, Language Models Augmented with Long-Term Memory (LONGMEM), which enables LLMs to memorize long history. We design a novel decoupled network architecture with the original backbone LLM frozen as a memory encoder and an adaptive residual side-network as a memory retriever and reader. Such a decoupled memory design can easily cache and update long-term past contexts for memory retrieval without suffering from memory staleness. Enhanced with memory-augmented adaptation training, LONGMEM can thus memorize long past context and use long-term memory for language modeling. The proposed memory retrieval module can handle unlimited-length context in its memory bank to benefit various downstream tasks. Typically, LONGMEM can enlarge the long-form memory to $6 5 \\mathrm { k }$ tokens and thus cache many-shot extra demonstration examples as long-form memory for in-context learning. Experiments show that our method outperforms strong longcontext models on ChapterBreak, a challenging long-context modeling benchmark, and achieves remarkable improvements on memory-augmented in-context learning over LLMs. The results demonstrate that the proposed method is effective in helping language models to memorize and utilize long-form contents. Our code is open-sourced at https://aka.ms/LongMem. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            654,
+            310,
+            671
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Large language models (LLMs) have revolutionized natural language processing with great successes in advancing the state-of-the-art on various understanding and generation tasks [DCLT19, $\\mathrm { R W C ^ { + } } 1 9$ , $\\mathrm { L O G ^ { + } } 1 9$ , $\\bar { \\mathrm { Y } } \\mathrm { { D Y } ^ { + } 1 9 }$ , $\\mathrm { B M R } ^ { + } 2 0$ , $\\mathrm { R S R } ^ { + } 2 0 ]$ . Most LLMs benefit from self-supervised training over large corpora via harvesting knowledge from fix-sized local context, showing emergent abilities, e.g., zero-shot prompting $[ \\mathrm { R W C ^ { + } } 1 9 ]$ , in-context learning $[ \\mathrm { B M R } ^ { + } 2 0 ]$ , and Chain-of-Thought (CoT) reasoning $[ \\mathrm { W } \\bar { \\mathrm { W } } \\mathrm { S } ^ { + } \\bar { 2 } 2 ]$ . Nevertheless, the input length limit of existing LLMs prevents them from generalizing to real-world scenarios where the capability of processing long-form information beyond a fix-sized session is critical, e.g., long horizontal planning. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "To address the length limit issue, the most straightforward method is to simply scale up the input context length. For instance, GPT-3 $[ \\mathrm { B M R } ^ { + } 2 0 ]$ increases the input length from 1k tokens in GPT-2 $[ \\mathrm { R W C ^ { + } } 1 9 ]$ to $2 \\mathrm { k }$ tokens, thereby allowing for better capture of long-range dependencies. However, this approach typically incurs computation-intensive training from scratch and the in-context dense attention is still heavily constrained by the quadratic computation complexity of Transformer self-attention $[ \\mathrm { V S P ^ { + } 1 7 } ]$ . Another recent line of work [BPC20, $\\mathrm { Z G D ^ { + } } 2 0 ]$ instead focuses on developing in-context sparse attention to avoid the quadratic cost of self-attention, which still largely requires training from scratch. In contrast, the prominent work, Memorizing Transformer (MemTRM) [WRHS22], approximates in-context sparse attention via dense attention over both incontext tokens and memorized tokens retrieved from a non-differentiable memory for Transformers. Thus, MemTRM scales up the resulting language model to handle up to 65k tokens and achieves substantial perplexity gains in modeling full-length books or long papers. However, MemTRM faces the memory staleness challenge during training due to its coupled memory design, which uses a single model for encoding memory and fusing memory for language modeling. In other words, as the model parameters are updated, cached older representations in memory may have distributional shifts from those from the latest model, thereby limiting the effectiveness of the memory augmentation. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/519066b13ea667f961d700ed9c3ecfb54d07e061e20fe2698ba0a94c8f74e2a8.jpg",
+        "image_caption": [
+            "Figure 1: Overview of the memory caching and retrieval flow of LONGMEM. The long text sequence is divided into fix-length segments with each previous segment processed through a frozen backbone LLM and the corresponding attention key and value vectors of $m$ -th layer are cached into the memory bank. Given current inputs, the corresponding attention query vectors are used to retrieve the top- $K$ attention key-value pairs from previous segments stored in the memory bank, which will be then fused with local context for language modeling. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            271,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "In this paper, we present a framework for Language Models Augmented with Long-Term Memory (LONGMEM). This framework enables language models to cache lengthy previous context or knowledge into a non-differentiable memory bank, and then utilize them via a decoupled memory module to mitigate the issue of memory staleness. To achieve decoupled memory, we design a novel residual side-network (SideNet) in conjunction with a frozen backbone LLM. Paired attention keys and values of the previous context are extracted using the frozen backbone LLM, which are subsequently stored in the memory bank. In the memory-augmented layer of SideNet, the generated attention query of the current input is used to retrieve cached key-value pairs of previous contexts from the memory, and the corresponding memory augmentations are then fused into adaptable hidden states via a joint-attention mechanism. Furthermore, newly designed cross-network residual connections between the SideNet and the frozen backbone LLM facilitate better knowledge transfer from the pretrained backbone LLM. Through continuous training of the residual SideNet to retrieve and fuse memory augmentations, the pre-trained LLM can be adapted to effectively leverage longcontextual memory for enhanced modeling. The detailed memory cache, retrieval and fusion process is illustrated in Figure 1. ",
+        "bbox": [
+            174,
+            525,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our decoupled memory design offers two key advantages. First, our proposed architecture effectively separates the process of encoding previous inputs into memory and the process of memory retrieval and fusion, thanks to the decoupled frozen backbone LLM and SideNet. In this way, the backbone LLM only works as the long-context knowledge encoder, while the residual SideNet works as the memory retriever and reader, which effectively resolves the issue of memory staleness. Second, directly adapting the entire LLM with memory augmentations is computationally inefficient and also prone to catastrophic forgetting. As the backbone LLM is frozen during the efficient memoryaugmented adaptation stage, LONGMEM can not only tap into the pretrained knowledge but also avoid catastrophic forgetting. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "LONGMEM is capable of taking various types of long-form text and knowledge into the memory bank based on downstream tasks. Here, we consider two representative cases, language modeling with full-length book contexts, and memory-augmented in-context learning with thousands of task-relevant demonstration examples. Specifically, we evaluate the effectiveness of the proposed LONGMEM on various long-text language modeling, and memory-augmented in-context learning for natural language understanding (NLU) tasks. Experimental results demonstrate that our model consistently outperforms the strong baselines in terms of long-text modeling and in-context learning abilities. Our method substantially improves LLM’s long-context language modeling capabilities, with a reduction in perplexity of $1 . 3 8 { \\sim } 1 . 6 2$ over different length splits of Gutenberg-2022 corpus. Notably, our model achieves state-of-the-art performance of $4 0 . 5 \\%$ identification accuracy on ChapterBreak, a challenging long-context modeling benchmark, significantly surpassing existing strong $\\mathbf { X }$ -former baselines. Finally, with 2k demonstration examples in memory, LONGMEM shows pronounced improvements in in-context learning on popular NLU tasks, compared with prominent memoryaugmented and non-memory-augmented baselines. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/d5df7c5e3ae9fa9662e6eb6a4ae1aa993ad2d4d732eab292a975c3119339853b.jpg",
+        "image_caption": [
+            "Figure 2: Overview of LONGMEM architecture. “MemAug” represents Memory-Augmented Layer. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2 Methods ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            507,
+            277,
+            523
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To enable LLMs to harvest relevant information from the past long context in memory, we propose to augment the frozen backbone LLM with a decoupled memory module. To fuse the memory context information, we design a novel lightweight residual SideNet, which can be continually trained in an efficient way. In the following, we first discuss the problem formulation of language modeling with memory augmentations. Then, we formally introduce our efficient residual SideNet for adapting the frozen pretrained LLM to jointly attend over local input context and retrieved memory context. Lastly, we provide our designed processes of how past memory is encoded, stored, recalled and fused for language modeling. ",
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+        "text": "2.1 Language Models Augmented with Long-Term Memory ",
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+        "text": "Here, we focus on the high-level problem setup and defer more component details to later sections. Given its wide adoption for pretrained LLMs, our LONGMEM model is built on the Transformer architecture $[ \\mathrm { V S P ^ { + } \\bar { 1 } 7 } ]$ . For LONGMEM, there are three key components: the frozen backbone LLM, SideNet, and Cache Memory Bank. As most existing pretrained LLMs can only take a fix-sized input, only the input segment of a long sequence (e.g., a book) that can fit in the length limit is denoted as the current input as done for most existing autoregressive language models. Those previous segments that can not fit are denoted as previous inputs, which are used for memory augmentations. To tap into the learned knowledge of the pretrained LLM, both previous and current inputs are encoded using the frozen backbone LLM but different representations are extracted. For previous inputs, the key-value pairs from the Transformer self-attention at $m$ -th layer are stored in Cache Memory Bank, whereas the hidden states from each LLM decoder layer for the current inputs are retained and transferred to SideNet. For each current input token, top relevant key-value vector pairs are retrieved as memory augmentations for language modeling. The SideNet module can be viewed as an efficient adaption model that is trained to fuse the current input context and relevant cached previous contexts in the decoupled memory. ",
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+        "text": "Formally, for a fix-sized input text sequence $\\{ { \\bf x } _ { i } \\} _ { i = 1 } ^ { | x | }$ (the current input), LONGMEM first performs a forward pass using the backbone LLM (indicated in blue in Figure 2) without any gradient calculation. The embedding layer of the backbone LLM first encodes the input $\\{ \\mathbf { x } _ { i } \\} _ { i = 1 } ^ { | x | }$ into embedding space and outputs the initial hidden states, $\\mathbf { H } _ { \\mathrm { L L M } } ^ { 0 } \\in \\mathbb { R } ^ { | x | \\times E }$ , where $E$ is the hidden dimension. Then each successive Transformer decoder layer of the frozen backbone LLM computes the new hidden states using the hidden states from the previous layer, Hl′LLM = fθl′LLM ( $\\mathbf { H } _ { \\mathrm { L L M } } ^ { l ^ { \\prime } } = f _ { \\theta _ { \\mathrm { L L M } } ^ { l ^ { \\prime } } } ( \\mathbf { H } _ { \\mathrm { L L M } } ^ { l ^ { \\prime } - 1 } ) , \\forall l ^ { \\prime } \\in$ $[ 1 , L ^ { \\prime } ]$ and $L ^ { \\prime }$ is the total # layers for the backbone LLM. During the forward pass with the backbone LLM for all previous inputs, the key-value pairs used for self-attention at the $m$ -th Transformer decoder layer are stored in Cached Memory Bank (highlighted in orange in upper-left of Figure 2). These pairs are subsequently recalled as memory augmentations for future inputs. ",
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+        "text": "Cached Memory Bank is a head-wise vector queue $\\mathcal { Z } _ { k } , \\mathcal { Z } _ { v } \\in \\mathbb { R } ^ { H \\times M \\times d }$ , which maintains attention key-value pairs of latest $M$ previous inputs $\\widetilde { \\mathbf { K } } , \\widetilde { \\mathbf { V } } \\in \\mathbb { R } ^ { H \\times | x | \\times d }$ , where $H , d$ denotes the number of attention heads and per-head dimension respectively. After memory retrieval and fusion (§2.3), the memory bank removes the key-value pairs of the oldest sequences and appends the current sequences to the cached vector bank. This update mechanism ensures the language modeling causality at the sequences level and enables the memory bank to consistently maintain records of the most recent previous context for the current inputs. ",
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+        "text": "After the forward pass with the backbone LLM, the SideNet module then takes all current input hidden states from the backbone LLM {Hl′LLM}L′l′=1 and the past key-value pairs in the Cached Memory Bank for computing memory-augmented representations. Specifically, our SideNet of LONGMEM consists of $( L - 1 )$ normal Transformer decoder layers and one special memory-augmented decoder layer. For efficient purposes, we mainly consider the case where #layers $L$ of the SideNet is smaller than that of the backbone LLM, i.e., $L < L ^ { \\prime }$ . Our SideNet encodes $\\mathbf { H } ^ { 0 }$ into memory-augmented contextual representation via $( L - 1 )$ normal Transformer decoder layers and a special memory-augmented layer. ",
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+        "type": "text",
+        "text": "The memory-augmented layer is an extension of the vanilla Transformer decoder layer that takes a memory-augmented input, including both top relevant key-value pairs in memory and the hidden states from the current input. Here, the cached key-value pairs are recalled using a token-based memory retrieval module $( \\ S 2 . 3 )$ . For each current input token, the memory retrieval module $s _ { r t } ( : )$ retrieves top- $K$ relevant key-value pairs in the memory bank $\\{ \\widetilde { \\pmb { k } } _ { i j } , \\widetilde { \\pmb { v } } _ { i j } \\} _ { j = 1 } ^ { K } = s _ { r t } ( \\mathbf { x } _ { i } ) .$ . Then SideNet computes the output using the memory-augmented input, $\\mathbf { H } _ { \\mathrm { S i d e } } ^ { m _ { s } } = f _ { \\theta _ { \\mathrm { M e m } } } ( \\mathbf { H } _ { \\mathrm { S i d e } } ^ { m _ { s } - 1 } , \\{ \\{ \\widetilde { \\mathbf { k } } _ { i j } , \\widetilde { \\mathbf { v } } _ { i j } \\} _ { j = 1 } ^ { K } \\} _ { i = 1 } ^ { | x | } )$ , where is the layer index where we inject the memory-augmentation layer. ",
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+        "type": "text",
+        "text": "Finally, the token probability is computed using the last SideNet hidden states $P ( \\mathbf { x } _ { i } | \\mathbf { x } _ { 1 } , \\cdot \\cdot \\cdot , \\mathbf { x } _ { i - 1 } ) =$ softmax $( W \\mathbf { H } ^ { L } )$ , where $W$ is the frozen output embedding weight shared by both the backbone LLM and SideNet. We perform a memory-augmented adaptation training for LONGMEM to utilize the decoupled memory. Following the generative unsupervised pre-training [RNSS18], the training objective of LONGMEM is the standard left-to-right language modeling objective, which maximizes the likelihood of the next token based on the left context: max $\\begin{array} { r } { \\sum _ { x \\in \\mathcal { D } } \\sum _ { i = 1 } ^ { | \\mathbf { x } | } \\log P ( \\mathbf { x } _ { i } | \\mathbf { x } _ { 1 } , \\cdots , \\mathbf { x } _ { i - 1 } ) } \\end{array}$ , where $x$ is a randomly sampled sentence from the pre-training text corpus $\\mathcal { D }$ . ",
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+        "type": "text",
+        "text": "2.2 Residual SideNet ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "SideNet Architecture and Initialization. Here, we implement SideNet based on Transformer $[ \\mathrm { V S P ^ { + } 1 7 } ]$ . Specifically, the number of decoder layers $L$ in SideNet is equal to the number of layers $L ^ { \\prime }$ in the backbone LLM divided by a reduction factor (a layer reduction factor of 2 is used throughout this work, i.e., $L ^ { \\prime } = 2 L$ ). The weights of each decoder layer in SideNet are initialized from the corresponding pre-trained decoder layer of the backbone LLM at the same depth: $\\Theta _ { \\mathrm { S i d e } } ^ { l } = \\Theta _ { \\mathrm { L L M } } ^ { 2 l }$ . As illustrated in Figure 2, the SideNet model takes the output of backbone LLM’ser and reuses the language modeling head of the backbone LLM, which remains frozen during the continual adaption stage. Throughout the memory-augmented adaptation stage, all other parameters of SideNet are updated based on the training signal. In this way, the lightweight SideNet adaptation achieves fast convergence with knowledge transferred from pre-trained parameters. ",
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+        "type": "text",
+        "text": "Cross-Network Residual Connections. To tap into knowledge from the pretrained backbone LLM, we utilize our proposed cross-network residual connections to fuse representations from the backbone ",
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+        "type": "text",
+        "text": "LLM into SideNet. Specifically, we add the difference between output hidden states at $2 l$ -th and $( 2 l - 2 )$ -th layers of the backbone LLM as the residual connections to the output hidden states at $l$ -th layer of SideNet. Then, the input to the next $( l + 1 )$ -th layer of SideNet is the sum of the original hidden state forwarded through the previous layer $f _ { \\Theta _ { \\mathrm { S i d e } } ^ { l } } ( \\mathbf { H } _ { \\mathrm { S i d e } } ^ { l - 1 } )$ and the cross-network residual connection of the hidden state difference from the backbone LLM ",
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+        "page_idx": 4
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+    {
+        "type": "equation",
+        "img_path": "images/040828e0245aa9e8d567ab7b330a216b431fe020694158056838a8164d07d476.jpg",
+        "text": "$$\n\\mathbf { H } _ { \\mathrm { S i d e } } ^ { l } = f _ { \\ominus _ { \\mathrm { S i d e } } ^ { l } } ( \\mathbf { H } _ { \\mathrm { S i d e } } ^ { l - 1 } ) + ( \\mathbf { H } _ { \\mathrm { L L M } } ^ { 2 l } - \\mathbf { H } _ { \\mathrm { L L M } } ^ { 2 l - 2 } ) , \\forall l \\in [ 1 , L ] ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\mathbf { H } ^ { 0 }$ is the output of embedding layer. It is worth noting that the residual connections after the self-attention and feed-forward network of a decoder layer $[ \\mathrm { V S P ^ { + } 1 7 } ]$ will be performed as normal in $f _ { \\Theta _ { \\mathrm { S i d e } } ^ { l } } ( \\mathbf { H } _ { \\mathrm { S i d e } } ^ { l - 1 } )$ and parallel to the proposed cross-network residual connections. ",
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+    {
+        "type": "text",
+        "text": "2.3 Memory Retrieval and Fusion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The long-term memory capability of LONGMEM is achieved via a memory-augmentation module for retrieval and fusion. ",
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+        "type": "text",
+        "text": "Token-to-Chunk Memory Retrieval. Instead of performing token-to-token retrieval, we focus on token-to-chunk retrieval for acceleration and integrity. A text-chunk refers to an n-gram structure of chunk-size $c s z$ number of contiguous tokens. The memory bank stores cached key-value pairs at the level of token chunks. We divide the memory bank into $M / c s z$ attention key-value paired chunks and use the mean-pooled vector on the chunk-size dimension to get the key vector for retrieval. Then we retrieve the top- $\\left( K / c s z \\right)$ attention key-value chunks w.r.t the dot product between the attention query of the current input token and the mean-pooled attention key of a candidate chunk. Finally, we squeeze the chunk-size dimension for retrieved key-value paired chunks and flatten them into $K$ key-value pairs at token-level  the retrieval index and acceler $\\{ \\widetilde { \\mathbf { K } } _ { j } , \\widetilde { \\mathbf { V } } _ { j } \\} _ { j = 1 } ^ { K }$ . Adopting token-to-chunk retrieval reduces the sizess. Meanwhile, the retrieval accuracy can be further improved, which is also observed in $[ \\mathrm { L G W } ^ { + } 2 3 ]$ and $[ \\mathrm { B M H ^ { + } } 2 1 ]$ . The hyperparameter chunk-size $c s z$ controls the granularity of retrieved contexts, which can be empirically adjusted based on downstream tasks. For instance, in-context learning requires more fine-grained label tokens from demonstration examples cached in memory, where a smaller $c s z$ is helpful. ",
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+    {
+        "type": "text",
+        "text": "Memory Fusion. The memory fusion is performed within a special memory-augmented layer. As the conventional Transformer decoder layer uses the multi-head self-attention $[ \\bar { \\mathrm { V } } \\mathrm { S P ^ { + } 1 7 } ]$ , we follow [WRHS22] to extend it to a joint-attention mechanism and propose a long-term memory fusion process to enable each token to attend on both local contexts and retrieved memory contexts. With the head-wise hidden state output from previous layer $\\mathbf { H } ^ { l - 1 } \\in \\mathbb { R } ^ { | x | \\times d }$ and the corresponding retrieved attention key-value pairs are $\\{ \\widetilde { \\mathbf { K } } _ { i } , \\widetilde { \\mathbf { V } } _ { i } \\} _ { i = 1 } ^ { | x | } \\in \\mathbb { R } ^ { | x | \\times \\mathrm { K } \\times \\mathrm { d } }$ , the output hidden state for the $l$ -th memory-augmented layer $\\mathbf { H } ^ { l }$ is computed as: ",
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+        "type": "equation",
+        "img_path": "images/68b8fc294f00baf996704deea45628f6b7e88f240defb47c1e900ffc3f9c256c.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathbf { A } = \\mathrm { s o f t m a x } ( \\frac { \\mathbf { Q } \\mathbf { K } ^ { T } } { \\sqrt { d } } ) \\mathbf { V } , \\mathbf { M } = \\mathrm { C o n c a t } \\{ \\mathrm { s o f t m a x } ( \\frac { \\mathbf { Q } _ { i } \\widetilde { \\mathbf { K } } _ { i } ^ { T } } { \\sqrt { d } } ) \\widetilde { \\mathbf { V } } _ { i } \\} _ { i = 1 } ^ { | x | } , } \\\\ & { \\mathbf { H } ^ { l } = \\mathrm { s i g m o i d } ( g ) \\cdot \\mathbf { A } + ( 1 - \\mathrm { s i g m o i d } ( g ) ) \\cdot \\mathbf { M } , } \\end{array}\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\mathbf { Q } , \\mathbf { K } , \\mathbf { V } , \\mathbf { A } , \\mathbf { M } \\in \\mathbb { R } ^ { | x | \\times \\mathrm { d } }$ , $\\mathrm { K }$ is the number of retrieved attention key-value pairs in cached memory for each token, and $g$ is a trainable head-wise gating vector. The hidden state output from previous layer $\\mathbf { H } ^ { ( l - 1 ) }$ is linearly projected into attention queries, keys, and values $\\mathbf { Q } , \\mathbf { K } , \\mathbf { V }$ separately via three matrices $W ^ { Q } , W ^ { K } , \\bar { W } ^ { V } \\in \\mathbb { R } ^ { \\mathrm { d } \\times \\mathrm { d } }$ . It is worth noting that the retrieved attention key-value pairs in cached memory are distinct to each token. ",
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+    {
+        "type": "text",
+        "text": "3 Experiments ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We evaluate our proposed LONGMEM model on different tasks that require long-context modeling: a) long-text language modeling and language understanding when loading the past long-context into cached memory; b) infinite-length in-context learning when loading a large number of demonstration examples into cached memory. ",
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+    {
+        "type": "image",
+        "img_path": "images/14da8024824c325b74cd1423e98cb487ba217111ca406b50973d6930b171469c.jpg",
+        "image_caption": [
+            "Figure 3: Batchfying the large text corpora into batches to ensure that each consecutive segments within each document is distributed in consecutive batches. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "3.1 Training Setup ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Batchfying the training corpora. The conventional batchyfing process for large corpora truncates the whole corpora into consecutive fix-length text segments without padding and shuffles all segments to construct mini-batches $[ \\mathrm { R W C ^ { + } } 1 9 ]$ . In contrast, LONGMEM must disable global shuffling and ensure the global causality at the segment level. Firstly, we divide all long documents in training corpora into batch-size number of document groups with equivalent length and then perform a document-level shuffling within each group. Then, we concatenate shuffled documents within one group and truncate them into ordered segments. In order to ensure that two consecutive segments of one long document are distributed in two consecutive input batches after batchfying, we select one segment from batch-size number of document groups with the same inner-group index. Thus a mini-batch with batch-size number of segments are constructed from exactly the batch-size number of document groups. In this way, as the training iteration steps, the cached attention key-value pairs in the memory bank are previous context of current inputs within the same document. The batchfying process is illustrated in Figure 3. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Training Corpus, Backbone LLM and Hyperparameter. We sample a subset of the Pile $[ \\mathrm { G B B ^ { + } } 2 0 ]$ as the training corpus, including BookCorpus2, Books3, OpenWebText2, Stack Exchange, Wikipedia, Gutenberg (PG-19), NIH ExPorter, and Pile-CC datasets. We reproduce GPT- $^ { . 2 ^ { * } }$ (407M-params) as the pre-trained backbone LLM with Alibi [PSL21] position embedding because original GPT$2 \\left[ \\mathrm { R W } \\bar { \\mathrm { C } } ^ { + } 1 9 \\right]$ adopts absolute position embedding, which is found to perform poorly to enable LLM to learn long-distance dependencies $\\mathrm { [ D Y Y ^ { + } 1 9 ] }$ . The backbone LLM holds a $L ^ { \\prime } = 2 4 , H = 1 6 , d = 6 4$ architecture. The SideNet holds a $L = 1 2 , H = 1 6 , d = 6 4$ architecture. The training for memoryaugmented adaptation iterates on 26B tokens, with a global 256 batch-size and 1024 sequence length. The chunk-size $c s z$ is 4 tokens and the memory size $M$ is $6 5 \\mathrm { k }$ key-value pairs of tokens. For each token, we retrieve $K { = } 6 4$ attention key-value pairs for augmentation, which are $K / c s z { = } 1 6$ text chunks. The memory-augmentation layer is the 9-th layer of SideNet. The attention keys and values from 18-th layer of backbone LLM is cached into memory and used for future retrieval. Other training details are presented in Appendix C. ",
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+    {
+        "type": "text",
+        "text": "Memory Retrieval Module. The fixed memory-size of cached memory bank in one GPU is 65536 key-value pairs of tokens. We enable each GPU to construct and update their own memory retrieval module for efficiency. For the implementation of the efficient token-to-chunk retrieval, we use the faiss [JDJ21] toolkit to construct an exact-search index on GPU to store the mean-pooled attention keys of text chunks and perform efficient retrieval. The faiss index maintains a fixed $M / c s z$ keys and provides the efficient exact search w.r.t. inner product. The retrieval takes about 15ms per 1k tokens, which is $55 \\%$ timecost of backbone LLM forwarding pass. We can easily adapt the exact search index to approximate search index to gain more retrieval efficiency. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Baselines. In addition to the baseline of our pre-trained GPT- $^ { 2 ^ { * } }$ variant, we consider Memorizing Transformer (MemTRM) [WRHS22] and TRIME [ZLC22] as two memory-augmented baselines. The MemTRM model can be easily adapted to tune a pre-trained LLM to use external memory. We insert the KNN-augmented layer proposed by MemTRM as the same 18-th layer in the LLM decoder. ",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/767e8ee56de095af38507a92e5f16ee5ec3b11a1b236012a9f8d8e42d178e8ae.jpg",
+        "table_caption": [],
+        "table_footnote": [
+            "Table 1: Dataset Statistics of five splits of PG-22 based on length range and ArXiv. "
+        ],
+        "table_body": "<table><tr><td>Dataset Splits</td><td>S2</td><td></td><td>PG-22 S3</td><td>S4</td><td>S5</td><td>ArXiv</td></tr><tr><td>Len. Range</td><td>5K-10K</td><td>10K-100K</td><td>100K-500K</td><td>500K-1M</td><td>&gt;1M</td><td>&lt;60K</td></tr><tr><td>#Documents</td><td>500</td><td>100</td><td>30</td><td>8</td><td>1</td><td>100</td></tr><tr><td>Avg. #tokens</td><td>7.6K</td><td>47.6K</td><td>140K</td><td>640K</td><td>1.2M</td><td>15.4K</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To adapt TRIME for our experiments, we replace the batchfying function and loss function of training GPT- $^ { 2 ^ { * } }$ with those proposed by TRIME, which enables a memory-augmented adaptation tuning method for LLMs. The two reproduced baselines are trained for the same number of tokens under the same hyperparameter setting as LONGMEM. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.2 Long-Context Language Modeling ",
+        "text_level": 1,
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "The long-context language modeling can potentially benefit from the augmented memory of past longcontexts. The knowledge stored in retrieved attention key-values can provide valuable background and contextual information, helping models perform better in long-context language modeling. For instance, when trying to model a long-text book, acquiring knowledge from previous background and character relationships can be helpful in modeling the subsequent stories. ",
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+    {
+        "type": "text",
+        "text": "Evaluation Setting. We first compare LONGMEM and baselines on three long-context modeling datasets, Project Gutenberg 2020-2022, ArXiv, and ChapterBreak. The majority of included books or papers in these datasets have the length of at least 16k tokens. All listed datasets are evaluated in a zero-shot manner without any task-specific tuning. The detailed evaluation settings on the three datasets are as follows: ",
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+    {
+        "type": "text",
+        "text": "• Project Gutenberg 2020-2022 Language Modeling Dataset. We crawled and cleaned the books published between 2020 and 2022 under Project Gutenberg Library1 to build up a completely new long-text modeling dataset, named PG-22. It is significantly different from our training subset PG-19 in terms of domains and writing styles, because books in PG-19 [RPJL19] are published before 1919. We provide different validation splits of PG-22 based on length range, and the data statistics are presented in Table 1. ",
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+    {
+        "type": "text",
+        "text": "• ArXiv Dataset. The ArXiv dataset includes papers in the areas of Math, Computer Science, and Physics. We select a validation split of ArXiv paper subset in the Pile corpus $[ \\mathrm { G B B ^ { + } } 2 0 ]$ . The ArXiv subset of Pile is excluded from our training and serves an out-of-distribution dataset. We report the token-level language modeling perplexity on the long-context language modeling benchmarks of PG-22 and ArXiv. ",
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+    },
+    {
+        "type": "text",
+        "text": "• ChapterBreak Benchmark. ChapterBreak [STI22] is a challenging suffix identification dataset that requires LLMs to distinguish the beginning of the ground-truth next chapter from a set of hard negative segments sampled from the same book, given the long context of previous chapters. ChapterBreak requires processing global long-context to comprehend and identify the correct suffix. [STI22] demonstrated that even state-of-the-art $\\mathbf { X }$ -formers for long-text processing fail to effectively leverage long-range context to perform well on ChapterBreak. ChapterBreak has two subsets, the PG-19 subset and the Archive of Our Own (AO3) subset. As the PG-19 corpus has been included in the pre-training corpus of LONGMEM, it cannot be further used for evaluation. Thus, we select AO3 subset, which contains fan-fictions extracted from AO3. ChapterBreak provides 8 splits based on the prefix length from $0 . 5 \\mathrm { k }$ to $^ \\mathrm { 8 k }$ tokens to fit the length limit of different models. The splits of 4k, 6k, and $^ \\mathrm { 8 k }$ prefix are selected for evaluation. For LLMs that cannot process over 4k tokens, we abandon the front prefix to fulfill the maximum input length of LLMs. For memory-augmented models (MemTRM and LONGMEM), we load the given $4 \\mathrm { k } / 6 \\mathrm { k } / 8 \\mathrm { k }$ prefix contexts into the cached memory and then do the scoring. we use the perplexity as the scorer for each candidate suffix segment in a zero-shot manner. Then the suffix segment with lower perplexity is selected as the label. The suffix identification accuracy is used as the evaluation metric. ",
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+    {
+        "type": "text",
+        "text": "Results. The main results on evaluated long-context datasets are summarized in Table 2. The proposed LONGMEM model significantly outperforms all considered baselines on long-text language modeling datasets, with improvements of 1.38 to 1.62 perplexity on different length splits of $P G \\mathrm { - } 2 2$ , and 1.0 on ARXIV datasets. Surprisingly, the proposed method achieves the state-of-the-art performance of $40 . 5 \\%$ accuracy on ChapterBreakAO3 suffix identification benchmark and outperforms both the strong long-context transformers and GPT-3 with $3 1 3 \\mathrm { x }$ larger parameters. The substantial improvements on these datasets demonstrate that LONGMEM can comprehend past long-context in cached memory well for predicting future inputs. ",
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+        "type": "table",
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+        "table_caption": [
+            "Table 2: Evaluation results on long-context language modeling datasets. We report token-level perplexity (PPL) (lower the better) on all datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">In-Context Len.</td><td rowspan=\"2\">In-Memory Len.</td><td colspan=\"5\">PG-22</td><td rowspan=\"2\">ArXiv</td></tr><tr><td>5K-10K</td><td>10K-100K</td><td>100K-500K</td><td>500K-1M</td><td>&gt;1M</td></tr><tr><td>GPT-2*</td><td>1k</td><td>N/A</td><td>22.78</td><td>24.39</td><td>24.12</td><td>24.97</td><td>18.07</td><td>11.05</td></tr><tr><td>MemTRM</td><td>1k</td><td>65K</td><td>21.77</td><td>23.56</td><td>23.23</td><td>24.16</td><td>17.39</td><td>10.81</td></tr><tr><td>TRIME</td><td>1k</td><td>65K</td><td>22.21</td><td>23.50</td><td>23.74</td><td>24.32</td><td>17.80</td><td>10.95</td></tr><tr><td>LONGMEM</td><td>1k</td><td>65K</td><td>21.29</td><td>23.01</td><td>22.55</td><td>23.35</td><td>16.71</td><td>10.05</td></tr></table>",
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+    },
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+        "type": "table",
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+        "table_caption": [
+            "Table 3: Zero-shot Suffix Identification Accuracy on AO3 subset of ChapterBreak. Baselines marked with † are directly cited from [STI22]. The MemTRM and LONGMEM loads the given $4 \\mathrm { k } / 6 \\mathrm { k } / 8 \\mathrm { k }$ prefix contexts into cached memory, while the input length to local context is still 1k tokens. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">#Params</td><td rowspan=\"2\">In-Context Len.</td><td rowspan=\"2\">In-Memory Len.</td><td colspan=\"3\">ChapterBreakao3</td></tr><tr><td>ctx-4k</td><td>ctx-6k</td><td>ctx-8k</td></tr><tr><td>GPT-2-XLt [RWC+19]</td><td>1.5B</td><td>1K</td><td>N/A</td><td>24%</td><td>24%</td><td>24%</td></tr><tr><td>GPT-3† [BMR+20]</td><td>175B</td><td>2K</td><td>N/A</td><td>28%</td><td>28%</td><td>28%</td></tr><tr><td>LocalTRM+ [RSVG21]</td><td>516M</td><td>8K</td><td>N/A</td><td>24%</td><td>24%</td><td>24%</td></tr><tr><td>RoutTRM+ [RSVG21]</td><td>490M</td><td>8K</td><td>N/A</td><td>25%</td><td>24%</td><td>24%</td></tr><tr><td>Bigbirdt [ZGD+20]</td><td>128M</td><td>4K</td><td>N/A</td><td>26%</td><td>26%</td><td>26%</td></tr><tr><td>GPT-2*</td><td>407M</td><td>1K</td><td>N/A</td><td>18.4%</td><td>18.4%</td><td>18.4%</td></tr><tr><td>MemTRM</td><td>407M</td><td>1K</td><td>8</td><td>28.3%</td><td>28.7%</td><td>28.7%</td></tr><tr><td>LONGMEM</td><td>558M</td><td>1K</td><td>8</td><td>37.7%</td><td>39.4%</td><td>40.5%</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.3 Memory-Augmented In-Context Learning ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "LLMs have the emerging capability of in-context learning (ICL) via learning knowledge nonparametrically from few-shot demonstration examples in the local context. However, conventional in-context learning is heavily restricted by input context length, rendering it ineffective to absorb supervision from sufficient demonstration examples in the training set. With the proposed unlimited-length memory augmentation, LONGMEM can overcome the limitation of the number of demonstration examples in the local context and even attend on the whole training set by loading it into the cached memory. In this way, LONGMEM generalizes the conventional few-shot in-context learning to memory-augmented in-context learning with thousands of auxiliary demonstration examples. ",
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+    {
+        "type": "text",
+        "text": "Evaluation Setting. Here, we evaluate the in-context learning capability of baselines and the proposed LONGMEM model on five NLU datasets, SST-2 $[ \\mathrm { S P W ^ { + } } 1 \\bar { 3 } ]$ , MPQA [WWC05], MR $[ \\mathrm { A } \\mathrm { \\bar { B } } \\mathrm { K } ^ { + } 0 7 ]$ , Subj [PL04] and SST-5 $[ \\mathrm { S P W ^ { + } } 1 3 ]$ . We evaluate models on two few-shot settings, 4-shot and 20- shot. The 4-shot case is the data-insufficient scenario, while the 20-shot demonstrations can almost fulfill the 1k input length and provide sufficient contextual self-supervisions. We transform the $\\mathbf { k }$ -shot examples to semantically meaningful demonstration examples via fixed text template, i.e., $d _ { i } = \"$ \"Review: $x _ { i }$ Sentiment: $y _ { i } \" , \\forall \\{ ( x _ { i } , y _ { i } ) \\} _ { i = 1 } ^ { k } \\in { \\mathcal { D } } _ { \\operatorname { t r a i n } }$ for sentiment analysis tasks. Additionally, we evaluate the 3-shot ICL on question-answering using SQuAD [RZLL16] under an open-ended generation setting. The details of all prompt templates are presented in Appendix D. Then we concatenate the demonstration examples with newlines to delimit them. The prediction label is directly generated using greedy decoding given the demonstration examples and test cases in context. The prediction accuracy is used as the evaluation metric. We report the mean and standard deviation of 6 runs with different random seeds to assess the randomness in selecting $\\mathbf { k }$ -shot demonstration examples. As mentioned previously, the chunk size controls the granularity of retrieved text chunks. Since the considered NLU datasets require more fine-grained labels from cached memory, we perform a hyperparameter selection on the validation set of SST-2, and the best chunk-size 2 is used to report the results for MemTRM, TRIME and our model. ",
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+        "table_caption": [
+            "Table 5: Accuracy $[ \\% ]$ of 4-shot and 20-shot ICL on 5 NLU tasks (SST-2, mr, subj, SST-5, mpqa). We sample 2000 extra demonstration examples and load them into cached memory. The subscript is the standard deviation across 6 runs. Avg. refers to the average accuracy on 5 datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>In-Context #Demons.</td><td>In-Memory #Demons.</td><td>SST-2 ACC↑</td><td>MR ACC↑</td><td>Subj ACC↑</td><td>SST-5 ACC↑</td><td>MPQA ACC↑</td><td>Avg.</td></tr><tr><td>Majority</td><td>N/A</td><td>N/A</td><td>50.9</td><td>50.0</td><td>50.0</td><td>20.0</td><td>50.0</td><td>44.2</td></tr><tr><td>GPT-2*</td><td>4</td><td>N/A</td><td>68.311.6</td><td>64.712.5</td><td>51.94.2</td><td>31.44.4</td><td>61.511.8</td><td>55.6</td></tr><tr><td>MemTRM</td><td>4</td><td>2000</td><td>67.512.4</td><td>64.611.3</td><td>53.26.0</td><td>29.64.4</td><td>63.012.1</td><td>55.6</td></tr><tr><td>TRIME</td><td>4</td><td>2000</td><td>69.514.5</td><td>63.89.8</td><td>51.51.5</td><td>31.86.7</td><td>63.612.9</td><td>56.0</td></tr><tr><td>LONGMEM</td><td>4</td><td>2000</td><td>71.814.0</td><td>65.111.0</td><td>53.83.7</td><td>36.06.8</td><td>65.412.8</td><td>58.4</td></tr><tr><td>GPT-2*</td><td>20</td><td>N/A</td><td>68.211.5</td><td>63.45.2</td><td>57.610.2</td><td>33.66.0</td><td>70.87.6</td><td>58.7</td></tr><tr><td>MemTRM</td><td>20</td><td>2000</td><td>65.19.6</td><td>65.19.3</td><td>58.210.6</td><td>31.96.3</td><td>72.77.4</td><td>58.6</td></tr><tr><td>TRIME</td><td>20</td><td>2000</td><td>74.313.9</td><td>71.52.5</td><td>57.511.4</td><td>33.04.6</td><td>69.87.8</td><td>61.1</td></tr><tr><td>LONGMEM</td><td>20</td><td>2000</td><td>78.014.1</td><td>78.63.3</td><td>65.68.5</td><td>36.57.5</td><td>74.67.3</td><td>66.7</td></tr></table>",
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+        "text": "Results. The results on in-context learning are summarized in Table 5 and Table 4. LONGMEM achieves remarkable improvements on all NLU tasks under the 20-shot sufficient in-context setting, with $+ 5 . 6$ average scores increase over pretrained GPT- $^ { 2 ^ { * } }$ , MemTRM, and TRIME. ",
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+        "type": "text",
+        "text": "Meanwhile, LONGMEM also brings performance improvements on the 4-shot case. Additionally, LONGMEM improves the in-context learning capabilities of LLMs on open-ended generation tasks, with $+ 4 . 5$ EM score increase on SQuAD. The results indicate that having more demonstration examples loaded in cached memory can provide additional contextual cues to assist in-context learning. LONGMEM can utilize task-relevant knowledge from both local contextual demonstrations and in-memory augmented demonstrations, thereby achieving superior incontext learning capabilities. ",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 4: Exact match (EM) and F1 scores of 3-shot (about 1k tokens) in-context learning on SQuAD. LONGMEM loads 200 extra demonstration examples into cached memory. "
+        ],
+        "table_body": "<table><tr><td>Model</td><td>EM</td><td>F1</td></tr><tr><td>GPT-2*</td><td>22.282.3</td><td>30.782.0</td></tr><tr><td>MemTRM</td><td>22.843.5</td><td>32.652.8</td></tr><tr><td>LONGMEM</td><td>26.772.3</td><td>35.702.0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "3.4 Ablation Studies ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "So far, we empirically verify the effectiveness and superiority of LONGMEM in utilizing cached memory for long-context modeling, long-context understanding, and many-shot in-context learning. Furthermore, we would like to investigate the extend to which the cached memory contributes to the long-context understanding capability of LONGMEM through an ablation study of removing memory augmentations. Besides, since the design of the cached memory bank involves several hyperparameters, such as memory size $m s z$ and chunk-size $c s z$ , we conduct a series of ablation studies to evaluate the effects of those choices. ",
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+        "text": "Effects of Long-Term Memory Augmentation. To evaluate the effects and contributions of memory augmentations, we set the memory-size to 0 and maintain the SideNet parameters during inference. The results of LONGMEM without memory augmentation are shown in Table 6 of Appendix. As expected, without augmented long-term memory, the vanilla model with only backbone LLM and SideNet only gains 59.4 average scores on ICL NLU tasks, which is a 7.3 average accuracy decrease due to the removal of memory augmentation. ",
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+        "type": "text",
+        "text": "Effects of Chunk-Size. As analyzed before, the chunk-size $c s z$ controls the granularity of retrieval and thus it may make a difference to tasks with requirements of fine-grained retrieval. We perform an ablation study on the effects of various chunk-size choices $c s z \\in \\bar { \\{ 2 , 4 , 8 \\} }$ for in-context learning and the results are presented in 4(a). The chunk size of 2 yields the best performance on in-context learning tasks on five NLU datasets, which is consistent with the property of NLU tasks with the requirement of fine-grained retrieval and fusion towards classification label tokens. ",
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+    {
+        "type": "text",
+        "text": "Effects of Memory Size. The memory size (msz) controls the capacity of the memory bank. In general, the memory size should be compatible with the average length of documents or contexts, i.e., a set of books with average 16k tokens should deploy the memory size of 16k tokens in cached memory. The training $m s z$ of 65 tokens is excessive for downstream tasks such as ChapterBreak as the whole prefix context length does not exceed $6 5 \\mathrm { k }$ tokens. Thus, we perform an ablation study on the effects of memory size $m s z \\in \\{ 8 k , 1 6 k , 3 2 k , 6 5 k \\}$ during the inference stage on the PG-22 language modeling datasets and the results are shown in 4(b). To model the books with lengths of $8 \\mathrm { k } { - } 5 0 \\mathrm { k }$ , the smaller memory size $1 6 k$ which is consistent with the average length of target books yields the best perplexity. ",
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+    {
+        "type": "image",
+        "img_path": "images/de4bcd827ba3f0d14048dea90d518ae335fe99f3a1ab8e426f36f59efb7a7395.jpg",
+        "image_caption": [
+            "Figure 4: (a) Accuracy on 5 NLU datasets given different chunk size during inference; (b) ∆Perplexity on 4 splits of PG-22 given different memory size during inference, in which the perplexity when $\\scriptstyle { m s z = 6 5 \\mathrm { k } }$ is used as baseline. "
+        ],
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+    {
+        "type": "text",
+        "text": "4 Related Work ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Large Language Models. Large Language Models, i.e., GPT-3 $[ \\mathrm { B M R } ^ { + } 2 0 ]$ , LLAMA $[ \\mathrm { T M S ^ { + } } 2 3 ]$ , GPT-4 [Ope23], significantly revolutionized NLP research and promoted the state-of-the-art of various language understanding, language generation $[ \\mathrm { W } Z \\mathrm { G } ^ { + } 2 2 ]$ , and even vision-language tasks $[ \\mathrm { W D C ^ { + } } 2 2 ]$ . Additionally, enabled by multi-task instruction tuning $[ \\mathrm { W B } Z ^ { + } 2 1$ , $\\mathrm { O W J ^ { + } } 2 2 ]$ , LLMs exhibit “emergent abilities“ $[ \\dot { \\mathrm { W } } \\mathrm { T B } ^ { + } 2 2 ]$ like mathematical reasoning $[ \\mathrm { W } \\mathrm { W } \\mathrm { S } ^ { + } 2 2 ]$ , code completion $[ \\mathbf { C } \\mathbf { T } \\mathbf { J } ^ { + } 2 1 ]$ , etc. ",
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+    {
+        "type": "text",
+        "text": "$\\mathbf { X }$ -formers. To enable transformers to attend on longer context, many variants of “ $\\mathbf { \\dot { x } }$ -formers“ are proposed. Transformer-XL $\\mathrm { [ D Y Y ^ { + } 1 9 ] }$ proposes to cache attention keys and values of past segment and reuse them in recurrent manner. Recent seminal works of $\\mathbf { X }$ -formers, including LinFormer $[ \\bar { \\mathrm { W } } \\mathrm { L K } ^ { + } 2 0 ]$ , LongFormer [BPC20], Routing Transformer [RSVG21], proposed various sparse attention mechanisms for decreasing $O ( n ^ { 2 } )$ complexity to $O ( n \\log n )$ or even $O ( n )$ . BigBird $[ Z \\mathrm { G D } ^ { + } 2 0 ]$ achieves a $4 \\mathrm { k }$ sequence length via attending on a subset of context tokens. Although these $\\mathbf { X }$ -formers achieve substantial efficiency improvements, such efficiency gains are not remarkable when modeling sequences that spans book-level length. Moreover, the largest sequence length of these methods is still upper-bounded by 16k tokens, making them invalid in modeling long-sequences at the book or wikipedia-page level (i.e., average 70k tokens for full-length books in PG19 dataset [RPJL19]). ",
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+    {
+        "type": "text",
+        "text": "Side-Tuning. The method of Side-Tuning $[ Z \\mathrm { S } Z ^ { + } 2 0$ , SCB22] is a task-specific tuning method for pre-trained models via training a lightweight side-network that is fused with the fixed pre-trained network via summation. Our method inherits the idea of adopting a side-network but distinguishes the side-tuning method in terms of learning objective and cross-network fusion ways. LONGMEM proposes to augment LLMs with decoupled memory to retrain information from long past inputs without any task-specific tuning. The cross-network residual connections introduced here are novel and distinct from the vanilla summation used in Side-Tuning. ",
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+    {
+        "type": "text",
+        "text": "5 Conclusion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we propose to augment LLMs with long-term memory for enabling them to memorize long-form context and gain long-form memory. The designed decoupled memory module can cache attention key and value pairs of past inputs for future retrieval and fusion. A decoupled residual SideNet is introduced as the memory retriever and reader, meanwhile the LLM itself is frozen and works as knowledge and memory encoder. Experiments on various long-contextual language modeling datasets demonstrate the effectiveness of our model over other memory-augmentation baselines. The proposed method can also enable in-context learning of LLMs to overcome the limited number of demonstration examples in context, which is constrained by the contextual length, via caching thousands of auxiliary demonstration examples in memory. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgement ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This work is done during the first author’s internship at Microsoft Research. We would like to thank the anonymous reviewers for the helpful comments. We appreciate Yutao Sun and Yaru Hao for helpful suggestions on implementation and evaluation benchmarks. The first author was partly sponsored by the DARPA PTG program (HR001122C0009). Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of funding agencies. ",
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+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            223,
+            266,
+            238
+        ],
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+    },
+    {
+        "type": "text",
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Side-tuning: a baseline for network adaptation via additive side networks. In Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part III 16, pages 698–714. Springer, 2020. ",
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+    {
+        "type": "table",
+        "img_path": "images/41ee4fba3ae19faab87c83e8b488ff35ae3d64a49f42261ffd95e5e279236023.jpg",
+        "table_caption": [
+            "A Ablation Study on the Effect of Memory Augmentation "
+        ],
+        "table_footnote": [
+            "Table 6: Ablation study results on the effect of memory augmentation of 4-shot and 20-shot ICL on 5 NLU tasks (SST-2, mr, subj, SST-5, mpqa). We sample 2000 extra demonstration examples and load them into cached memory. The subscript is the standard deviation across 6 runs. Avg. refers to the average accuracy on 5 datasets. \"w/o\" is short for \"without\". "
+        ],
+        "table_body": "<table><tr><td>Model</td><td>In-Context #Demons.</td><td>In-Memory #Demons.</td><td>SST-2 ACC↑</td><td>MR ACC↑</td><td>Subj ACC↑</td><td>SST-5 ACC↑</td><td>MPQA ACC↑</td><td>Avg.</td></tr><tr><td>Majority</td><td>N/A</td><td>N/A</td><td>50.9</td><td>50.0</td><td>50.0</td><td>20.0</td><td>50.0</td><td>44.2</td></tr><tr><td>GPT-2*</td><td>4</td><td>N/A</td><td>68.311.6</td><td>64.712.5</td><td>51.94.2</td><td>31.44.4</td><td>61.511.8</td><td>55.6</td></tr><tr><td>MemTRM</td><td>4</td><td>2000</td><td>67.512.4</td><td>64.611.3</td><td>53.26.0</td><td>29.64.4</td><td>63.012.1</td><td>55.6</td></tr><tr><td>TRIME</td><td>4</td><td>2000</td><td>69.514.5</td><td>63.89.8</td><td>51.51.5</td><td>31.86.7</td><td>63.612.9</td><td>56.0</td></tr><tr><td>LONGMEM</td><td>4</td><td>2000</td><td>71.814.0</td><td>65.111.0</td><td>53.83.7</td><td>36.06.8</td><td>65.412.8</td><td>58.4</td></tr><tr><td>w/o Memory</td><td>4</td><td>0</td><td>69.412.4</td><td>64.312.1</td><td>53.47.7</td><td>29.05.2</td><td>62.512.3</td><td>55.7</td></tr><tr><td>GPT-2*</td><td>20</td><td>N/A</td><td>68.211.5</td><td>63.45.2</td><td>57.610.2</td><td>33.66.0</td><td>70.87.6</td><td>58.7</td></tr><tr><td>MemTRM</td><td>20</td><td>2000</td><td>65.19.6</td><td>65.19.3</td><td>58.210.6</td><td>31.96.3</td><td>72.77.4</td><td>58.6</td></tr><tr><td>TRIME</td><td>20</td><td>2000</td><td>74.313.9</td><td>71.52.5</td><td>57.511.4</td><td>33.04.6</td><td>69.87.8</td><td>61.1</td></tr><tr><td>LONGMEM</td><td>20</td><td>2000</td><td>78.014.1</td><td>78.63.3</td><td>65.68.5</td><td>36.57.5</td><td>74.67.3</td><td>66.7</td></tr><tr><td>w/o Memory</td><td>20</td><td>0</td><td>70.012.8</td><td>70.86.2</td><td>52.94.6</td><td>30.96.4</td><td>72.57.5</td><td>59.4</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "B Inference Efficiency and GPU-Memory Efficiency ",
+        "text_level": 1,
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+            676,
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+    {
+        "type": "text",
+        "text": "When the model is required to comprehend long sequences, the proposed method LONGMEM can load the out-of-boundary inputs into the cached memory as previous context. Thus, the memory usage and inference speed can be significantly improved compared with vanilla self-attention-based models. The detailed statistics in terms of the efficiency is presented in Table 7. ",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 7: The superiority of our method over fully dense self-attention (GPT- $2 ^ { * }$ ) in terms of inference speed and GPU-memory utilization. "
+        ],
+        "table_body": "<table><tr><td>Model</td><td>In-Context Len.</td><td>In-Memory Len.</td><td>Inference Speed (tokens/s)↑</td><td>GPU-Memory Usage (MBs)↓</td></tr><tr><td>GPT-2*</td><td>4k</td><td>N/A</td><td>14666</td><td>20671</td></tr><tr><td>LONGMEM</td><td>1k</td><td>3k</td><td>22638</td><td>13335</td></tr><tr><td>GPT-2*</td><td>8k</td><td>N/A</td><td>8417</td><td>54195</td></tr><tr><td>LONGMEM</td><td>1k</td><td>7k</td><td>21343</td><td>13437</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "C Training Details ",
+        "text_level": 1,
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+            174,
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+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "The pre-training of reproduced GPT- $^ { 2 ^ { * } }$ iterates on 117B tokens in total, with 512 batch-size and 1024-token fixed segment-length. The Adam optimizer [KB15] is adopted in memory-augmented adaptation training. The pre-training and adaptation are trained on 16 32GB-Tesla-V100 GPUs. Other detailed training hypperparamters and settings are presented in Table 8. ",
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+    {
+        "type": "table",
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 8: Memory-Augmented Adaptation and Architectural Hyperparameters. "
+        ],
+        "table_body": "<table><tr><td>Hyperparameter</td><td>LONGMEM</td></tr><tr><td colspan=\"2\">Reproduced GPT-2* Backbone LLMHyperparameters</td></tr><tr><td>Parameters</td><td>407M</td></tr><tr><td>Precision</td><td>float16</td></tr><tr><td>Layers Hidden dim.</td><td>24</td></tr><tr><td>Attention heads</td><td>1024</td></tr><tr><td></td><td>16</td></tr><tr><td>Head Dim</td><td>64</td></tr><tr><td>Vocab size</td><td>52k</td></tr><tr><td>Sequence length</td><td>1024</td></tr><tr><td>Position emb.</td><td>Alibi</td></tr><tr><td>Tied embedding</td><td>False</td></tr><tr><td colspan=\"2\">SideNetHyperparameters</td></tr><tr><td>Parameters</td><td>151M</td></tr><tr><td>Precision</td><td>float16</td></tr><tr><td>Layers</td><td>12</td></tr><tr><td>Hidden dim.</td><td>1024</td></tr><tr><td>Attention heads</td><td>16</td></tr><tr><td>Head Dim</td><td>64</td></tr><tr><td>Sequence length</td><td>1024</td></tr><tr><td colspan=\"2\">Memory-Augmented Adaptation Hyperparameters</td></tr><tr><td>Global Batch Size</td><td>256</td></tr><tr><td>Learning rate</td><td>2.0e-4</td></tr><tr><td>Total tokens</td><td>26B</td></tr><tr><td>Warmup tokens</td><td>0</td></tr><tr><td>LR Decay style</td><td>polynomial</td></tr><tr><td>Adam(β1,β2)</td><td>(0.9, 0.98)</td></tr><tr><td>Adam eps</td><td>1e-06</td></tr><tr><td>Weight decay</td><td>0.01</td></tr><tr><td></td><td></td></tr><tr><td>Gradient clipping</td><td>2.0</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "D Prompting Templates ",
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+        "type": "text",
+        "text": "We present all hand-crafted in-context learning prompting templates and labels for 5 NLU datasets and Squad QA dataset in Tabel 9. ",
+        "bbox": [
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+        "table_caption": [],
+        "table_footnote": [
+            "Table 9: The hand-crafted prompts used to query the model predictions on the zero-shot evaluation of 5 NLU datasets and one question-answering dataset Squad. "
+        ],
+        "table_body": "<table><tr><td>Task</td><td>Prompt</td><td>Labels</td></tr><tr><td>SST-2</td><td>Review: [Sentence] Sentiment: [Label]</td><td>{positive, negative}</td></tr><tr><td>MR</td><td>Review: [Sentence] Sentiment: [Label]</td><td>{positive, negative}</td></tr><tr><td>MPQA</td><td>Review: [Sentence] Sentiment: [Label]</td><td>{positive, negative}</td></tr><tr><td>SST-5</td><td>input: [Sentence] type: [Label]</td><td>{terrible,bad,okay,good,great}</td></tr><tr><td>Subj</td><td>input: [Sentence] type: [Label]</td><td>{objective, subjective}</td></tr><tr><td> Squad</td><td colspan=\"2\">Passage: [Passage]\\n Question: [Question] Answer: [Answer]</td></tr></table>",
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parse/dev/DhmYYrH_M3m/DhmYYrH_M3m.md

@@ -0,0 +1,319 @@
+# Trajectory-guided Control Prediction for End-to-end Autonomous Driving: A Simple yet Strong Baseline
+
+Penghao Wu∗† Shanghai AI Laboratory   
+Shanghai Jiao Tong University   
+wupenghaocraig@sjtu.edu.cn
+
+Li Chen∗ Shanghai AI Laboratory lichen@pjlab.org.cn
+
+Xiaosong Jia∗ Shanghai Jiao Tong University Shanghai AI Laboratory jiaxiaosong@sjtu.edu.cn
+
+# Hongyang Li
+
+Junchi Yan† Shanghai Jiao Tong University Shanghai AI Laboratory yanjunchi@sjtu.edu.cn
+
+Yu Qiao Shanghai AI Laboratory qiaoyu@pjlab.org.cn
+
+Shanghai AI Laboratory Shanghai Jiao Tong University lihongyang@pjlab.org.cn
+
+# Abstract
+
+Current end-to-end autonomous driving methods either run a controller based on a planned trajectory or perform control prediction directly, which have spanned two separately studied lines of research. Seeing their potential mutual benefits to each other, this paper takes the initiative to explore the combination of these two well-developed worlds. Specifically, our integrated approach has two branches for trajectory planning and direct control, respectively. The trajectory branch predicts the future trajectory, while the control branch involves a novel multi-step prediction scheme such that the relationship between current actions and future states can be reasoned. The two branches are connected so that the control branch receives corresponding guidance from the trajectory branch at each time step. The outputs from two branches are then fused to achieve complementary advantages. Our results are evaluated in the closed-loop urban driving setting with challenging scenarios using the CARLA simulator. Even with a monocular camera input, the proposed approach ranks first on the official CARLA Leaderboard, outperforming other complex candidates with multiple sensors or fusion mechanisms by a large margin. The source code is publicly available at https://github.com/OpenPerceptionX/TCP.
+
+# 1 Introduction
+
+End-to-end autonomous driving methods, which directly map raw sensor data to a planned trajectory or low-level control actions, show the virtue of simplicity, conceptually avoiding the cascading error of complex modular design and heavy hand-crafted rules. The output prediction of the model for end-toend autonomous driving generally falls into two forms: trajectory/waypoints [48, 4, 11, 46, 15, 29, 10] and direct control actions [17, 39, 18, 42, 12, 60, 9]. However, there is still no clear conclusion as to which of these two forms is better for all circumstances or certain scenarios.
+
+Different from control predictions that could be directly applied to the vehicle, for methods that plan trajectory, additional controllers such as PID controllers are usually needed as a subsequent step to convert the planned trajectory into control signals. One attractive and potential supremacy of trajectory-based prediction is that it actually considers a relatively longer time horizon into the future and could be further combined with other modules (e.g., multi-agent trajectory prediction [59, 10], semantic or occupancy prediction modules [15, 8, 25]) to reduce possible collisions. However, turning the trajectory into control actions so that the vehicle could follow the planned trajectory is not trivial [57]. The industry usually adopts sophisticated control algorithms such as model predictive control to achieve reliable trajectory-following performance [5, 21]. Simple PID controllers may perform worse in situations such as taking a big turn or starting at the red light due to the inertial problem of end-to-end models [29]. For control-based methods, the control signals are directly optimized. Nevertheless, their focus on the current step may cause deferred reactions to avoid potential collisions with other moving agents. The independence between the control predictions of different steps also makes the actions of the vehicle more unstable or discontinuous. Fig. 1 shows two typical cases where two paradigms fail respectively. How to combine these two forms of prediction model as well as their outputs is an interesting yet relatively rarely studied area, which motivates this work.
+
+![](images/dc328a5f264bf26dbd64785b080f1b34da0a839f92d97a09d835508162b051d8.jpg)  
+Figure 1: Typical failure cases of two prediction paradigms. Red dots indicate the trajectory prediction, blue dots are the actual path following the red trajectory with PID controllers, and green dots denote the actual path from control-based method. (a) trajectory-based methods may struggle for big turns. (b) control-based methods may have a reaction latency and suffer from abrupt obstacles due to focusing on current time step only. These observations motivate us to propose a unified framework to combine these two worlds for mutual benefits.
+
+One straightforward (but in fact rarely studied in literature) idea is to train a control prediction model and a trajectory planning model separately, and combine their ultimate outputs directly. It can be viewed as an ensemble of two different models. However, such a naive approach not only doubles the size of the model, but also ignores possible useful correlations between these two forms. To this end, we introduce the TCP (Trajectory-guided Control Prediction) framework, packing these two branches into a unified framework. It can be viewed as a multi-task learning (MTL) [7, 2] framework where a shared backbone extracts common features with decreased computational complexity as well as the increased ability of generalization due to the close relationship between the two tasks [38, 34, 13]. Furthermore, to address the drawbacks of current control prediction methods, we delicately devise a novel multi-step control branch and a trajectory-guided control prediction scheme.
+
+While trajectory planning considers several steps into the future, directly learning the control in a behavior cloning fashion [44, 41, 17, 18, 11] often focuses on the current time step only, given prior on each state-action pair as independent and identical distributed (IID). This assumption is not accurate and may hamper the long-term performance since the driving task is a sequential decisionmaking problem. To alleviate the problem, we propose to predict multi-step control actions into the future. However, the multi-step control process needs interactions with the environment. Thus we formulate a temporal module to learn the forward process and interactions between the ego agent and the environment. A temporal module implemented with GRU [16] progressively deals with the feature representation for each time step, implicitly taking into account the dynamic motion of agents, interaction among them and dynamic environment information such as the changing of traffic lights.
+
+Additionally, to generate accurate control signals in the multi-step prediction scheme, the model should retrieve proper location information from current sensor input for different future time steps. For example, an agent may pay more attention to nearby regions for a few early future time steps and far away regions for the remote ones. Considering that the knowledge has already been partly encoded in the trajectory branch, we adopt the attention mechanism to locate those critical and helpful areas in the long-term trajectory prediction branch, and guide the control prediction branch to pay attention to them at each future step in a corresponding way. As a result, our model is capable of reasoning about how to optimize current control prediction so that the future states are similar to those from the expert when the predicted control actions are applied.
+
+With the predicted trajectory and control signals from two branches, we propose a situation based fusion scheme to adaptively combine these two forms in a self-ensemble way to form the ultimate output according to the experiments results and prior knowledge. It combines the best of these two forms, which further boosts the performance under different scenarios.
+
+TCP has shown superior performance when being validated in the CARLA driving simulator [20]. Our method, which only uses a monocular camera, achieves a 75.137 driving score and ranks 1st on the public CARLA Leaderboard [1], even surpassing prior state-of-the-art methods using multiple cameras and a LiDAR by 13.291 points. The main contributions of this paper include:
+
+• We examine two dominant paradigms for end-to-end autonomous driving: trajectory planning and direct control, and propose to combine them in an integrated learning pipeline. To our knowledge, this is the first time that such two branches are jointly learned and fused for prediction.   
+• A multi-step control prediction branch with a temporal module and trajectory-guided attention is devised to enable temporal reasoning. To combine the best of two branches, we design a situation based scheme to fuse the two outputs.   
+• As a simple yet strong baseline, our method with only a monocular camera as input achieves new state-of-the-art on the CARLA Leaderboard with many competitors using multiple sensors. We conduct thorough ablation studies to verify the effectiveness of our approach.
+
+# 2 Related Work
+
+# 2.1 End-to-end Autonomous Driving
+
+Learning-based end-to-end autonomous driving has emerged as an active research topic in recent years. Studies usually fall into two categories: reinforcement learning (RL) and imitation learning. RL is a promising way to address the problem of being more robust to the distribution shifts of datasets. Liang et al. [39] use DDPG to train a policy which is pre-trained in a supervised way. Kendall et al. [30] train their deep RL algorithm onboard to efficiently learn to drive a real-world vehicle. The perception task is decoupled out of the online RL process in [50, 9, 62]. The model-based method WoR [12] assumes world on rails and uses policy distillation to realize powerful performance.
+
+Imitation learning (IL), especially behavior cloning, collects recorded data for models to mimic with high data efficiency. The expert data typically has two forms, trajectories and control actions. Zeng et al. [58] train a cost volume to generate the planning route, while [49, 8, 25] explicitly design safety and comfort costs based on semantic occupancy maps to select the best one in the expert trajectory sets. Zhang et al. [59] predict trajectories of surrounding vehicles with labeled BEV map. LBC [11] and NEAT [15] decode waypoints from a dense heatmap or offset map. These approaches aforementioned all utilize a relatively dense representation to obtain results which increases model complexity. Transfuser and its variants [46, 29] adopt a simple GRU to auto-regress waypoints. LAV [10] adopts a temporal GRU module to further refine the trajectory. They unanimously achieve impressive performance on the CARLA leaderboard, motivating us to adapt the auto-regression scheme as well in our design. On the other hand, all trajectory-based methods use PID controllers to get the ultimate actions, which may cause inferior effects in complicated scenarios.
+
+Another genre to predict control actions directly is proposed in [44, 40, 3, 54]. CIL [17] adds a measurement encoder and multiple branches for different high level commands with the image encoder. CILRS [18] is proposed afterwards and further introduces a speed prediction head. They stand as classic baselines for IL in the CARLA driving simulator. Diverse optimized approaches are presented based on them, such as multi-modal inputs [22, 53], multi-task learning [56, 37, 24, 27, 31, 26, 63], dataset aggregation [45] and knowledge distillation [61, 60]. However, the compact control-based methods often have higher vehicles collision rates, remaining an interesting domain to explore. Similar work exists in other related domains such as robotic navigation as well. [43] learns a controller after a local trajectory planner to improve the overall navigation behavior.
+
+# 2.2 Multi-task and Ensemble Learning for Autonomous Driving
+
+Multi-task learning is a popular approach to train several related tasks simultaneously to help each other and improve generalization [7, 2]. Combinations of various autonomous driving tasks such as object detection, lane detection, semantic segmentation, depth estimation, etc. have been proved to be capable of achieving incredible performance [38, 14, 47, 34, 52, 13]. MTL is also suitable in the end-to-end problem since it is observed the performance of a direct mapping from an image to control signals is limited. [56] adds a speed prediction task similar to CIL [17] and [63] separates the lateral and longitudinal controls as two tasks. LAV [10] trains an extra scene mapping network, and [24, 27, 29] additionally predict optical flow or dense depth. Our idea of training trajectory and control simultaneously is closely related to FASNet [31]. FASNet predicts future positions of the ego agent as an auxiliary task and adds a kinematic loss considering the relation between control and locations. However, the constrain is based on a constant velocity model which neglects the important throttle and brake, and it does not work at the inference time. On the other hand, our TCP framework has feature interactions at an earlier stage to fully explore their potential mutual benefits.
+
+Ensembles of models have long been utilized to improve the performance in computer vision [19, 33, 35, 51, 55, 45]. Besides the normal combination of models, two classic ensemble learning methods are particularly preferred in the autonomous driving regime. One is the Test-Time Augmentation (TTA), which is of great help to the 3D object detection task with LiDAR [6, 36]. Another one is the fusion of experts [28] where experts are trained on a subset of the input space and a gating network is trained to provide the fusion weights. LSD [42] and MoDE [32] divide a dataset into sub-scenarios to get different sub-policies for end-to-end autonomous driving. These traditional ensemble approaches combine models of the same structure while our approach tries to combine two different representations. Also, the multiple experts design increases the complexity of the training strategy and we seek to have a simpler situation based fusion scheme to boost the performance.
+
+# 3 Trajectory-guided Control Prediction
+
+# 3.1 Problem Setting
+
+Problem formulation. Given the state x comprised of the sensor signal i, the speed of the vehicle $v$ , and the high level navigation information $\mathbf { g }$ including a discrete navigation command and the coordinates of navigation target provided by the global planner, the end-to-end model needs to output control signals a comprised of longitudinal control signals throttle $\in [ 0 , 1 ]$ and brake $\in [ 0 , 1 ]$ , and the lateral control signal steer $\in [ - 1 , 1 ]$ .
+
+Conventional methods tackle this problem with either a trajectory-output or a control-output only model. However, TCP combines both of them as two branches: a trajectory branch which predicts the planned trajectory and a control branch which is guided by the trajectory one and outputs both current and multi-step control signals into the future. Both branches are trained in a supervised manner. Consider an expert which directly outputs the control signals at each step, supervising the predicted trajectory with the ground truth trajectory makes it not strictly satisfy the setting of behavior cloning in imitation learning. The ground truth trajectory indeed involves future expert actions and future states about the environment, so we formulate it as a trajectory planning task with ground truth trajectory as supervision for our trajectory branch. As for the control branch, training a control model which makes current control prediction supervised by the expert control is just behavior cloning in imitation learning, and it can be formulated as:
+
+$$
+\arg \operatorname* { m i n } _ { \theta } \mathbb { E } _ { ( \mathbf { x } , \mathbf { a } ^ { * } ) \sim \mathrm { D } } [ \mathcal { L } ( \mathbf { a } ^ { * } , \pi _ { \theta } ( \mathbf { x } ) ) ] ,
+$$
+
+where $D = \{ ( { \bf x } , { \bf a } ^ { * } ) \}$ is a dataset comprised of state-action pairs collected from the expert. $\pi _ { \theta }$ denotes the policy of the control branch, and $\mathcal { L }$ is the loss measuring how close the action from the expert and the action from our model is. The expert collects the dataset by controlling the vehicle and interacting with the world. Each collected route is a trajectory $\xi = ( { \bf x } _ { 0 } , { \bf a } _ { 0 } ^ { * } , { \bf x } _ { 1 } , { \bf a } _ { 1 } ^ { * } , \cdot \cdot \ , { \bf x } _ { \mathrm { T } } )$ as a sequence of state action pairs $\{ ( \mathbf { x } _ { \mathrm { i } } , \mathbf { a } _ { \mathrm { i } } ^ { * } ) \} _ { \mathrm { i = 0 } } ^ { \mathrm { T } }$ , which is then added into the whole dataset $D$ .
+
+Expert demonstration. Here we choose Roach [60] as the expert. Roach is a simple model trained by RL with privileged information, including roads, lanes, routes, vehicles, pedestrians, traffic lights, and stops, all being rendered into a 2D BEV image. Such a learning-based expert can transfer more information besides the direct supervision signals compared with an expert made by hand-crafted rules. Specifically, we have a feature loss which forces the latent features before the final output head from the student model to be similar to that of the expert. A value loss is also added as an auxiliary task for the student model to predict an expected return.
+
+![](images/fee42be328edcdba4670ef51cd570a25aecc8c5ad8913a4b67b4fa9191c7581f.jpg)  
+Figure 2: Overview of Trajectory-guided Control Prediction (TCP). The encoded features are shared by the trajectory and multi-step control branch. The trajectory branch provides per-step guidance for multi-step control prediction. Outputs from two branches are combined according to our situation based fusion scheme to generate the ultimate control actions.
+
+# 3.2 Architecture Design
+
+Overview. As illustrated in Fig. 2, the whole architecture is comprised of an input encoding stage and two subsequent branches. The input image i goes through a CNN based image encoder, such as ResNet [23], to generate a feature map $\mathbf { F }$ . In the meantime, the navigation information $\mathbf { g }$ is concatenated with the current speed $v$ to form the measurement input m, then an MLP based measurement encoder takes m as its input and outputs the measurement feature $\mathbf { j } _ { \mathrm { { m } } }$ . The encoded features are then shared by two branches for subsequent trajectory and control predictions. Specifically, the control branch is a novel multi-step prediction design with guidance from the trajectory one, which will be illustrated in detail in the following sections. Finally, a situation based fusion scheme is adopted to combine the best of the two output paradigms. We will go over each part in detail below.
+
+# 3.2.1 Trajectory planning branch
+
+Different from control prediction which directly predicts control actions, the trajectory planning branch first generates a planned trajectory comprised of waypoints at $K$ steps for the agent to follow, and then the trajectory is processed by low-level controllers to get the final control actions. With the shared feature from the input encoder, the image feature map $\mathbf { F }$ is average pooled and concatenated with the measurement feature $\mathbf { j } _ { \mathrm { { m } } }$ to form $\mathbf { j } ^ { \mathrm { t r a j } }$ . Inspired by [46], we feed $\mathbf { \hat { j } } ^ { \mathrm { t r a j } }$ into a GRU [16] to auto-regressively obtain future waypoints one by one to form the planned trajectory altogether.
+
+We have two PID controllers for longitudinal and lateral control respectively. With the planned trajectory, we first calculate the vectors between consecutive waypoints. The magnitudes of these vectors represent the desired speed and are sent to the longitudinal controller to generate throttle and brake control actions, and the orientations are sent to the lateral controller to get the steer action.
+
+# 3.2.2 Multi-step control prediction branch
+
+As discussed in Sec. 3.1, for a control model predicting current control actions based on current input only, the supervised training is just behavior cloning, which relies on the independent and identically distributed (IID) assumption. This assumption apparently does not hold because of the distribution shifts in test cases, since the closed-loop tests require sequential decision making where the historical actions will affect the future states and actions. Instead of modeling it as a Markov Decision Process (MDP) and resorting to reinforcement learning, here we devise a simple way to mitigate the problem by predicting multi-step control into the future.
+
+Given the current state $\mathbf { x } _ { \mathrm { t } }$ , now our multi-step control prediction branch outputs multiple actions: $\pi _ { \theta _ { m u l t i } } = ( \mathbf { a } _ { \mathrm { t } } , \mathbf { a } _ { \mathrm { t + 1 } } , \cdot \cdot \cdot , \mathbf { a } _ { \mathrm { t + K } } )$ . However, it is difficult to predict future control actions since we only have sensor inputs at the current time step. Towards this problem, we devise a temporal module to implicitly carry out the changing and interaction process of the environment and our agent. It is supposed to provide mainly dynamic information about the environment and the status of the agent itself, such as the motion of other objects, the changing of traffic lights, and the status of the ego agent. Meanwhile, to improve the ability of incorporating critical static information (e.g., curbs and lanes) and boost the spatial consistency of two branches, we propose to use the trajectory branch to guide the control counterpart to attend to proper regions of the input image at each future time step.
+
+Temporal module. Our temporal module is implemented with a GRU for better consistency with the trajectory branch. At step $t$ $( 0 \leq t \leq K - 1 )$ , the input for the temporal module is the concatenation of the current feature $\mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } }$ (more construction details in the next section) and current predicted action $\mathbf { a } _ { \mathrm { t } }$ , which is a compact representation about the current states of the environment and the agent itself. The temporal module is supposed to reason about the dynamic changing process based on current feature vector and the predicted action. Then the updated hidden state $\bar { \mathbf { h } } _ { \mathrm { t + 1 } } ^ { \mathrm { c t l } }$ will contain dynamic information about the environment and the updated status of the agent at time step $t + 1$ . To some extent, the temporal module acts as a coarse simulator with the whole environment and the agent being abstracted as a feature vector. It then simulates the interaction between the environment and the agent based on current prediction of actions.
+
+Trajectory-guided attention. With the sensor input at current step only, it is hard to pick out desirable regions where the model should focus on at future steps. However, the location of the ego agent contains important cues about how to find those regions containing critical static information for control prediction at each step.
+
+Therefore, we seek help from the trajectory planning branch to get information about the possible location of our agent at that corresponding step. As shown in Fig. 3, TCP implements this by learning an attention map to extract important information from the encoded feature map. The interaction between two branches enhances the consistency of these two strongly related output paradigms and further elaborates the multi-task spirit. Specifically, with the 2D feature map extracted by the image encoder $\mathbf { F }$ at time step $t \left( 1 \leq t \leq K \right)$ , we calculate an attention map $\mathbf { w } _ { \mathrm { t } } \in \mathbb { R } ^ { 1 \times \mathrm { H } \times \mathrm { W } }$ using the corresponding hidden states from the control branch and the trajectory branch:
+
+![](images/25b080d38b97bd1dfc38f40927262d28a3b1c74c42cf2a7dda2e2fb99ef54e45.jpg)  
+Figure 3: Detailed trajectory guiding process. For predictions at time step $t$ , the hidden states from the waypoint GRU and the temporal module are combined to learn an attention weight map to re-aggregate the 2D image feature map for control prediction.
+
+$$
+\mathbf { w } _ { \mathrm { t } } = \mathrm { M L P } ( \mathrm { C o n c a t } [ \mathbf { h } _ { \mathrm { t } } ^ { \mathrm { t r a j } } , \mathbf { h } _ { \mathrm { t } } ^ { \mathrm { c t l } } ] ) .
+$$
+
+The attention map $\mathbf { w } _ { \mathrm { t } } \in \mathbb { R } ^ { 1 \times \mathrm { H } \times \mathrm { W } }$ is adopted to aggregate the feature map $\mathbf { F }$ for this step. We then combine the attended feature map with $\mathbf { h } _ { \mathrm { t } } ^ { \mathrm { c t l } }$ to form the informative representation feature $\mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } }$ containing both static and dynamic information about the environment and the ego agent. The process can be described as follows:
+
+$$
+\mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } } = \mathrm { M L P } ( \mathrm { C o n c a t } [ \mathrm { S u m } ( \mathrm { S o f t m a x } ( \mathbf { w } _ { \mathrm { t } } ) \odot \mathbf { F } ) , \mathbf { h } _ { \mathrm { t } } ^ { \mathrm { c t l } } ] ) .
+$$
+
+The informative representation feature $\mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } }$ is fed into a policy head which is shared among all time steps to predict the corresponding control action $\mathbf { a } _ { \mathrm { t } }$ . Note that for the initial step, we only use the measurement feature to calculate the initial attention map and combine the attended image feature with the measurement feature to form the initial feature vector $\mathbf { j } _ { 0 } ^ { \mathrm { c t l } }$ . To guarantee the feature $\mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } }$ does describe the state at that step and contain the important information for control prediction, we add a feature loss at each step to make $\mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } }$ close to the feature of the expert as well.
+
+To this end, our TCP framework endows the model with the reasoning ability along a short time horizon. It emphasizes how to make current control prediction close to the one from the expert. Furthermore, it takes into account what current control prediction can make the environment states and status of ego agent in future time steps similar to the ones from the expert.
+
+# 3.3 Loss Design
+
+Our loss contains trajectory planning loss $\mathcal { L } _ { t r a j }$ , control prediction $\mathcal { L } _ { c t l }$ , and auxiliary loss $\mathcal { L } _ { a u x }$
+
+For the trajectory planning branch, the loss $\mathcal { L } _ { t r a j }$ can be expressed as:
+
+$$
+\mathcal { L } _ { t r a j } = \sum _ { t = 1 } ^ { K } \| \mathbf { w p } _ { \mathrm { t } } - \mathbf { w } \mathbf { \hat { p } } _ { \mathrm { t } } \| _ { 1 } + \lambda _ { \mathrm { F } } \cdot \mathcal { L } _ { \mathrm { F } } \left( \mathbf { j } _ { 0 } ^ { \mathrm { t r a j } } , \mathbf { j } _ { 0 } ^ { \mathrm { E x p e r t } } \right) ,
+$$
+
+where $\mathbf { w p } _ { \mathrm { t } } , \mathbf { w } \mathbf { \hat { p } _ { \mathrm { t } } }$ are the predicted and ground truth waypoint at the $t ^ { t h }$ step respectively. $\mathcal { L } _ { F }$ indicates the feature loss measuring the $L _ { 2 }$ distance between $\mathbf { j } _ { 0 } ^ { \mathrm { t r a j } }$ j and the feature jEx0 pert from the expert at the current step as an additional supervision signal [60]. $\lambda _ { F }$ is a tunable loss weight.
+
+For the control prediction branch, we model the action as a beta distribution. The loss $\mathcal { L } _ { c t l }$ is:
+
+$$
+\begin{array} { r l r } {  { \mathcal { L } _ { c t l } = \mathbf { K } \mathbf { L } ( \mathrm { B e t a } ( \mathbf { a } _ { 0 } ) | | \mathrm { B e t a } ( \hat { \mathbf { a } } _ { 0 } ) ) + \frac { 1 } { K } \sum _ { t = 1 } ^ { K } \mathbf { K } \mathbf { L } ( \mathrm { B e t a } ( \mathbf { a } _ { \mathrm { t } } ) | | \mathrm { B e t a } ( \hat { \mathbf { a } } _ { \mathrm { t } } ) ) } } \\ & { } & { +  \lambda _ { F } \cdot \mathcal { L } _ { F } ( \mathbf { j } _ { 0 } ^ { \mathrm { c t l } } , \mathbf { j } _ { 0 } ^ { \mathrm { E x p e r t } } ) + \frac { 1 } { K } \sum _ { t = 1 } ^ { K } \mathcal { L } _ { F } ( \mathbf { j } _ { \mathrm { t } } ^ { \mathrm { c t l } } , \mathbf { j } _ { \mathrm { t } } ^ { \mathrm { E x p e r t } } ) , } \end{array}
+$$
+
+where $\mathrm { B e t a } ( \mathbf { a } )$ denotes the beta distribution represented by the corresponding predicted distribution parameters and KL-divergence is used to measure the similarity between the predicted control distribution and the one from expert, i.e., Beta(aˆ). Feature loss is applied here as well. Note that all losses for future time steps $( t \geq 1 )$ ) are averaged and then added to the loss for the current time step $( t = 0$ ), since the action executed immediately should be our key target to optimize.
+
+To help the agent better estimate its current state, we add a speed prediction head to predict current speed $s$ from the image feature and a value prediction head to predict the expected return estimated by the expert, similarly as in [60]. We take the $L _ { 1 }$ loss for the speed prediction and $L _ { 2 }$ loss for the value prediction, denoting their weighted sum as $\mathcal { L } _ { a u x }$ .
+
+The overall loss is as follows, as weighted by $\lambda _ { t r a j } , \lambda _ { c t l } , \lambda _ { a u x }$ :
+
+$$
+\mathcal { L } = \lambda _ { t r a j } \cdot \mathcal { L } _ { t r a j } + \lambda _ { c t l } \cdot \mathcal { L } _ { c t l } + \lambda _ { a u x } \cdot \mathcal { L } _ { a u x } .
+$$
+
+# 3.4 Output Fusion
+
+We have two forms of output representations from our TCP framework: the planned trajectory and the predicted control. To further combine their advantages, we devise a situation-based fusion strategy as depicted in Algorithm 1. Specifically, denote $\alpha$ as a combination weight whose value is between 0 to 0.5, in a certain situation where one representation is more suitable according to our prior belief, we combine the results from trajectory and control predictions by taking average with weight $\alpha$ so that the more suitable one takes up more weight $( 1 - \alpha )$ . Note that the combination weight $\alpha$ indeed does not need to be
+
+<table><tr><td>Algorithm1:Situation based fusion scheme to com- bine the two output paradigms</td></tr><tr><td>Input: sensory input i, speed of the ego vehicle v, high level navigation information g.</td></tr><tr><td>Hyper parameters:combination weight α E [0,0.5] Output: final control signals a</td></tr><tr><td>{wpt}=o,actl ← TCP(i,u, g) atraj ←Low-level Controller ({wpt}ε=0) a</td></tr><tr><td>Getcurrent situation if situationis trajectory specialized then</td></tr><tr><td>a←α×act1+(1-α)×atraj</td></tr><tr><td></td></tr><tr><td>else a←α×atraj+(1-α) ×actl</td></tr></table>
+
+a constant or symmetric, which means we can set it to different values under different situations or different for specific control signals. In our experiment, we choose the situation according to whether the ego vehicle is turning, implying that if it is turning, the situation is control specialized otherwise trajectory specialized.
+
+# 4 Experiments
+
+# 4.1 Experimental Setup
+
+Task & Evaluation metrics. Our method is validated and tested in the CARLA driving simulator [20]. Given a route defined by a sequence of sparse navigation points together with high level commands (straight, turn left/right, lane changing, and lane following), the closed-loop driving task requires the autonomous agent to drive towards the destination point. It is designed to simulate realistic traffic situations and includes different challenging scenarios such as obstacle avoidance, crossing an unsignalized intersection, and sudden control loss. There are three major metrics: Driving Score, Route Completion, and Infraction Score. Route Completion is the percentage of the route completed by the autonomous agent. Infraction Score measures the number of infractions made along the route, with pedestrians, vehicles, road layouts, red lights, and etc. Driving Score is the main metric which is the product of Route Completion and Infraction Score.
+
+Table 1: Evaluation on the public CARLA Leaderboard [1] (accessed in May 2022). Our method TCP and TCP-Ens achieve a driving score of 69.714 and 75.137 respectively with only a monocular camera. More detailed infraction statistics can be found in the Supplementary.   
+
+<table><tr><td rowspan="2">Rank</td><td rowspan="2">Method</td><td colspan="2">Sensor Inputs</td><td colspan="3">Key Metrics ↑</td></tr><tr><td>#Cameras</td><td>LiDAR</td><td>Driving Score</td><td>Route Completion</td><td>Infraction Score</td></tr><tr><td>1</td><td>TCP-Ens (ours)</td><td>1</td><td>X</td><td>75.137</td><td>85.629</td><td>0.873</td></tr><tr><td>1</td><td>TCP (ours)</td><td>1</td><td>X</td><td>69.714</td><td>82.962</td><td>0.851</td></tr><tr><td>1</td><td>TCP-SB (ours)</td><td>1</td><td>X</td><td>68.695</td><td>82.957</td><td>0.833</td></tr><tr><td>2</td><td>LAV [10]</td><td>4</td><td>√</td><td>61.846</td><td>94.459</td><td>0.640</td></tr><tr><td>3</td><td>Transfuser</td><td>3</td><td>√</td><td>61.181</td><td>86.694</td><td>0.714</td></tr><tr><td>4</td><td>Latent Transfuser</td><td>3</td><td></td><td>45.029</td><td>75.366</td><td>0.618</td></tr><tr><td>5</td><td>GRIAD [9]</td><td>3</td><td>xx/</td><td>36.787</td><td>61.855</td><td>0.597</td></tr><tr><td>6</td><td>Transfuser+ [29]</td><td>4</td><td></td><td>34.577</td><td>69.841</td><td>0.562</td></tr><tr><td>7</td><td>WoR[12]</td><td>4</td><td>X</td><td>31.370</td><td>57.647</td><td>0.557</td></tr><tr><td>8</td><td>MaRLn [50]</td><td>1</td><td>X</td><td>24.980</td><td>46.968</td><td>0.518</td></tr><tr><td>9</td><td>NEAT[15]</td><td>3</td><td>X</td><td>21.832</td><td>41.707</td><td>0.650</td></tr></table>
+
+Table 2: Comparison between the control and trajectory only model in terms of infractions frequency. TurnRatio means the corresponding ratio of happening during turning.   
+
+<table><tr><td rowspan="2">Model</td><td rowspan="2">Driving Score</td><td colspan="2">Collisions vehicles</td><td colspan="2">Collisions layout</td><td colspan="2">Off-road infractions</td><td colspan="2">Agent blocked</td></tr><tr><td>#/km↓</td><td>TurnRatio</td><td>#/km↓</td><td>TurnRatio</td><td>#/km↓</td><td>TurnRatio</td><td>#/km↓</td><td>TurnRatio</td></tr><tr><td>Control-Only</td><td>32.45±2.23</td><td>1.25</td><td>50.90%</td><td>0.23</td><td>10.00%</td><td>0.59</td><td>46.15%</td><td>0.41</td><td>50.00%</td></tr><tr><td>Trajectory-Only</td><td>28.29±3.03</td><td>0.85</td><td>38.70%</td><td>0.77</td><td>64.20%</td><td>0.74</td><td>62.90%</td><td>0.77</td><td>64.20%</td></tr></table>
+
+Dataset. We use randomly generated routes under random weather conditions to collect 420K data in the 8 public towns offered by the CARLA simulator. Similar to [10], we train TCP on 189K of data in 4 out of 8 towns (Town01, Town03, Town04, and Town06) for ablations and train with all 420K data for our online leaderboard submission.
+
+# 4.2 State-of-the-art Comparison
+
+Table 1 shows the result of the comparison between our method and the top 8 entries on the public CARLA Leaderboard [1]. We report the results of TCP and two variants. TCP-SB replaces shared encoders of TCP with two separate ones for two branches, and TCP-Ens is the ensemble of TCP and TCP-SB. Our method TCP-Ens ranks first on the leaderboard with a 75.137 driving score and highest infraction score, and TCP alone also surpasses prior methods. Note that our method only uses a monocular camera while the top 2-4 methods all use multiple cameras and a LiDAR. Our driving score is 50.157 higher than the second-best monocular camera method, MaRLn [50]. Our route completion is slightly inferior to the LiDAR candidates - one reason is that methods using LiDAR may have a better object detection ability. Based on the detection results, they usually adopt a crawling strategy, indicating that the vehicle would move slowly when it has stopped for a long time and there are no obstacles ahead. As described in [29], this could alleviate ego vehicle’s blocking problems to boost the route completion performance.
+
+![](images/53625470e10efe8de104f7eaed01f6b709a62241dccde0c71d9743b472e0849d.jpg)  
+Figure 4: The trajectory-guided attention maps in two cases. In each case (row), from the left to right we show that the input image with the predicted trajectory (the first waypoint is projected out of the image), the predicted trajectory in the top-down view, the attention map $\mathbf { w } _ { 1 }$ , the attention map $\mathbf { w } _ { 3 }$ .
+
+Table 3: Ablative study on the effectiveness of different components design of our model.   
+
+<table><tr><td>Exp.</td><td>Driving Score</td><td>Route Completion</td><td>Infraction Score</td></tr><tr><td>Control</td><td>32.45±2.23</td><td>76.54±3.22</td><td>0.45±0.03</td></tr><tr><td>+ traj-task</td><td>34.98±1.96</td><td>81.32±5.50</td><td>0.49±0.05</td></tr><tr><td>+ temporal</td><td>42.87±4.77</td><td>87.51±3.63</td><td>0.49±0.07</td></tr><tr><td>+ traj-attn</td><td>46.08±3.47</td><td>84.95±1.84</td><td>0.56±0.03</td></tr><tr><td>+ fusion</td><td>57.01±1.88</td><td>85.27±1.20</td><td>0.67±0.01</td></tr></table>
+
+Table 4: Comparison between MTL and ensemble methods ( $\alpha$ is 0.3 for all experiments).   
+
+<table><tr><td>Exp.</td><td>Driving Score</td><td>#Param.</td><td>FLOPs</td><td>FPS</td></tr><tr><td>Ensemble</td><td>45.03±1.28</td><td>46.81M</td><td>17.07G</td><td>69.47</td></tr><tr><td>MTL</td><td>48.27±0.58</td><td>23.58M</td><td>8.54G</td><td>133.30</td></tr><tr><td>TCP-SB</td><td>52.46±4.66</td><td>47.26M</td><td>17.07G</td><td>69.35</td></tr><tr><td>TCP</td><td>57.01±1.88</td><td>25.77M</td><td>8.54G</td><td>125.71</td></tr><tr><td>TCP-Ens</td><td>59.09±3.66</td><td>73.03M</td><td>25.61G</td><td>44.70</td></tr></table>
+
+# 4.3 Control vs. Trajectory
+
+In this section, we conduct quantitative experiments to compare the Control-Only model and the Trajectory-Only model to demonstrate their advantages and disadvantages. For both models, we use the same setting except for the output head and its corresponding loss. We use a ResNet-34 to encode visual inputs and a measurement module to encode the navigation information. Similar to [60], we add speed and value heads as auxiliary tasks to help the model better encode the environment. For Control-Only, we predict the control distribution based on the concatenated latent feature from the two encoders. As for Trajectory-Only, we feed the feature to a GRU decoder to generate waypoints. As shown in Table 2, though Trajectory-Only collides with vehicles less frequently than Control-Only, it has more layout collisions, off-road infractions, and agent blocks. We also count the ratio of each kind of infraction that occurs during turning. It can be observed that for Trajectory-Only, a large portion of such infractions happen when the ego agent is turning compared to Control-Only. This has verified that Trajectory-Only performs worse when the agent is turning, which is probably caused by the unsatisfactory trajectory following performance of simple PID controllers as discussed in Sec. 1. As for the fact that Control-Only has a higher vehicle-collision rate, it is because the model focuses on the current time step and the reaction to potential collisions tends to be late, as depicted in Sec. 1 as well. The results above further validate the necessity of combining the two output paradigms.
+
+# 4.4 Ablative Study and Visualization
+
+Component analysis. We first validate the effectiveness of the trajectory-guided multi-step control prediction design, as shown in Table 3. We only employ the control branch output except for the last complete one when fusion is applied for these ablations. Adding a trajectory branch as an auxiliary task improves the performance by 2.5 points. The multi-step predictions with our temporal module greatly help with 7.9 points gain, and adding the trajectory-guided attention further acquires an improvement of 3.2 points. Finally, applying our situation based fusion scheme $\alpha$ is set to 0.3) significantly boosts the infraction score, leading the overall driving score to 57.
+
+Multi-task vs. Ensemble. The comparison regarding their performances and computational complexity is given in Table 4. Ensemble denotes directly combining the outputs of Control-Only and Trajectory-Only with our situation based fusion scheme. MTL represents the model with a shared CNN backbone and measurement encoders followed by a trajectory branch and a control branch, but the control branch predicts current step prediction only and there are no interactions between the two branches. We conclude that directly combining two models with our fusion scheme greatly improves the performance, and using an MTL approach works better than ensemble but with a much smaller model size and GFLOPs. A conventional ensemble approach to combine results from TCP and TCP-SB as TCP-Ens brings further performance gain at the cost of computational complexity.
+
+Situation based fusion weight. We investigate the choice of the combination weight $\alpha$ in the situation based fusion scheme and show the box plot of the driving scores in the figure to the right. Besides $\alpha \in [ 0 , 0 . 5 ]$ , we additionally test 0.7 and 1, meaning that two results are conversely mixed with our specialization definition. We see that only using the control from the specialized branch $\alpha = 0$ performs poorly while directly taking the average or fusing conversely still has comparable results. One reason is that the situation criterion used here is whether the vehicle is turning, making most cases trajectory specialized, and the stronger control branch is not utilized enough if $\alpha$ is small. Note that the situation based fusion scheme is general and flexible, and the criterion or $\alpha$ value used here is relatively coarse.
+
+![](images/ae0af0918b5103ea2f1a91df9591e840d500bd976dd0ad542cf879b0a8494b56.jpg)  
+Figure 5: Box plot of the driving score with different $\alpha$ values (3 trials for each $\alpha$ ).
+
+Visualization. Fig. 4 visualizes the trajectory-guided attention maps. The trajectory branch provides location-related information to guide the control branch to focus on important regions which are useful for future control prediction. See more qualitative results in the Supplementary.
+
+# 5 Conclusion
+
+In this work, we study two learning and prediction paradigms based on trajectory and direct control, respectively, for end-to-end autonomous driving. We propose a unified framework comprised of a trajectory branch and a novel multi-step control branch with interactions in between. We design a situation based fusion scheme to combine the results from two branches. Our method with only a monocular camera has achieved state-of-the-art performance on the CARLA Leaderboard.
+
+# Acknowledgments
+
+This work was partly supported by National Key Research and Development Program of China (2020AAA0107600), NSFC (62206172, 61972250), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and Shanghai Committee of Science and Technology (21DZ1100100, 22511105100).
+
+# References
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+
+# Checklist
+
+The checklist follows the references. Please read the checklist guidelines carefully for information on how to answer these questions. For each question, change the default [TODO] to [Yes] , [No] , or [N/A] . You are strongly encouraged to include a justification to your answer, either by referencing the appropriate section of your paper or providing a brief inline description. For example:
+
+• Did you include the license to the code and datasets? [Yes] See Section XX.   
+• Did you include the license to the code and datasets? [No] The code and the data are proprietary.   
+• Did you include the license to the code and datasets? [N/A]
+
+Please do not modify the questions and only use the provided macros for your answers. Note that the Checklist section does not count towards the page limit. In your paper, please delete this instructions block and only keep the Checklist section heading above along with the questions/answers below.
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes] See the Supplementary.   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See the Supplementary.   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A]
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] The zip file of source code and the URL of data are in the Supplementary.   
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Sec. 4.1 and the Supplementary.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] See Sec. 4.   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See the Supplementary.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] We use the CARLA simulator and pretrained ResNet model.   
+(b) Did you mention the license of the assets? [Yes] See the Supplementary.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] The zip file of source code and the URL of data are in the Supplementary.   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No] CARLA is a public simulator.   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No] Data in the public simulator does not have these issues.
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/dev/DhmYYrH_M3m/DhmYYrH_M3m_content_list.json

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+        "type": "text",
+        "text": "Trajectory-guided Control Prediction for End-to-end Autonomous Driving: A Simple yet Strong Baseline ",
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Penghao Wu∗† Shanghai AI Laboratory   \nShanghai Jiao Tong University   \nwupenghaocraig@sjtu.edu.cn ",
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+    {
+        "type": "text",
+        "text": "Li Chen∗ Shanghai AI Laboratory lichen@pjlab.org.cn ",
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+    {
+        "type": "text",
+        "text": "Xiaosong Jia∗ Shanghai Jiao Tong University Shanghai AI Laboratory jiaxiaosong@sjtu.edu.cn ",
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+        "text": "Hongyang Li ",
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Junchi Yan† Shanghai Jiao Tong University Shanghai AI Laboratory yanjunchi@sjtu.edu.cn ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yu Qiao Shanghai AI Laboratory qiaoyu@pjlab.org.cn ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Shanghai AI Laboratory Shanghai Jiao Tong University lihongyang@pjlab.org.cn ",
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+    {
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+        "text": "Abstract ",
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+        "text": "Current end-to-end autonomous driving methods either run a controller based on a planned trajectory or perform control prediction directly, which have spanned two separately studied lines of research. Seeing their potential mutual benefits to each other, this paper takes the initiative to explore the combination of these two well-developed worlds. Specifically, our integrated approach has two branches for trajectory planning and direct control, respectively. The trajectory branch predicts the future trajectory, while the control branch involves a novel multi-step prediction scheme such that the relationship between current actions and future states can be reasoned. The two branches are connected so that the control branch receives corresponding guidance from the trajectory branch at each time step. The outputs from two branches are then fused to achieve complementary advantages. Our results are evaluated in the closed-loop urban driving setting with challenging scenarios using the CARLA simulator. Even with a monocular camera input, the proposed approach ranks first on the official CARLA Leaderboard, outperforming other complex candidates with multiple sensors or fusion mechanisms by a large margin. The source code is publicly available at https://github.com/OpenPerceptionX/TCP. ",
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+        "text": "1 Introduction ",
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+    },
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+        "text": "End-to-end autonomous driving methods, which directly map raw sensor data to a planned trajectory or low-level control actions, show the virtue of simplicity, conceptually avoiding the cascading error of complex modular design and heavy hand-crafted rules. The output prediction of the model for end-toend autonomous driving generally falls into two forms: trajectory/waypoints [48, 4, 11, 46, 15, 29, 10] and direct control actions [17, 39, 18, 42, 12, 60, 9]. However, there is still no clear conclusion as to which of these two forms is better for all circumstances or certain scenarios. ",
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+    {
+        "type": "text",
+        "text": "Different from control predictions that could be directly applied to the vehicle, for methods that plan trajectory, additional controllers such as PID controllers are usually needed as a subsequent step to convert the planned trajectory into control signals. One attractive and potential supremacy of trajectory-based prediction is that it actually considers a relatively longer time horizon into the future and could be further combined with other modules (e.g., multi-agent trajectory prediction [59, 10], semantic or occupancy prediction modules [15, 8, 25]) to reduce possible collisions. However, turning the trajectory into control actions so that the vehicle could follow the planned trajectory is not trivial [57]. The industry usually adopts sophisticated control algorithms such as model predictive control to achieve reliable trajectory-following performance [5, 21]. Simple PID controllers may perform worse in situations such as taking a big turn or starting at the red light due to the inertial problem of end-to-end models [29]. For control-based methods, the control signals are directly optimized. Nevertheless, their focus on the current step may cause deferred reactions to avoid potential collisions with other moving agents. The independence between the control predictions of different steps also makes the actions of the vehicle more unstable or discontinuous. Fig. 1 shows two typical cases where two paradigms fail respectively. How to combine these two forms of prediction model as well as their outputs is an interesting yet relatively rarely studied area, which motivates this work. ",
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+        "img_path": "images/dc328a5f264bf26dbd64785b080f1b34da0a839f92d97a09d835508162b051d8.jpg",
+        "image_caption": [
+            "Figure 1: Typical failure cases of two prediction paradigms. Red dots indicate the trajectory prediction, blue dots are the actual path following the red trajectory with PID controllers, and green dots denote the actual path from control-based method. (a) trajectory-based methods may struggle for big turns. (b) control-based methods may have a reaction latency and suffer from abrupt obstacles due to focusing on current time step only. These observations motivate us to propose a unified framework to combine these two worlds for mutual benefits. "
+        ],
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+        "type": "text",
+        "text": "One straightforward (but in fact rarely studied in literature) idea is to train a control prediction model and a trajectory planning model separately, and combine their ultimate outputs directly. It can be viewed as an ensemble of two different models. However, such a naive approach not only doubles the size of the model, but also ignores possible useful correlations between these two forms. To this end, we introduce the TCP (Trajectory-guided Control Prediction) framework, packing these two branches into a unified framework. It can be viewed as a multi-task learning (MTL) [7, 2] framework where a shared backbone extracts common features with decreased computational complexity as well as the increased ability of generalization due to the close relationship between the two tasks [38, 34, 13]. Furthermore, to address the drawbacks of current control prediction methods, we delicately devise a novel multi-step control branch and a trajectory-guided control prediction scheme. ",
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+        "type": "text",
+        "text": "While trajectory planning considers several steps into the future, directly learning the control in a behavior cloning fashion [44, 41, 17, 18, 11] often focuses on the current time step only, given prior on each state-action pair as independent and identical distributed (IID). This assumption is not accurate and may hamper the long-term performance since the driving task is a sequential decisionmaking problem. To alleviate the problem, we propose to predict multi-step control actions into the future. However, the multi-step control process needs interactions with the environment. Thus we formulate a temporal module to learn the forward process and interactions between the ego agent and the environment. A temporal module implemented with GRU [16] progressively deals with the feature representation for each time step, implicitly taking into account the dynamic motion of agents, interaction among them and dynamic environment information such as the changing of traffic lights. ",
+        "bbox": [
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+        "type": "text",
+        "text": "Additionally, to generate accurate control signals in the multi-step prediction scheme, the model should retrieve proper location information from current sensor input for different future time steps. For example, an agent may pay more attention to nearby regions for a few early future time steps and far away regions for the remote ones. Considering that the knowledge has already been partly encoded in the trajectory branch, we adopt the attention mechanism to locate those critical and helpful areas in the long-term trajectory prediction branch, and guide the control prediction branch to pay attention to them at each future step in a corresponding way. As a result, our model is capable of reasoning about how to optimize current control prediction so that the future states are similar to those from the expert when the predicted control actions are applied. ",
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+        "type": "text",
+        "text": "With the predicted trajectory and control signals from two branches, we propose a situation based fusion scheme to adaptively combine these two forms in a self-ensemble way to form the ultimate output according to the experiments results and prior knowledge. It combines the best of these two forms, which further boosts the performance under different scenarios. ",
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+        "text": "TCP has shown superior performance when being validated in the CARLA driving simulator [20]. Our method, which only uses a monocular camera, achieves a 75.137 driving score and ranks 1st on the public CARLA Leaderboard [1], even surpassing prior state-of-the-art methods using multiple cameras and a LiDAR by 13.291 points. The main contributions of this paper include: ",
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+        "type": "text",
+        "text": "• We examine two dominant paradigms for end-to-end autonomous driving: trajectory planning and direct control, and propose to combine them in an integrated learning pipeline. To our knowledge, this is the first time that such two branches are jointly learned and fused for prediction.   \n• A multi-step control prediction branch with a temporal module and trajectory-guided attention is devised to enable temporal reasoning. To combine the best of two branches, we design a situation based scheme to fuse the two outputs.   \n• As a simple yet strong baseline, our method with only a monocular camera as input achieves new state-of-the-art on the CARLA Leaderboard with many competitors using multiple sensors. We conduct thorough ablation studies to verify the effectiveness of our approach. ",
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+        "type": "text",
+        "text": "2 Related Work ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "2.1 End-to-end Autonomous Driving ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Learning-based end-to-end autonomous driving has emerged as an active research topic in recent years. Studies usually fall into two categories: reinforcement learning (RL) and imitation learning. RL is a promising way to address the problem of being more robust to the distribution shifts of datasets. Liang et al. [39] use DDPG to train a policy which is pre-trained in a supervised way. Kendall et al. [30] train their deep RL algorithm onboard to efficiently learn to drive a real-world vehicle. The perception task is decoupled out of the online RL process in [50, 9, 62]. The model-based method WoR [12] assumes world on rails and uses policy distillation to realize powerful performance. ",
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+    {
+        "type": "text",
+        "text": "Imitation learning (IL), especially behavior cloning, collects recorded data for models to mimic with high data efficiency. The expert data typically has two forms, trajectories and control actions. Zeng et al. [58] train a cost volume to generate the planning route, while [49, 8, 25] explicitly design safety and comfort costs based on semantic occupancy maps to select the best one in the expert trajectory sets. Zhang et al. [59] predict trajectories of surrounding vehicles with labeled BEV map. LBC [11] and NEAT [15] decode waypoints from a dense heatmap or offset map. These approaches aforementioned all utilize a relatively dense representation to obtain results which increases model complexity. Transfuser and its variants [46, 29] adopt a simple GRU to auto-regress waypoints. LAV [10] adopts a temporal GRU module to further refine the trajectory. They unanimously achieve impressive performance on the CARLA leaderboard, motivating us to adapt the auto-regression scheme as well in our design. On the other hand, all trajectory-based methods use PID controllers to get the ultimate actions, which may cause inferior effects in complicated scenarios. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Another genre to predict control actions directly is proposed in [44, 40, 3, 54]. CIL [17] adds a measurement encoder and multiple branches for different high level commands with the image encoder. CILRS [18] is proposed afterwards and further introduces a speed prediction head. They stand as classic baselines for IL in the CARLA driving simulator. Diverse optimized approaches are presented based on them, such as multi-modal inputs [22, 53], multi-task learning [56, 37, 24, 27, 31, 26, 63], dataset aggregation [45] and knowledge distillation [61, 60]. However, the compact control-based methods often have higher vehicles collision rates, remaining an interesting domain to explore. Similar work exists in other related domains such as robotic navigation as well. [43] learns a controller after a local trajectory planner to improve the overall navigation behavior. ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "2.2 Multi-task and Ensemble Learning for Autonomous Driving ",
+        "text_level": 1,
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+        "text": "Multi-task learning is a popular approach to train several related tasks simultaneously to help each other and improve generalization [7, 2]. Combinations of various autonomous driving tasks such as object detection, lane detection, semantic segmentation, depth estimation, etc. have been proved to be capable of achieving incredible performance [38, 14, 47, 34, 52, 13]. MTL is also suitable in the end-to-end problem since it is observed the performance of a direct mapping from an image to control signals is limited. [56] adds a speed prediction task similar to CIL [17] and [63] separates the lateral and longitudinal controls as two tasks. LAV [10] trains an extra scene mapping network, and [24, 27, 29] additionally predict optical flow or dense depth. Our idea of training trajectory and control simultaneously is closely related to FASNet [31]. FASNet predicts future positions of the ego agent as an auxiliary task and adds a kinematic loss considering the relation between control and locations. However, the constrain is based on a constant velocity model which neglects the important throttle and brake, and it does not work at the inference time. On the other hand, our TCP framework has feature interactions at an earlier stage to fully explore their potential mutual benefits. ",
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+        "text": "Ensembles of models have long been utilized to improve the performance in computer vision [19, 33, 35, 51, 55, 45]. Besides the normal combination of models, two classic ensemble learning methods are particularly preferred in the autonomous driving regime. One is the Test-Time Augmentation (TTA), which is of great help to the 3D object detection task with LiDAR [6, 36]. Another one is the fusion of experts [28] where experts are trained on a subset of the input space and a gating network is trained to provide the fusion weights. LSD [42] and MoDE [32] divide a dataset into sub-scenarios to get different sub-policies for end-to-end autonomous driving. These traditional ensemble approaches combine models of the same structure while our approach tries to combine two different representations. Also, the multiple experts design increases the complexity of the training strategy and we seek to have a simpler situation based fusion scheme to boost the performance. ",
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+    {
+        "type": "text",
+        "text": "3 Trajectory-guided Control Prediction ",
+        "text_level": 1,
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+        "text": "3.1 Problem Setting ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Problem formulation. Given the state x comprised of the sensor signal i, the speed of the vehicle $v$ , and the high level navigation information $\\mathbf { g }$ including a discrete navigation command and the coordinates of navigation target provided by the global planner, the end-to-end model needs to output control signals a comprised of longitudinal control signals throttle $\\in [ 0 , 1 ]$ and brake $\\in [ 0 , 1 ]$ , and the lateral control signal steer $\\in [ - 1 , 1 ]$ . ",
+        "bbox": [
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+        "type": "text",
+        "text": "Conventional methods tackle this problem with either a trajectory-output or a control-output only model. However, TCP combines both of them as two branches: a trajectory branch which predicts the planned trajectory and a control branch which is guided by the trajectory one and outputs both current and multi-step control signals into the future. Both branches are trained in a supervised manner. Consider an expert which directly outputs the control signals at each step, supervising the predicted trajectory with the ground truth trajectory makes it not strictly satisfy the setting of behavior cloning in imitation learning. The ground truth trajectory indeed involves future expert actions and future states about the environment, so we formulate it as a trajectory planning task with ground truth trajectory as supervision for our trajectory branch. As for the control branch, training a control model which makes current control prediction supervised by the expert control is just behavior cloning in imitation learning, and it can be formulated as: ",
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+        "type": "equation",
+        "img_path": "images/0c254f11455176f7d5c53eea78227e0b74fd4ce54c0c8b5e8642e58c2f7939ed.jpg",
+        "text": "$$\n\\arg \\operatorname* { m i n } _ { \\theta } \\mathbb { E } _ { ( \\mathbf { x } , \\mathbf { a } ^ { * } ) \\sim \\mathrm { D } } [ \\mathcal { L } ( \\mathbf { a } ^ { * } , \\pi _ { \\theta } ( \\mathbf { x } ) ) ] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "where $D = \\{ ( { \\bf x } , { \\bf a } ^ { * } ) \\}$ is a dataset comprised of state-action pairs collected from the expert. $\\pi _ { \\theta }$ denotes the policy of the control branch, and $\\mathcal { L }$ is the loss measuring how close the action from the expert and the action from our model is. The expert collects the dataset by controlling the vehicle and interacting with the world. Each collected route is a trajectory $\\xi = ( { \\bf x } _ { 0 } , { \\bf a } _ { 0 } ^ { * } , { \\bf x } _ { 1 } , { \\bf a } _ { 1 } ^ { * } , \\cdot \\cdot \\ , { \\bf x } _ { \\mathrm { T } } )$ as a sequence of state action pairs $\\{ ( \\mathbf { x } _ { \\mathrm { i } } , \\mathbf { a } _ { \\mathrm { i } } ^ { * } ) \\} _ { \\mathrm { i = 0 } } ^ { \\mathrm { T } }$ , which is then added into the whole dataset $D$ . ",
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+    {
+        "type": "text",
+        "text": "Expert demonstration. Here we choose Roach [60] as the expert. Roach is a simple model trained by RL with privileged information, including roads, lanes, routes, vehicles, pedestrians, traffic lights, and stops, all being rendered into a 2D BEV image. Such a learning-based expert can transfer more information besides the direct supervision signals compared with an expert made by hand-crafted rules. Specifically, we have a feature loss which forces the latent features before the final output head from the student model to be similar to that of the expert. A value loss is also added as an auxiliary task for the student model to predict an expected return. ",
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+    {
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+        "img_path": "images/fee42be328edcdba4670ef51cd570a25aecc8c5ad8913a4b67b4fa9191c7581f.jpg",
+        "image_caption": [
+            "Figure 2: Overview of Trajectory-guided Control Prediction (TCP). The encoded features are shared by the trajectory and multi-step control branch. The trajectory branch provides per-step guidance for multi-step control prediction. Outputs from two branches are combined according to our situation based fusion scheme to generate the ultimate control actions. "
+        ],
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+    {
+        "type": "text",
+        "text": "3.2 Architecture Design ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Overview. As illustrated in Fig. 2, the whole architecture is comprised of an input encoding stage and two subsequent branches. The input image i goes through a CNN based image encoder, such as ResNet [23], to generate a feature map $\\mathbf { F }$ . In the meantime, the navigation information $\\mathbf { g }$ is concatenated with the current speed $v$ to form the measurement input m, then an MLP based measurement encoder takes m as its input and outputs the measurement feature $\\mathbf { j } _ { \\mathrm { { m } } }$ . The encoded features are then shared by two branches for subsequent trajectory and control predictions. Specifically, the control branch is a novel multi-step prediction design with guidance from the trajectory one, which will be illustrated in detail in the following sections. Finally, a situation based fusion scheme is adopted to combine the best of the two output paradigms. We will go over each part in detail below. ",
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+    {
+        "type": "text",
+        "text": "3.2.1 Trajectory planning branch ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Different from control prediction which directly predicts control actions, the trajectory planning branch first generates a planned trajectory comprised of waypoints at $K$ steps for the agent to follow, and then the trajectory is processed by low-level controllers to get the final control actions. With the shared feature from the input encoder, the image feature map $\\mathbf { F }$ is average pooled and concatenated with the measurement feature $\\mathbf { j } _ { \\mathrm { { m } } }$ to form $\\mathbf { j } ^ { \\mathrm { t r a j } }$ . Inspired by [46], we feed $\\mathbf { \\hat { j } } ^ { \\mathrm { t r a j } }$ into a GRU [16] to auto-regressively obtain future waypoints one by one to form the planned trajectory altogether. ",
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+        "type": "text",
+        "text": "We have two PID controllers for longitudinal and lateral control respectively. With the planned trajectory, we first calculate the vectors between consecutive waypoints. The magnitudes of these vectors represent the desired speed and are sent to the longitudinal controller to generate throttle and brake control actions, and the orientations are sent to the lateral controller to get the steer action. ",
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+    {
+        "type": "text",
+        "text": "3.2.2 Multi-step control prediction branch ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As discussed in Sec. 3.1, for a control model predicting current control actions based on current input only, the supervised training is just behavior cloning, which relies on the independent and identically distributed (IID) assumption. This assumption apparently does not hold because of the distribution shifts in test cases, since the closed-loop tests require sequential decision making where the historical actions will affect the future states and actions. Instead of modeling it as a Markov Decision Process (MDP) and resorting to reinforcement learning, here we devise a simple way to mitigate the problem by predicting multi-step control into the future. ",
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+        "type": "text",
+        "text": "Given the current state $\\mathbf { x } _ { \\mathrm { t } }$ , now our multi-step control prediction branch outputs multiple actions: $\\pi _ { \\theta _ { m u l t i } } = ( \\mathbf { a } _ { \\mathrm { t } } , \\mathbf { a } _ { \\mathrm { t + 1 } } , \\cdot \\cdot \\cdot , \\mathbf { a } _ { \\mathrm { t + K } } )$ . However, it is difficult to predict future control actions since we only have sensor inputs at the current time step. Towards this problem, we devise a temporal module to implicitly carry out the changing and interaction process of the environment and our agent. It is supposed to provide mainly dynamic information about the environment and the status of the agent itself, such as the motion of other objects, the changing of traffic lights, and the status of the ego agent. Meanwhile, to improve the ability of incorporating critical static information (e.g., curbs and lanes) and boost the spatial consistency of two branches, we propose to use the trajectory branch to guide the control counterpart to attend to proper regions of the input image at each future time step. ",
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+        "text": "Temporal module. Our temporal module is implemented with a GRU for better consistency with the trajectory branch. At step $t$ $( 0 \\leq t \\leq K - 1 )$ , the input for the temporal module is the concatenation of the current feature $\\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } }$ (more construction details in the next section) and current predicted action $\\mathbf { a } _ { \\mathrm { t } }$ , which is a compact representation about the current states of the environment and the agent itself. The temporal module is supposed to reason about the dynamic changing process based on current feature vector and the predicted action. Then the updated hidden state $\\bar { \\mathbf { h } } _ { \\mathrm { t + 1 } } ^ { \\mathrm { c t l } }$ will contain dynamic information about the environment and the updated status of the agent at time step $t + 1$ . To some extent, the temporal module acts as a coarse simulator with the whole environment and the agent being abstracted as a feature vector. It then simulates the interaction between the environment and the agent based on current prediction of actions. ",
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+        "type": "text",
+        "text": "Trajectory-guided attention. With the sensor input at current step only, it is hard to pick out desirable regions where the model should focus on at future steps. However, the location of the ego agent contains important cues about how to find those regions containing critical static information for control prediction at each step. ",
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+        "type": "text",
+        "text": "Therefore, we seek help from the trajectory planning branch to get information about the possible location of our agent at that corresponding step. As shown in Fig. 3, TCP implements this by learning an attention map to extract important information from the encoded feature map. The interaction between two branches enhances the consistency of these two strongly related output paradigms and further elaborates the multi-task spirit. Specifically, with the 2D feature map extracted by the image encoder $\\mathbf { F }$ at time step $t \\left( 1 \\leq t \\leq K \\right)$ , we calculate an attention map $\\mathbf { w } _ { \\mathrm { t } } \\in \\mathbb { R } ^ { 1 \\times \\mathrm { H } \\times \\mathrm { W } }$ using the corresponding hidden states from the control branch and the trajectory branch: ",
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+        "image_caption": [
+            "Figure 3: Detailed trajectory guiding process. For predictions at time step $t$ , the hidden states from the waypoint GRU and the temporal module are combined to learn an attention weight map to re-aggregate the 2D image feature map for control prediction. "
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+        "img_path": "images/47f265125f1ec50517a85a1d219a63de9fd06fa429fc489727daced7c8b1bc5c.jpg",
+        "text": "$$\n\\mathbf { w } _ { \\mathrm { t } } = \\mathrm { M L P } ( \\mathrm { C o n c a t } [ \\mathbf { h } _ { \\mathrm { t } } ^ { \\mathrm { t r a j } } , \\mathbf { h } _ { \\mathrm { t } } ^ { \\mathrm { c t l } } ] ) .\n$$",
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+        "text": "The attention map $\\mathbf { w } _ { \\mathrm { t } } \\in \\mathbb { R } ^ { 1 \\times \\mathrm { H } \\times \\mathrm { W } }$ is adopted to aggregate the feature map $\\mathbf { F }$ for this step. We then combine the attended feature map with $\\mathbf { h } _ { \\mathrm { t } } ^ { \\mathrm { c t l } }$ to form the informative representation feature $\\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } }$ containing both static and dynamic information about the environment and the ego agent. The process can be described as follows: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3c9f4b4a79e1a9c6f15088941125bd50c3647447a9691bb3192b00e49433693c.jpg",
+        "text": "$$\n\\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } } = \\mathrm { M L P } ( \\mathrm { C o n c a t } [ \\mathrm { S u m } ( \\mathrm { S o f t m a x } ( \\mathbf { w } _ { \\mathrm { t } } ) \\odot \\mathbf { F } ) , \\mathbf { h } _ { \\mathrm { t } } ^ { \\mathrm { c t l } } ] ) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            316,
+            675,
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+            694
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The informative representation feature $\\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } }$ is fed into a policy head which is shared among all time steps to predict the corresponding control action $\\mathbf { a } _ { \\mathrm { t } }$ . Note that for the initial step, we only use the measurement feature to calculate the initial attention map and combine the attended image feature with the measurement feature to form the initial feature vector $\\mathbf { j } _ { 0 } ^ { \\mathrm { c t l } }$ . To guarantee the feature $\\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } }$ does describe the state at that step and contain the important information for control prediction, we add a feature loss at each step to make $\\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } }$ close to the feature of the expert as well. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To this end, our TCP framework endows the model with the reasoning ability along a short time horizon. It emphasizes how to make current control prediction close to the one from the expert. Furthermore, it takes into account what current control prediction can make the environment states and status of ego agent in future time steps similar to the ones from the expert. ",
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+    },
+    {
+        "type": "text",
+        "text": "3.3 Loss Design ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our loss contains trajectory planning loss $\\mathcal { L } _ { t r a j }$ , control prediction $\\mathcal { L } _ { c t l }$ , and auxiliary loss $\\mathcal { L } _ { a u x }$ ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "For the trajectory planning branch, the loss $\\mathcal { L } _ { t r a j }$ can be expressed as: ",
+        "bbox": [
+            173,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8f9c417e8d44545ec7cba4c9784e875fcb2d8dcfd37e235b59816c92fc49e844.jpg",
+        "text": "$$\n\\mathcal { L } _ { t r a j } = \\sum _ { t = 1 } ^ { K } \\| \\mathbf { w p } _ { \\mathrm { t } } - \\mathbf { w } \\mathbf { \\hat { p } } _ { \\mathrm { t } } \\| _ { 1 } + \\lambda _ { \\mathrm { F } } \\cdot \\mathcal { L } _ { \\mathrm { F } } \\left( \\mathbf { j } _ { 0 } ^ { \\mathrm { t r a j } } , \\mathbf { j } _ { 0 } ^ { \\mathrm { E x p e r t } } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            312,
+            113,
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+            156
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { w p } _ { \\mathrm { t } } , \\mathbf { w } \\mathbf { \\hat { p } _ { \\mathrm { t } } }$ are the predicted and ground truth waypoint at the $t ^ { t h }$ step respectively. $\\mathcal { L } _ { F }$ indicates the feature loss measuring the $L _ { 2 }$ distance between $\\mathbf { j } _ { 0 } ^ { \\mathrm { t r a j } }$ j and the feature jEx0 pert from the expert at the current step as an additional supervision signal [60]. $\\lambda _ { F }$ is a tunable loss weight. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For the control prediction branch, we model the action as a beta distribution. The loss $\\mathcal { L } _ { c t l }$ is: ",
+        "bbox": [
+            173,
+            214,
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6b9bee417c2aa9d56263b0b28438619aef5954f13c1005e336979b127873ecda.jpg",
+        "text": "$$\n\\begin{array} { r l r } {  { \\mathcal { L } _ { c t l } = \\mathbf { K } \\mathbf { L } ( \\mathrm { B e t a } ( \\mathbf { a } _ { 0 } ) | | \\mathrm { B e t a } ( \\hat { \\mathbf { a } } _ { 0 } ) ) + \\frac { 1 } { K } \\sum _ { t = 1 } ^ { K } \\mathbf { K } \\mathbf { L } ( \\mathrm { B e t a } ( \\mathbf { a } _ { \\mathrm { t } } ) | | \\mathrm { B e t a } ( \\hat { \\mathbf { a } } _ { \\mathrm { t } } ) ) } } \\\\ & { } & { +  \\lambda _ { F } \\cdot \\mathcal { L } _ { F } ( \\mathbf { j } _ { 0 } ^ { \\mathrm { c t l } } , \\mathbf { j } _ { 0 } ^ { \\mathrm { E x p e r t } } ) + \\frac { 1 } { K } \\sum _ { t = 1 } ^ { K } \\mathcal { L } _ { F } ( \\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { c t l } } , \\mathbf { j } _ { \\mathrm { t } } ^ { \\mathrm { E x p e r t } } ) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            264,
+            234,
+            730,
+            324
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathrm { B e t a } ( \\mathbf { a } )$ denotes the beta distribution represented by the corresponding predicted distribution parameters and KL-divergence is used to measure the similarity between the predicted control distribution and the one from expert, i.e., Beta(aˆ). Feature loss is applied here as well. Note that all losses for future time steps $( t \\geq 1 )$ ) are averaged and then added to the loss for the current time step $( t = 0$ ), since the action executed immediately should be our key target to optimize. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To help the agent better estimate its current state, we add a speed prediction head to predict current speed $s$ from the image feature and a value prediction head to predict the expected return estimated by the expert, similarly as in [60]. We take the $L _ { 1 }$ loss for the speed prediction and $L _ { 2 }$ loss for the value prediction, denoting their weighted sum as $\\mathcal { L } _ { a u x }$ . ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The overall loss is as follows, as weighted by $\\lambda _ { t r a j } , \\lambda _ { c t l } , \\lambda _ { a u x }$ : ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/75207cebe1df83cb9e916d658f1fe79f7ab74d832cb33adbe353d7f9cebddac3.jpg",
+        "text": "$$\n\\mathcal { L } = \\lambda _ { t r a j } \\cdot \\mathcal { L } _ { t r a j } + \\lambda _ { c t l } \\cdot \\mathcal { L } _ { c t l } + \\lambda _ { a u x } \\cdot \\mathcal { L } _ { a u x } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3.4 Output Fusion ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We have two forms of output representations from our TCP framework: the planned trajectory and the predicted control. To further combine their advantages, we devise a situation-based fusion strategy as depicted in Algorithm 1. Specifically, denote $\\alpha$ as a combination weight whose value is between 0 to 0.5, in a certain situation where one representation is more suitable according to our prior belief, we combine the results from trajectory and control predictions by taking average with weight $\\alpha$ so that the more suitable one takes up more weight $( 1 - \\alpha )$ . Note that the combination weight $\\alpha$ indeed does not need to be ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/098539f595937f71f2a16721946283e39b6677e8b19afaf0e58f92056957d02c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Algorithm1:Situation based fusion scheme to com- bine the two output paradigms</td></tr><tr><td>Input: sensory input i, speed of the ego vehicle v, high level navigation information g.</td></tr><tr><td>Hyper parameters:combination weight α E [0,0.5] Output: final control signals a</td></tr><tr><td>{wpt}=o,actl ← TCP(i,u, g) atraj ←Low-level Controller ({wpt}ε=0) a</td></tr><tr><td>Getcurrent situation if situationis trajectory specialized then</td></tr><tr><td>a←α×act1+(1-α)×atraj</td></tr><tr><td></td></tr><tr><td>else a←α×atraj+(1-α) ×actl</td></tr></table>",
+        "bbox": [
+            486,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "a constant or symmetric, which means we can set it to different values under different situations or different for specific control signals. In our experiment, we choose the situation according to whether the ego vehicle is turning, implying that if it is turning, the situation is control specialized otherwise trajectory specialized. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.1 Experimental Setup ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Task & Evaluation metrics. Our method is validated and tested in the CARLA driving simulator [20]. Given a route defined by a sequence of sparse navigation points together with high level commands (straight, turn left/right, lane changing, and lane following), the closed-loop driving task requires the autonomous agent to drive towards the destination point. It is designed to simulate realistic traffic situations and includes different challenging scenarios such as obstacle avoidance, crossing an unsignalized intersection, and sudden control loss. There are three major metrics: Driving Score, Route Completion, and Infraction Score. Route Completion is the percentage of the route completed by the autonomous agent. Infraction Score measures the number of infractions made along the route, with pedestrians, vehicles, road layouts, red lights, and etc. Driving Score is the main metric which is the product of Route Completion and Infraction Score. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/2f1a100f50c77049356a8acbdf4588aa785bbc7c0ace574a5e344059d7679db3.jpg",
+        "table_caption": [
+            "Table 1: Evaluation on the public CARLA Leaderboard [1] (accessed in May 2022). Our method TCP and TCP-Ens achieve a driving score of 69.714 and 75.137 respectively with only a monocular camera. More detailed infraction statistics can be found in the Supplementary. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Rank</td><td rowspan=\"2\">Method</td><td colspan=\"2\">Sensor Inputs</td><td colspan=\"3\">Key Metrics ↑</td></tr><tr><td>#Cameras</td><td>LiDAR</td><td>Driving Score</td><td>Route Completion</td><td>Infraction Score</td></tr><tr><td>1</td><td>TCP-Ens (ours)</td><td>1</td><td>X</td><td>75.137</td><td>85.629</td><td>0.873</td></tr><tr><td>1</td><td>TCP (ours)</td><td>1</td><td>X</td><td>69.714</td><td>82.962</td><td>0.851</td></tr><tr><td>1</td><td>TCP-SB (ours)</td><td>1</td><td>X</td><td>68.695</td><td>82.957</td><td>0.833</td></tr><tr><td>2</td><td>LAV [10]</td><td>4</td><td>√</td><td>61.846</td><td>94.459</td><td>0.640</td></tr><tr><td>3</td><td>Transfuser</td><td>3</td><td>√</td><td>61.181</td><td>86.694</td><td>0.714</td></tr><tr><td>4</td><td>Latent Transfuser</td><td>3</td><td></td><td>45.029</td><td>75.366</td><td>0.618</td></tr><tr><td>5</td><td>GRIAD [9]</td><td>3</td><td>xx/</td><td>36.787</td><td>61.855</td><td>0.597</td></tr><tr><td>6</td><td>Transfuser+ [29]</td><td>4</td><td></td><td>34.577</td><td>69.841</td><td>0.562</td></tr><tr><td>7</td><td>WoR[12]</td><td>4</td><td>X</td><td>31.370</td><td>57.647</td><td>0.557</td></tr><tr><td>8</td><td>MaRLn [50]</td><td>1</td><td>X</td><td>24.980</td><td>46.968</td><td>0.518</td></tr><tr><td>9</td><td>NEAT[15]</td><td>3</td><td>X</td><td>21.832</td><td>41.707</td><td>0.650</td></tr></table>",
+        "bbox": [
+            251,
+            143,
+            745,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/54cf02afd8a2b5388701c9b2f82a3edd772dd819b3ad7704744443e308153477.jpg",
+        "table_caption": [
+            "Table 2: Comparison between the control and trajectory only model in terms of infractions frequency. TurnRatio means the corresponding ratio of happening during turning. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td rowspan=\"2\">Driving Score</td><td colspan=\"2\">Collisions vehicles</td><td colspan=\"2\">Collisions layout</td><td colspan=\"2\">Off-road infractions</td><td colspan=\"2\">Agent blocked</td></tr><tr><td>#/km↓</td><td>TurnRatio</td><td>#/km↓</td><td>TurnRatio</td><td>#/km↓</td><td>TurnRatio</td><td>#/km↓</td><td>TurnRatio</td></tr><tr><td>Control-Only</td><td>32.45±2.23</td><td>1.25</td><td>50.90%</td><td>0.23</td><td>10.00%</td><td>0.59</td><td>46.15%</td><td>0.41</td><td>50.00%</td></tr><tr><td>Trajectory-Only</td><td>28.29±3.03</td><td>0.85</td><td>38.70%</td><td>0.77</td><td>64.20%</td><td>0.74</td><td>62.90%</td><td>0.77</td><td>64.20%</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Dataset. We use randomly generated routes under random weather conditions to collect 420K data in the 8 public towns offered by the CARLA simulator. Similar to [10], we train TCP on 189K of data in 4 out of 8 towns (Town01, Town03, Town04, and Town06) for ablations and train with all 420K data for our online leaderboard submission. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.2 State-of-the-art Comparison ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            712,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows the result of the comparison between our method and the top 8 entries on the public CARLA Leaderboard [1]. We report the results of TCP and two variants. TCP-SB replaces shared encoders of TCP with two separate ones for two branches, and TCP-Ens is the ensemble of TCP and TCP-SB. Our method TCP-Ens ranks first on the leaderboard with a 75.137 driving score and highest infraction score, and TCP alone also surpasses prior methods. Note that our method only uses a monocular camera while the top 2-4 methods all use multiple cameras and a LiDAR. Our driving score is 50.157 higher than the second-best monocular camera method, MaRLn [50]. Our route completion is slightly inferior to the LiDAR candidates - one reason is that methods using LiDAR may have a better object detection ability. Based on the detection results, they usually adopt a crawling strategy, indicating that the vehicle would move slowly when it has stopped for a long time and there are no obstacles ahead. As described in [29], this could alleviate ego vehicle’s blocking problems to boost the route completion performance. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/53625470e10efe8de104f7eaed01f6b709a62241dccde0c71d9743b472e0849d.jpg",
+        "image_caption": [
+            "Figure 4: The trajectory-guided attention maps in two cases. In each case (row), from the left to right we show that the input image with the predicted trajectory (the first waypoint is projected out of the image), the predicted trajectory in the top-down view, the attention map $\\mathbf { w } _ { 1 }$ , the attention map $\\mathbf { w } _ { 3 }$ . "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            178,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/5eebe91fbd82f69a1db359a12723bdc8752dbef9e86d494a30e25f3d53bce238.jpg",
+        "table_caption": [
+            "Table 3: Ablative study on the effectiveness of different components design of our model. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Exp.</td><td>Driving Score</td><td>Route Completion</td><td>Infraction Score</td></tr><tr><td>Control</td><td>32.45±2.23</td><td>76.54±3.22</td><td>0.45±0.03</td></tr><tr><td>+ traj-task</td><td>34.98±1.96</td><td>81.32±5.50</td><td>0.49±0.05</td></tr><tr><td>+ temporal</td><td>42.87±4.77</td><td>87.51±3.63</td><td>0.49±0.07</td></tr><tr><td>+ traj-attn</td><td>46.08±3.47</td><td>84.95±1.84</td><td>0.56±0.03</td></tr><tr><td>+ fusion</td><td>57.01±1.88</td><td>85.27±1.20</td><td>0.67±0.01</td></tr></table>",
+        "bbox": [
+            176,
+            294,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/79d743380124702e004eaa2f584b254a65cc6de98406944f1b0b99bf92b3e8f1.jpg",
+        "table_caption": [
+            "Table 4: Comparison between MTL and ensemble methods ( $\\alpha$ is 0.3 for all experiments). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Exp.</td><td>Driving Score</td><td>#Param.</td><td>FLOPs</td><td>FPS</td></tr><tr><td>Ensemble</td><td>45.03±1.28</td><td>46.81M</td><td>17.07G</td><td>69.47</td></tr><tr><td>MTL</td><td>48.27±0.58</td><td>23.58M</td><td>8.54G</td><td>133.30</td></tr><tr><td>TCP-SB</td><td>52.46±4.66</td><td>47.26M</td><td>17.07G</td><td>69.35</td></tr><tr><td>TCP</td><td>57.01±1.88</td><td>25.77M</td><td>8.54G</td><td>125.71</td></tr><tr><td>TCP-Ens</td><td>59.09±3.66</td><td>73.03M</td><td>25.61G</td><td>44.70</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "4.3 Control vs. Trajectory ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "In this section, we conduct quantitative experiments to compare the Control-Only model and the Trajectory-Only model to demonstrate their advantages and disadvantages. For both models, we use the same setting except for the output head and its corresponding loss. We use a ResNet-34 to encode visual inputs and a measurement module to encode the navigation information. Similar to [60], we add speed and value heads as auxiliary tasks to help the model better encode the environment. For Control-Only, we predict the control distribution based on the concatenated latent feature from the two encoders. As for Trajectory-Only, we feed the feature to a GRU decoder to generate waypoints. As shown in Table 2, though Trajectory-Only collides with vehicles less frequently than Control-Only, it has more layout collisions, off-road infractions, and agent blocks. We also count the ratio of each kind of infraction that occurs during turning. It can be observed that for Trajectory-Only, a large portion of such infractions happen when the ego agent is turning compared to Control-Only. This has verified that Trajectory-Only performs worse when the agent is turning, which is probably caused by the unsatisfactory trajectory following performance of simple PID controllers as discussed in Sec. 1. As for the fact that Control-Only has a higher vehicle-collision rate, it is because the model focuses on the current time step and the reaction to potential collisions tends to be late, as depicted in Sec. 1 as well. The results above further validate the necessity of combining the two output paradigms. ",
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+    {
+        "type": "text",
+        "text": "4.4 Ablative Study and Visualization ",
+        "text_level": 1,
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+        "text": "Component analysis. We first validate the effectiveness of the trajectory-guided multi-step control prediction design, as shown in Table 3. We only employ the control branch output except for the last complete one when fusion is applied for these ablations. Adding a trajectory branch as an auxiliary task improves the performance by 2.5 points. The multi-step predictions with our temporal module greatly help with 7.9 points gain, and adding the trajectory-guided attention further acquires an improvement of 3.2 points. Finally, applying our situation based fusion scheme $\\alpha$ is set to 0.3) significantly boosts the infraction score, leading the overall driving score to 57. ",
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+        "text": "Multi-task vs. Ensemble. The comparison regarding their performances and computational complexity is given in Table 4. Ensemble denotes directly combining the outputs of Control-Only and Trajectory-Only with our situation based fusion scheme. MTL represents the model with a shared CNN backbone and measurement encoders followed by a trajectory branch and a control branch, but the control branch predicts current step prediction only and there are no interactions between the two branches. We conclude that directly combining two models with our fusion scheme greatly improves the performance, and using an MTL approach works better than ensemble but with a much smaller model size and GFLOPs. A conventional ensemble approach to combine results from TCP and TCP-SB as TCP-Ens brings further performance gain at the cost of computational complexity. ",
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+        "text": "Situation based fusion weight. We investigate the choice of the combination weight $\\alpha$ in the situation based fusion scheme and show the box plot of the driving scores in the figure to the right. Besides $\\alpha \\in [ 0 , 0 . 5 ]$ , we additionally test 0.7 and 1, meaning that two results are conversely mixed with our specialization definition. We see that only using the control from the specialized branch $\\alpha = 0$ performs poorly while directly taking the average or fusing conversely still has comparable results. One reason is that the situation criterion used here is whether the vehicle is turning, making most cases trajectory specialized, and the stronger control branch is not utilized enough if $\\alpha$ is small. Note that the situation based fusion scheme is general and flexible, and the criterion or $\\alpha$ value used here is relatively coarse. ",
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+            "Figure 5: Box plot of the driving score with different $\\alpha$ values (3 trials for each $\\alpha$ ). "
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+        "text": "Visualization. Fig. 4 visualizes the trajectory-guided attention maps. The trajectory branch provides location-related information to guide the control branch to focus on important regions which are useful for future control prediction. See more qualitative results in the Supplementary. ",
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+        "text": "5 Conclusion ",
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+        "text": "In this work, we study two learning and prediction paradigms based on trajectory and direct control, respectively, for end-to-end autonomous driving. We propose a unified framework comprised of a trajectory branch and a novel multi-step control branch with interactions in between. We design a situation based fusion scheme to combine the results from two branches. Our method with only a monocular camera has achieved state-of-the-art performance on the CARLA Leaderboard. ",
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+        "text": "Acknowledgments ",
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+        "text": "This work was partly supported by National Key Research and Development Program of China (2020AAA0107600), NSFC (62206172, 61972250), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and Shanghai Committee of Science and Technology (21DZ1100100, 22511105100). ",
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+        "text": "References ",
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Cadre: A cascade deep reinforcement learning framework for vision-based autonomous urban driving. In AAAI, 2022. 3   \n[63] Zeyu Zhu and Huijing Zhao. Multi-task conditional imitation learning for autonomous navigation at crowded intersections. arXiv preprint arXiv:2202.10124, 2022. 3, 4 ",
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parse/dev/JvIFpZOjLF4/JvIFpZOjLF4.md

@@ -0,0 +1,391 @@
+# Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction
+
+Qiancheng $\mathbf { F u } ^ { 1 * }$ Qingshan $\mathbf { X } \mathbf { u } ^ { 2 * }$ Yew-Soon Ong2,3 Wenbing Tao1†
+
+Huazhong University of Science and Technology 2Nanyang Technological University 3A\*STAR, Singapore 1{fqc98,wenbingtao}@hust.edu.cn 2{qingshan.xu,asysong}@ntu.edu.sg
+
+# Abstract
+
+Recently, neural implicit surfaces learning by volume rendering has become popular for multi-view reconstruction. However, one key challenge remains: existing approaches lack explicit multi-view geometry constraints, hence usually fail to generate geometry-consistent surface reconstruction. To address this challenge, we propose geometry-consistent neural implicit surfaces learning for multi-view reconstruction. We theoretically analyze that there exists a gap between the volume rendering integral and point-based signed distance function (SDF) modeling. To bridge this gap, we directly locate the zero-level set of SDF networks and explicitly perform multi-view geometry optimization by leveraging the sparse geometry from structure from motion (SFM) and photometric consistency in multi-view stereo. This makes our SDF optimization unbiased and allows the multi-view geometry constraints to focus on the true surface optimization. Extensive experiments show that our proposed method achieves high-quality surface reconstruction in both complex thin structures and large smooth regions, thus outperforming the state-ofthe-arts by a large margin. Code: https://github.com/GhiXu/Geo-Neus.
+
+# 1 Introduction
+
+Reconstructing surfaces from calibrated multi-view images is a long-standing problem in computer vision and graphics. In the past years, traditional methods [30, 37, 15, 17] have adopted a multi-step pipeline to achieve impressive reconstruction results. Such a pipeline requires depth maps or point clouds to generate surface meshes. These intermediate representations inevitably introduce accumulated errors for the final reconstructed geometry. Recently, directly reconstructing surfaces from images [25, 43, 35, 42, 26] has attracted great interest for its potential to alleviate the accumulated errors and produce high-quality reconstructions. To achieve this, existing approaches represent surfaces as neural implicit representations and leverage volume rendering [21] to optimize them.
+
+Inspired by neural volume rendering [23, 45] that simultaneously learns volume density and radiance field from input images, recent works [35, 42] use signed distance functions (SDF) [27] for surface representation and introduce the SDF-induced density function to enable the volume rendering to learn an implicit SDF representation. In essence, these works still focus on direct color field modeling by volume rendering integral rather than explicit multi-view geometry optimization. Therefore, existing approaches usually fail to generate geometry-consistent surface reconstruction. Intuitively, volume rendering samples multiple points along each ray and expresses the output pixel colors as the integral of the radiance field, or the weighted sum of sampled colors along the ray (cf. Fig. 1(a)). It means that the volume rendering integral directly optimizes the integral of geometry instead of the single surface intersection along the ray. This obviously introduces bias for geometry modeling, thus hindering true surface optimization. In Fig.1(b), we show the reconstruction case of NeuS [35], in which the bias between rendered colors and object geometry can be observed intuitively. Rendered colors are obtained by the color network via volume rendering. Surface colors are formed by the predicted colors of the surface where the SDF values are zeroes. It can be easily seen that there exists a gap between the rendered colors and the surface colors. Thus the reconstructed surface is imprecise despite the high-quality rendered image, indicating the bias between the color rendering and implicit geometry. (Detailed theoretical analysis will be elaborated later).
+
+![](images/90a6b99b8c1b05b232700c2d8987b12e9830cd5cf62799f60db308efab134256.jpg)  
+Figure 1: (a) Illustration of volume rendering. (b) A visual example. The volume rendering in NeuS uses integral colors to implicitly supervise surface modeling. Although its rendered colors achieve good results, the colors of estimated surface fail to preserve object geometry information. This shows the bias between rendered colors and geometry. In contrast, our approach achieves structurepreserving colors of estimated surface and produces geometry-consistent surface reconstruction.
+
+To address the above problem, we propose Geo-Neus to devise an explicit and accurate neural geometry optimization model for geometry-consistent neural implicit surfaces learning by volume rendering, leading to better multi-view 3D reconstruction. Specifically, we directly locate the zerolevel set of SDF networks and explicitly perform multi-view geometry optimization by leveraging the sparse geometry from structure from motion (SFM) and photometric consistency in multi-view stereo. This model has several benefits. First, directly locating the zero-level set of SDF networks guarantees that our geometry modeling is unbiased. This enables our method to focus on true surface optimization. Second, we show that explicitly enforcing multi-view geometry constraints on the located zero-level set of SDF networks allows our method to generate geometry-consistent surface reconstruction. Previous neural implicit surfaces learning mainly uses the rendering loss to implicitly optimize SDF networks. This results in geometry ambiguity during the training optimization. Our introduced two types of explicit multi-view constraints encourage our SDF networks to reason about the correct geometry, including both complex thin structures and large smooth regions.
+
+In summary, our contributions are: 1) We theoretically analyze that there exists a gap between volume rendering integral and point-based SDF modeling. This demonstrates that it is necessary to directly supervise the SDF networks to boost the neural implicit surfaces learning. 2) Based on our theoretical analysis, we propose to directly locate the zero-level set of SDF networks and leverage multi-view geometry constraints to explicitly supervise the training of SDF networks. In this way, the SDF networks are encouraged to focus on true surface optimization. Extensive experiments further validate the effectiveness of our theoretical analysis and the proposed direct optimization of SDF networks. We show that our proposed Geo-Neus is capable to reconstruct both complex thin structures and large smooth regions. Therefore, it greatly outperforms the state-of-the-art surface reconstruction methods, including traditional methods and neural implicit surface learning methods.
+
+# 2 Related work
+
+Traditional multi-view 3D reconstruction. Traditional multi-view 3D reconstruction is the classical pipeline of surface reconstruction from multi-view images. Given multi-view input images, traditional multi-view 3D reconstruction uses structure from motion (SFM) [33, 29] to extract and match features of neighbor views, and estimate camera parameters and sparse 3D points. After that, multi-view stereo (MVS) [30, 9, 37, 38, 36] is applied to estimate dense depth maps for each view and then all the depth maps are fused into dense point clouds. Finally, the surface reconstruction method [15, 17, 6], e.g., screened Poisson Surface Reconstruction [15] is used to reconstruct surfaces from point clouds. Traditional methods have achieved great success on various occasions, but there exists incompleteness of surface in some cases because their multiple intermediate steps are not made into an ensemble. With the development of deep learning, many attempts have been made on learning-based multi-view reconstruction [14, 40, 39, 27, 22], but the problem still exists.
+
+Implicit representation of surface. Surface reconstruction methods can be generally divided into explicit methods and implicit methods, depending on the representation of surface. Explicit representation includes voxels [5, 31] and triangular mesh [3, 4, 16], which are limited by the resolution. Implicit representation uses an implicit function to represent the surface and thus is continuous. The surface can be extracted using the implicit function at any resolution. Traditional reconstruction methods, e.g., screened Poisson Surface Reconstruction [15], use basic functions to form the implicit function. As for learning-based methods, the most commonly used forms are the occupancy function [22, 28] and the signed distance function (SDF) [27] represented by the network. Based on these functions, many implicit surface reconstruction methods from point clouds have been proposed, e.g., ONet [22], DeepSDF [27], Point2Surf [8] and etc. For these methods, point clouds are obtained by scanner devices or multi-view stereo methods. That is, these point clouds are uniform and complete. Therefore, these methods are rarely applied on the sparse point clouds produced by SFM to reconstruct surfaces (In fact, we show that these methods degrade on sparse point clouds from SFM in our supplementary material). In this work, we use the sparse points from SFM as an explicit geometry supervision and show that they can facilitate the neural implicit surface reconstruction.
+
+Neural implicit surface reconstruction. Neural implicit field is a new way to represent the geometry of objects. With NeRF [23] first using the neural radiance field represented by Multi-Layer Perceptron (MLP) in novel view synthesis, plenty of works [32, 18, 20] have sprung up using neural networks to represent scenes. IDR [43] reconstructs surfaces with neural networks by representing the geometry as the zero level set of an MLP that is considered to be an SDF. MVSDF [44] imports information from the MVS network to arrive at more geometry priors. VolSDF [42] and NeuS [35] use the weight function that involved SDF during the rendering process to make colors and geometry closer. UNISURF [26] explores the balance between surface rendering and volume rendering. The surface reconstructed by the neural network shows better completeness compared with the traditional multi-view reconstruction methods, especially when dealing with non-Lambertian cases. However, complex structures are not handled well. Meanwhile, flat planes and sharp corners could not be guaranteed. NeuralWarp [7], a concurrent work, also explores the use of patch-match on neural surface reconstruction. It combines volumetric rendering with a patch warping integration technique, which aggregates colors from points sampled along the camera ray from source views with patch warping. This way of patch aggregation is similar with volume rendering and shares the same sampled points and the same weights with those used by color integration. Note that NeuralWarp uses patch match with the color aggregation to optimize weights of sampled points, and thus to optimize the geometry indirectly. As we will analyze later, this kind of color integration operation will cause bias in the colors and the geometry. Therefore, NeuralWarp could not be trained from scratch and relies on the pre-trained model of VolSDF. Differently from NeuralWarp, our method locates the predicted surface of the SDF network using SDF-based interpolation and uses patch match to measure the photometric consistency among neighboring views. In this way, Geo-Neus can be trained from scratch and gets much better performance.
+
+# 3 Method
+
+Given posed multi-view images of an object, we aim at reconstructing the surface by neural volume rendering without mask supervision. The spatial field of the object is represented by a signed distance function (SDF), and the corresponding surface is extracted using the zero level set of the SDF. In the process of volume rendering, our goal is to optimize the signed distance function. In this section, we first analyze the inherent bias in color rendering which causes the inconsistency between rendered colors and implicit geometry. Then we introduce explicit SDF optimization to achieve geometry consistency. An overview of our approach is shown in Fig. 2.
+
+# 3.1 Bias in color rendering
+
+In the process of volume rending, there is a gap between the rendered colors and the geometry of the object. The rendered colors are not consistent with the real colors of the surface.
+
+![](images/ee6db9693d98ca7f9ee408647ee199688745c46c7259cdefc676cf3a1efedfab.jpg)  
+Figure 2: Overview of Geo-Neus. Previous neural implicit surfaces learning methods mainly depend on the color loss to implicitly supervise the SDF network. Our proposed Geo-Neus explicitly supervises the SDF network by introducing the SDF loss from sparse 3D points and photometric consistency loss from multi-view stereo.
+
+For an opaque solid object $\varOmega \in \mathbb { R } ^ { 3 }$ , the opacity can be represented by an indicator function $\mathcal { O } ( \pmb { p } )$
+
+$$
+\begin{array} { r } { \mathscr { O } ( { p } ) = \left\{ \begin{array} { l l } { 1 , p \in \varOmega } \\ { 0 , p \notin \varOmega } \end{array} \right. . } \end{array}
+$$
+
+When we see some colors or we capture some colors with cameras, the colors are the light that transfers along the light ray into our eyes or cameras. Based on the inherent optical properties of the opaque solid object, we approximately assume that the colors $C$ of image set $\{ I _ { i } \}$ are the colors $c$ of object intersecting with the light ray $\nu$ from the corresponding camera position $\mathbf { \delta } _ { \pmb { o } }$ :
+
+$$
+C \left( \pmb { \sigma } , \pmb { \nu } \right) = c \left( \pmb { \sigma } + t ^ { * } \pmb { \nu } \right) ,
+$$
+
+where t∗ = argmin $\{ t | { \pmb { o } } + t { \pmb { v } } = { \pmb { p } }$ , $\pmb { p } \in \partial \Omega$ , $t \in ( 0 , \infty ) \}$ . $\partial \Omega$ represents geometry surfaces. The assumption is appropriate because light that transmits through the opaque object can be omitted. The intensity of light decays to about zero drastically when passing through the surface of the opaque object. Let us represent the surface of the object mathematically with the signed distance function. The signed distance function $s d f ( \pmb { p } )$ is the signed distance between a spatial point $\pmb { p }$ and the surface $\partial \varOmega$ . In this way, the surface $\partial \varOmega$ can be represented as:
+
+$$
+\partial \varOmega = \left\{ p | s d f \left( p \right) = 0 \right\} .
+$$
+
+With neural volume rendering, we estimate the signed distance function $s { \hat { d } } f$ and color field $\hat { c }$ by Multi-Layer Perceptron (MLP) networks $F _ { \Theta }$ and $G _ { \Phi }$ :
+
+$$
+s \hat { d } f \left( \pmb { p } \right) = F _ { \Theta } \left( \pmb { p } \right) ,
+$$
+
+$$
+\hat { c } \left( \pmb { \sigma } , \pmb { \nu } , t \right) = G _ { \Phi } \left( \pmb { \sigma } , \pmb { \nu } , t \right) .
+$$
+
+Thus the estimated colors of the image with camera position $\pmb { o }$ can be represented as:
+
+$$
+\hat { C } = \int _ { 0 } ^ { + \infty } w \left( t \right) \hat { c } \left( t \right) d t ,
+$$
+
+where $t$ is the depth along the ray that comes from $\mathbf { \delta } _ { \pmb { o } }$ with the direction $\nu$ and $w ( t )$ is a weight for the point at $t$ . For simplicity, the notes $\mathbf { \delta } _ { \pmb { o } }$ and $\nu$ are omitted. To obtain discrete counterparts of $w$ and $\hat { c }$ we also sample $t _ { i }$ discretely along the ray and use the Riemann sum:
+
+$$
+\hat { C } = \sum _ { i = 1 } ^ { n } w \left( t _ { i } \right) \hat { c } \left( t _ { i } \right) .
+$$
+
+Following NeuS [35], $w ( t _ { i } )$ is computed as $w ( t _ { i } ) = T ( t _ { i } ) \alpha ( t _ { i } )$ , where $\begin{array} { r } { T ( t _ { i } ) = \prod _ { j = 1 } ^ { i - 1 } ( 1 - \alpha ( t _ { j } ) ) } \end{array}$ represents accumulated transmittance, $\begin{array} { r } { \alpha ( t _ { i } ) = \operatorname* { m a x } ( \frac { \Phi _ { s } ( s d f ( p _ { i } ) ) - \Phi _ { s } ( s d f ( p _ { i + 1 } ) ) } { \Phi _ { s } ( s d f ( p _ { i } ) ) } , 0 ) } \end{array}$ j=1is opacity, and $\pmb { p } _ { i }$ represents the sampled spatial point at $t _ { i }$ . $\Phi _ { s } ( x ) = ( 1 + e ^ { - s x } ) ^ { - 1 }$ is a Sigmoid function, where $s$ is a learnable parameter which controls the smoothness of the transition at the surface.
+
+Notably, the goal of novel view synthesis is to make an accurate prediction of the colors $\hat { C }$ , and bend efforts to minimize the difference between the colors of ground truth images $C$ and the prediction $\hat { C }$ :
+
+$$
+C = \hat { C } = \sum _ { i = 1 } ^ { n } w \left( t _ { i } \right) \hat { c } \left( t _ { i } \right) .
+$$
+
+In surface reconstruction tasks, what we concentrate more is the surface of the object rather than the color. In this way, the above formula can be rewritten as:
+
+$$
+\begin{array} { l } { { \displaystyle C = \sum _ { i = 1 } ^ { j - 1 } w \left( t _ { i } \right) \hat { c } \left( t _ { i } \right) + w \left( t _ { j } \right) \hat { c } \left( \hat { t ^ { * } } \right) + w \left( t _ { j } \right) \left( \hat { c } \left( t _ { j } \right) - \hat { c } \left( \hat { t ^ { * } } \right) \right) + \sum _ { i = j + 1 } ^ { n } w \left( t _ { i } \right) \hat { c } \left( t _ { i } \right) } } \\ { { \displaystyle ~ = w \left( t _ { j } \right) \hat { c } \left( \hat { t ^ { * } } \right) + \varepsilon _ { s a m p l e } + \sum _ { i = 1 } ^ { n } w \left( t _ { i } \right) \hat { c } \left( t _ { i } \right) } } \\ { { \displaystyle ~ = w \left( t _ { j } \right) \hat { c } \left( \hat { t ^ { * } } \right) + \varepsilon _ { s a m p l e } + \varepsilon _ { w e i g h t } } , } \end{array}
+$$
+
+where $s \hat { d } f ( \hat { t ^ { * } } ) = 0$ , $t _ { j }$ denotes the nearest sample point from $\hat { t ^ { * } }$ , $\varepsilon _ { s a m p l e }$ denotes the bias caused by sampling operation and $\varepsilon _ { w e i g h t }$ denotes the bias caused by weighted sum operation of volume rendering. With Formula (2), it can be rewritten as:
+
+$$
+w \left( t _ { j } \right) \hat { c } \left( \hat { t ^ { * } } \right) + \varepsilon _ { s a m p l e } + \varepsilon _ { w e i g h t } = c \left( t ^ { * } \right) ,
+$$
+
+$$
+\hat { c } \left( t ^ { * } \right) = \frac { c \left( t ^ { * } \right) - \varepsilon _ { s a m p l e } - \varepsilon _ { w e i g h t } } { w \left( t _ { j } \right) } .
+$$
+
+There the total bias between the colors of object surface and estimated surface is:
+
+$$
+\Delta c = \hat { c } \left( \hat { t ^ { * } } \right) - c \left( t ^ { * } \right) = \frac { ( 1 - w \left( t _ { j } \right) ) c \left( t ^ { * } \right) - \varepsilon _ { s a m p l e } - \varepsilon _ { w e i g h t } } { w \left( t _ { j } \right) } .
+$$
+
+The relative bias is:
+
+$$
+\delta c = \frac { \Delta c } { c \left( t ^ { * } \right) } = \frac { 1 } { w \left( t _ { j } \right) } - 1 - \frac { \varepsilon _ { s a m p l e } + \varepsilon _ { w e i g h t } } { w \left( t _ { j } \right) c \left( t ^ { * } \right) } .
+$$
+
+When $w \left( t _ { j } \right)$ approaches to 1 $, \varepsilon _ { w e i g h t }$ approaches to 0 and $\delta c$ approaches to $\varepsilon _ { s a m p l e } \Big / c \big ( t ^ { * } \big )$ . In this case, the total bias is only caused by discrete sampling, which is small (but still exists). Simulated weights of some existing neural reconstruction methods are shown in Fig. 3. As can be seen, it is nearly impossible to get right there in practice, especially without any geometric constraints. Furthermore, the problem becomes more intractable when dealing with cases of occlusion. Therefore, the weighted manner of volume rendering integral introduces a bias to implicit geometry modeling. Because the supervision of the whole network almost depends exclusively on the difference between rendered colors and ground truth colors, the bias would make it difficult to supervise the colors of surface and the SDF network, leading to a gap between the colors and the geometry.
+
+![](images/9e4e9c119ac41a43ccfce41ffc4f5c370512d6c1e2b27ddbdd2b5c790a4f6136.jpg)  
+Figure 3: Simulated weight in color rendering process of neural reconstruction methods.
+
+A trivial solution is to directly supervise the geometry of the object. In this way, we design explicit supervision on the SDF network and geometry-consistent supervision with multi-view constraints.
+
+# 3.2 Explicit supervision on SDF network
+
+The SDF network, which estimates the signed distance from any spatial point to the surface of the object, is the key network that we need to optimize. So we propose an explicit supervision method on the SDF network to ensure its accuracy directly with points in 3D space.
+
+For less extra cost, we use points generated by structure from motion (SFM) [29, 33] to supervise the SDF network. In fact, SFM is a canonical solution to compute the camera parameters of input images, where 2D feature matches $X$ and sparse 3D points $P$ are also generated as byproducts. Thus, these sparse 3D points can be used as "free" explicit geometry information. Approximately, we suppose that these sparse points are on the surface of the object. That is, the SDF values of the sparse points are zeroes: sdf $( \bar { { \pmb p } _ { i } } ) = 0$ , where $\pmb { p } _ { i } \in \pmb { P }$ . In practice, after obtaining sparse 3D points, a radius filter is applied to exclude some outliers [46].
+
+Occlusion handling. Because we focus on opaque objects, some parts of objects are invisible from view of a certain camera position. Therefore, there are only some of the sparse points visible for each view. For an image $I _ { i }$ with camera position $\mathbf { \delta } _ { \pmb { o } _ { i } }$ , the visible points $\mathbf { \nabla } P _ { i }$ are consistent with feature points $X _ { i }$ of $I _ { i }$ :
+
+$$
+X _ { i } = K _ { i } \left[ { \pmb R } _ { i } | { \pmb t } _ { i } \right] P _ { i } ,
+$$
+
+where $\pmb { K } _ { i }$ is the internal calibration matrix, $\pmb { R } _ { i }$ is the rotation matrix and $t _ { i }$ is the translation vector for image $I _ { i }$ . The coordinates of $X _ { i }$ and $\mathbf { \nabla } P _ { i }$ are all homogeneous coordinates. The scale index before $X _ { i }$ is omitted for simplicity. According to feature points of each image, we get visible points for each view and use them to supervise the SDF network while rendering image from the corresponding view.
+
+View-aware SDF loss. While rendering image $I _ { i }$ from view $V _ { i }$ , we use the SDF network to estimate SDF values for the visible points $\mathbf { \nabla } P _ { i }$ of $V _ { i }$ (see supplementary for the SDF loss by random sampling from sparse 3D points). Based on the approximation that the SDF values of sparse points are zeroes, we propose the view-aware SDF loss:
+
+$$
+\mathcal { L } _ { S D F } = \sum _ { \pmb { p _ { j } \in P _ { i } } } \frac { 1 } { N _ { i } } | s \hat { d } f \left( \pmb { p _ { j } } \right) - s d f \left( \pmb { p _ { j } } \right) | = \sum _ { \pmb { p _ { j } \in P _ { i } } } \frac { 1 } { N _ { i } } | s \hat { d } f \left( \pmb { p _ { j } } \right) | ,
+$$
+
+where $N _ { i }$ is the number of points in $\mathbf { \nabla } P _ { i }$ and $| \cdot |$ denotes the $L _ { 1 }$ distance. It is worth noting that the loss we use to supervise the SDF network varies according to the view being rendered. In this way, the introduced SDF loss is consistent with the process of color rendering.
+
+With the explicit supervision on the SDF network, our network could converge faster owing to the use of geometry prior. Besides, because the complex geometric structures with strong textures are the concentrated distribution areas of the sparse points, our method could capture more meticulous geometries.
+
+# 3.3 Geometry-consistent supervision with multi-view constraints
+
+With SDF loss, our network could capture complex geometric details with strong textures. Since the sparse 3D points mainly provide the explicit constraints on the areas with rich textures, large smooth regions still lack explicit geometry constraints. To go a step further, we design geometry-consistent supervision on the implicit surface with multi-view stereo constraints.
+
+Occlusion-aware implicit surface capture. We use the implicit representation of the surface, and extract surface with the zero-level set of the implicit function. So the question is: Where is our implicit surface? According to Formula (3), the estimated surface is:
+
+$$
+\hat { \partial \Omega } = \left\{ \pmb { p } | s \hat { d } f ( \pmb { p } ) = 0 \right\} .
+$$
+
+We aim to optimize $ { \partial }  { \hat { \boldsymbol { \Omega } } }$ with geometry-consistent constraints among different views. Because the number of points on the surface is infinite, we need to sample points from $ { \partial }  { \hat { \varOmega } }$ in practice. To maintain consistency with the process of color rendering using view rays, we sample the surface points on these rays. As mentioned in 3.1, we sample $t$ discretely along the view ray and use the Riemann sum to obtain the rendered colors. Based on the sampled points, we use linear interpolation to get the surface points, which is similar to the root-finding used in [25, 26] to estimate the surface.
+
+Specifically, with sampled point $t$ on the ray, the corresponding 3D point is $\pmb { p } = \pmb { o } + t \pmb { \nu }$ , and the predicted SDF value is $s { \hat { d } } f ( \pmb { p } )$ . For simplicity, we further represent $s d f ( \pmb { p } )$ as $s { \hat { d } } f ( t )$ , which is the function of $t$ . We find the sample point $t _ { i }$ , the sign of whose SDF value is different from the next sample point $t _ { i + 1 }$ . The sample points set $T$ formed by $t _ { i }$ is:
+
+$$
+T = \left\{ t _ { i } | s \hat { d } f ( t _ { i } ) \cdot s \hat { d } f ( t _ { i + 1 } ) < 0 \right\} .
+$$
+
+In this situation, the line $t _ { i } t _ { i + 1 }$ intersects with the surface $ { \partial }  { \hat { \varOmega } }$ . The intersection points set $\hat { T } ^ { * }$ is:
+
+$$
+\hat { T ^ { * } } = \left\{ t | t = \frac { s \hat { d } f ( t _ { i } ) t _ { i + 1 } - s \hat { d } f ( t _ { i + 1 } ) t _ { i } } { s \hat { d } f ( t _ { i } ) - s \hat { d } f ( t _ { i + 1 } ) } , t _ { i } \in T \right\} .
+$$
+
+The ray that interacts with the object may have more than one intersection with the surface. Specifically speaking, there may be at least two intersections. Similar to the SDF supervision mechanism, we just use the first intersection point along the ray considering the occlusion problem:
+
+$$
+t ^ { * } = \mathrm { a r g m i n } \left. t | t \in \hat { T ^ { * } } \right. .
+$$
+
+The selection of $t ^ { * }$ guarantees the sample points of the implicit surface are all visible for the corresponding view and makes the supervision consistent with the process of color rendering.
+
+Multi-view photometric consistency constraints. We capture our estimated implicit surface, of which the geometric structures are supposed to be consistent among different views. Based on this intuition, we use the photometric consistency constraints in multi-view stereo (MVS) [9, 37, 10] to supervise our extracted implicit surface.
+
+For a small area $s$ on the surface, the projection of $s$ on the image is a small pixel patch $q$ . The patches corresponding to $s$ are supposed to be geometry-consistent among different views, except for occlusion occasions. Similar to patch warping in traditional MVS methods, we use the central point and its normal to represent $s$ . For convenience, we represent the plane equation of $s$ in the camera coordinate of the reference image $I _ { r }$ :
+
+$$
+\pmb { n } ^ { T } \pmb { p } + d = 0 ,
+$$
+
+where $\pmb { p }$ is the intersection point computed through Formula (19) and ${ \pmb n } ^ { T }$ is the normal computed with automatic differentiation of SDF network at $\pmb { p }$ . Then the image point $\boldsymbol { x }$ in the pixel patch $q _ { i }$ of reference image $I _ { r }$ is related to the corresponding point $ { \boldsymbol { { x } } } ^ { \prime }$ in the pixel patch $q _ { i s }$ of the source image $I _ { s }$ via the plane-induced homography $\pmb { H }$ [12]:
+
+$$
+\pmb { x } = \pmb { H } \pmb { x } ^ { \prime } , \pmb { H } = \pmb { K } _ { s } ( \pmb { R } _ { s } \pmb { R } _ { r } ^ { T } - \frac { \pmb { R } _ { s } ( \pmb { R } _ { s } ^ { T } \pmb { t } _ { s } - \pmb { R } _ { r } ^ { T } \pmb { t } _ { r } ) \pmb { n } ^ { T } } { \pmb { d } } ) \pmb { K } _ { r } ^ { - 1 } ,
+$$
+
+where $\pmb { K }$ donates the intrinsic matrix, $\pmb { R }$ donates the rotation matrix and $t$ donates the translation vector. The index indicates which image the donation belongs to. To concentrate on the geometric information, we convert color images $\{ I _ { i } \}$ into gray images $\left\{ { { I } _ { i } ^ { \prime } } \right\}$ , and supervise our implicit surface with the photometric consistency among patches in $\{ I _ { i } ^ { \prime } \}$ (see supplementary for RGB image settings).
+
+Photometric consistency loss. To measure the photometric consistency, we use the normalization cross correlation (NCC) of patches in the reference gray image $\left\{ I _ { r } ^ { \prime } \right\}$ and the source gray image $\{ I _ { s } ^ { \prime } \}$ :
+
+$$
+N C C ( I _ { r } ^ { \prime } ( q _ { i } ) , I _ { s } ^ { \prime } ( q _ { i s } ) ) = \frac { C o v ( I _ { r } ^ { \prime } ( q _ { i } ) , I _ { s } ^ { \prime } ( q _ { i s } ) ) } { \sqrt { V a r ( I _ { r } ^ { \prime } ( q _ { i } ) ) V a r ( I _ { s } ^ { \prime } ( q _ { i s } ) ) } } ,
+$$
+
+where $C o v$ denotes covariance and $V a r$ donates variance. While rendering colors for an image, we use the patches which take the pixels being rendered as center and the patch size is $1 1 \times 1 1$ . We take the rendered image as the reference image and compute NCC scores between its sampled patches and their corresponding patches on all source images. To handle occlusions, we find the best four of the computed NCC scores for each sampled patch following [10], and use them to compute the photometric consistency loss for the corresponding view:
+
+$$
+\mathcal { L } _ { p h o t o } = \frac { \sum _ { i = 1 } ^ { N } \sum _ { s = 1 } ^ { 4 } 1 - N C C ( I _ { r } ^ { \prime } ( q _ { i } ) , I _ { s } ^ { \prime } ( q _ { i s } ) ) } { 4 N } ,
+$$
+
+where $N$ is the number of sampled pixels on the rendered image. With the photometric consistency loss, the geometric consistency of the implicit surface among multiple views is guaranteed.
+
+# 3.4 Loss function
+
+During rendering colors from a specific view, our total loss is:
+
+$$
+\mathcal { L } = \mathcal { L } _ { c o l o r } + \alpha \mathcal { L } _ { r e g } + \beta \mathcal { L } _ { S D F } + \gamma \mathcal { L } _ { p h o t o } .
+$$
+
+$\mathcal { L } _ { c o l o r }$ is the difference between the ground truth colors and the rendered colors:
+
+$$
+\mathcal { L } _ { c o l o r } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } | C _ { i } - \hat { C } _ { i } | .
+$$
+
+And $\mathcal { L } _ { \boldsymbol { r } \boldsymbol { e } \boldsymbol { g } }$ is an eikonal term [11] to regularize the gradients of SDF network:
+
+$$
+\mathcal { L } _ { r e g } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } { \left( | \nabla \hat { s d f } ( \pmb { p } _ { i } ) | - 1 \right) ^ { 2 } } .
+$$
+
+In our experiments, we choose $\alpha$ , $\beta$ and $\gamma$ as 0.1, 1.0 and 0.5 respectively.
+
+# 4 Experiments
+
+# 4.1 Experimental setting
+
+Datasets. Following previous practices [43, 35, 42], we reconstruct surfaces from 15 scans of DTU dataset [1] to evaluate our method. DTU dataset has objects of various categories, which are quite different in terms of appearance and geometries. There are 49 or 64 images at a resolution of $1 2 0 0 \times$ 1600 in each scan with camera parameters. We also test on 7 challenging scenes from the low-res set of the BlendedMVS dataset [41] (CC-4 License). Scenes in BlendedMVS have various numbers of views and camera parameters. The scenes are captured by images at a resolution of $7 6 8 \times 5 7 6$ , and the numbers of views vary from 31 to 143. We evaluate our reconstructed surfaces on DTU dataset with the Chamfer Distance provided by DTU evaluation metrics [1]. For the BlendedMVS dataset, we show the visual effects of the reconstructed surfaces.
+
+Baselines. To better evaluate our method, we compare it with the-state-of-art learning-based methods and the traditional reconstruction method, colmap [30]. For learning-based methods, we compare with IDR [43], VolSDF [42], NeuS [35] and NeuralWarp [7]. For colmap, we use the reconstructed surface with trim parameter 7 (the best performance) [26].
+
+Implementation details. Similar to [43, 35, 42], the SDF network is modeled by an 8-layer MLP with 256 hidden units and a skip connection in the middle. It is initialized by the geometric initialization presented in [2]. The radiance network is parameterized by a 4-layer MLP with 256 hidden units. Positional encoding [20] is applied to 3D location with 6 frequencies and to viewing direction with 4 frequencies. We sample 512 rays per batch and follow the hierarchical sampling strategy in NeuS [35] to sample points for each ray. We train our model for $3 0 0 \mathrm { k }$ iterations for around 16 hours on a single NVIDIA RTX2080Ti GPU. After network training, a mesh can be extracted from the SDF in a predefined bounding box by the Marching Cube [19] with the volume size of $5 1 2 ^ { 3 }$
+
+# 4.2 Comparisons
+
+We compare the reconstruction quality of our method and baselines on DTU dataset. Table 1 shows the quantitative results. Notably, our method outperforms baselines by a large margin. Specifically, it outperforms state-of-the-art neural implicit surfaces learning methods by over $2 5 \%$ and outperforms the traditional method colmap by $2 2 \%$ . As shown qualitatively in Fig. 4, our method achieves high-quality surface reconstruction in both complex thin structures and large smooth regions. For example, our method can recover abrupt depth changes in Scan 37 and reconstruct planar structures in Scan 24 and 40. To test the capability of handling
+
+Table 1: Results on DTU scenes. The surfaces produced by colmap are trimmed with trimming value 7.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>with mask</td><td rowspan=1 colspan=5>without mask</td></tr><tr><td rowspan=1 colspan=1>Scan</td><td rowspan=1 colspan=1>IDR</td><td rowspan=1 colspan=1>NeuS</td><td rowspan=1 colspan=1>VolSDF</td><td rowspan=1 colspan=1>NeuS</td><td rowspan=1 colspan=1>NeuralWarp</td><td rowspan=1 colspan=1>colmap</td><td rowspan=1 colspan=1>Ours</td></tr><tr><td rowspan=1 colspan=1>37</td><td rowspan=1 colspan=1>1.87</td><td rowspan=1 colspan=1>0.95</td><td rowspan=1 colspan=1>1.26</td><td rowspan=1 colspan=1>1.21</td><td rowspan=1 colspan=1>0.71</td><td rowspan=1 colspan=1>0.91</td><td></td></tr><tr><td></td><td rowspan=3 colspan=1>0.63</td><td></td><td rowspan=3 colspan=1>0.81</td><td rowspan=3 colspan=1>0.73</td><td rowspan=3 colspan=1>0.38</td><td rowspan=3 colspan=1>0.37</td><td></td></tr><tr><td></td><td></td><td rowspan=2 colspan=1>0.5370.336</td></tr><tr><td rowspan=1 colspan=1>40</td><td rowspan=1 colspan=1>0.80</td></tr><tr><td rowspan=1 colspan=1>55</td><td rowspan=1 colspan=1>0.48</td><td rowspan=1 colspan=1>0.39</td><td rowspan=1 colspan=1>0.49</td><td rowspan=1 colspan=1>0.40</td><td rowspan=1 colspan=1>0.38</td><td rowspan=1 colspan=1>0.37</td><td rowspan=1 colspan=1>0.357</td></tr><tr><td rowspan=1 colspan=1>63</td><td rowspan=1 colspan=1>1.04</td><td rowspan=1 colspan=1>1.26</td><td rowspan=1 colspan=1>1.25</td><td rowspan=1 colspan=1>1.20</td><td rowspan=1 colspan=1>0.79</td><td rowspan=1 colspan=1>0.90</td><td rowspan=1 colspan=1>0.800</td></tr><tr><td rowspan=1 colspan=1>65</td><td rowspan=1 colspan=1>0.79</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>0.70</td><td rowspan=1 colspan=1>0.70</td><td rowspan=1 colspan=1>0.81</td><td rowspan=1 colspan=1>1.00</td><td rowspan=1 colspan=1>0.454</td></tr><tr><td rowspan=1 colspan=1>69</td><td rowspan=1 colspan=1>0.77</td><td rowspan=1 colspan=1>0.69</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>0.72</td><td rowspan=1 colspan=1>0.82</td><td rowspan=1 colspan=1>0.54</td><td rowspan=1 colspan=1>0.408</td></tr><tr><td rowspan=1 colspan=1>83</td><td rowspan=1 colspan=1>1.33</td><td rowspan=1 colspan=1>0.94</td><td rowspan=1 colspan=1>1.29</td><td rowspan=1 colspan=1>1.01</td><td rowspan=1 colspan=1>1.20</td><td rowspan=1 colspan=1>1.22</td><td rowspan=1 colspan=1>1.032</td></tr><tr><td rowspan=1 colspan=1>97</td><td rowspan=1 colspan=1>1.16</td><td rowspan=1 colspan=1>1.14</td><td rowspan=1 colspan=1>1.18</td><td rowspan=1 colspan=1>1.16</td><td rowspan=1 colspan=1>1.06</td><td rowspan=1 colspan=1>1.08</td><td rowspan=1 colspan=1>0.843</td></tr><tr><td rowspan=1 colspan=1>105</td><td rowspan=1 colspan=1>0.76</td><td rowspan=1 colspan=1>0.77</td><td rowspan=1 colspan=1>0.70</td><td rowspan=1 colspan=1>0.82</td><td rowspan=1 colspan=1>0.68</td><td rowspan=1 colspan=1>0.64</td><td rowspan=1 colspan=1>0.548</td></tr><tr><td rowspan=1 colspan=1>106</td><td rowspan=1 colspan=1>0.67</td><td rowspan=1 colspan=1>0.66</td><td rowspan=1 colspan=1>0.66</td><td rowspan=1 colspan=1>0.66</td><td rowspan=1 colspan=1>0.66</td><td rowspan=1 colspan=1>0.48</td><td rowspan=1 colspan=1>0.460</td></tr><tr><td rowspan=1 colspan=1>110</td><td rowspan=1 colspan=1>0.90</td><td rowspan=1 colspan=1>1.35</td><td rowspan=1 colspan=1>1.08</td><td rowspan=1 colspan=1>1.69</td><td rowspan=1 colspan=1>0.74</td><td rowspan=1 colspan=1>0.59</td><td rowspan=2 colspan=1>0.4730.294</td></tr><tr><td rowspan=1 colspan=1>114</td><td rowspan=1 colspan=1>0.42</td><td rowspan=1 colspan=1>0.39</td><td rowspan=1 colspan=1>0.42</td><td rowspan=1 colspan=1>0.39</td><td rowspan=1 colspan=1>0.41</td><td rowspan=1 colspan=1>0.32</td></tr><tr><td rowspan=2 colspan=1>118122</td><td rowspan=1 colspan=1>0.51</td><td rowspan=1 colspan=1>0.51</td><td rowspan=1 colspan=1>0.61</td><td rowspan=1 colspan=1>0.49</td><td rowspan=1 colspan=1>0.63</td><td rowspan=1 colspan=1>0.45</td><td rowspan=1 colspan=1>0.355</td></tr><tr><td rowspan=1 colspan=1>0.53</td><td rowspan=1 colspan=1>0.52</td><td rowspan=1 colspan=1>0.55</td><td rowspan=1 colspan=1>0.51</td><td rowspan=1 colspan=1>0.51</td><td rowspan=1 colspan=1>0.43</td><td rowspan=1 colspan=1>0.345</td></tr><tr><td rowspan=1 colspan=1>mean</td><td rowspan=1 colspan=1>0.90</td><td rowspan=1 colspan=1>0.82</td><td rowspan=1 colspan=1>0.86</td><td rowspan=1 colspan=1>0.87</td><td rowspan=1 colspan=1>0.68</td><td rowspan=1 colspan=1>0.65</td><td rowspan=1 colspan=1>0.508</td></tr></table>
+
+![](images/cb73f9cdbdd42118bd011d9fbfd86cd6b9ab775c99c884efef12e705d90a773a.jpg)  
+Figure 4: Surfaces reconstructed on DTU and BlendedMVS. We use NeuS trained with mask supervision and colmap with trimming value 7 (see supplementary for comparison with NeuralWarp).
+
+![](images/76152ed8adc8f74884a1cc6e8beeec59d9be8245837557a6452c4ce040d7a6e6.jpg)  
+Figure 5: Surface quality of ablation models.
+
+various scenes, we test on 7 challenging   
+scenes of the BlendedMVS dataset. Qualitative results in Fig. 4 show that our method yields more smooth and consistent surface quality than other methods.
+
+# 4.3 Analysis
+
+Ablation study. To evaluate the effect of our proposed contributions, we conduct an ablation study on DTU dataset. NeuS is adopted as our baseline. Different modules are progressively added to the baseline to investigate their efficacy. Results are reported in Table 2. We see that, with very sparse 3D supervision on SDF networks, Model-A has begun to outperform colmap (0.62 vs 0.65). This demonstrates that explicit SDF optimization is very beneficial to improve geometries. With the proposed photometric consistency loss, Model-B can optimize SDF networks more completely, leading to much more performance improvement. Fig. 5 shows how the proposed loss functions improve the surface quality. Model-A reconstructs the apple stem finely but the surface is not smooth enough. Model-B reconstructs the smooth surface but the apple stem is lost. That is, the SDF loss is better to improve the reconstruction of complex thin structures, while the photometric loss is better for the reconstruction of large smooth regions. Moreover, our full model, Geo-Neus absorbs their individual advantages and achieves the best performance.
+
+Geometry bias of volumetric integration. To further investigate the geometric bias of volumetric integration, we render the depth images from a particular pose in a similar fashion to rendering RGB pixels [20] (see supplementary for details), and then use the depth images to construct sparse 3D points and photometric consistency constraints. NeuS is also used as the baseline. Comparison results are shown in Table 3. As can be seen, compared with baseline (0.87), multi-view geometry constraints with depth integral bring little performance improvement or even degradation. It is a remarkable fact that photometric consistency supervision with depth integral surface location could not converge because of the initial immense bias while the SDF location model converges smoothly. As an alternative, we train these two models based on the baseline model pretrained with $2 0 0 \mathrm { k }$ iterations. The result of the depth integral model still degrades compared with the baseline. This verifies the existence of geometric bias in volumetric integration. With our proposed SDF-oriented optimization, surface reconstruction quality can be significantly boosted.
+
+Table 2: Ablation study on DTU scenes.   
+
+<table><tr><td>Method</td><td>Lcolor</td><td>LsDF</td><td>Lphoto</td><td>mean</td></tr><tr><td>Baseline</td><td>√</td><td></td><td></td><td>0.87</td></tr><tr><td>Model-A</td><td></td><td>厂</td><td></td><td>0.62</td></tr><tr><td>Model-B</td><td></td><td></td><td></td><td>0.54</td></tr><tr><td>Geo-Neus</td><td></td><td></td><td></td><td>0.51</td></tr></table>
+
+<table><tr><td rowspan=1 colspan=1>Constraint</td><td rowspan=1 colspan=1>Setting</td><td rowspan=1 colspan=1>mean</td></tr><tr><td rowspan=1 colspan=1>Sparse 3D points</td><td rowspan=1 colspan=1>DepthintegralSDF location</td><td rowspan=1 colspan=1>0.850.62</td></tr><tr><td rowspan=1 colspan=1>Photometric consistency</td><td rowspan=1 colspan=1>DepthintegralSDF location</td><td rowspan=1 colspan=1>1.080.57</td></tr></table>
+
+Table 3: Comparison results between depth integral and SDF location.
+
+Convergence speed. We further study the convergence speed of our proposed method, Geo-Neus, and baseline, NeuS. As shown in Fig. 6, our method converges rapidly from scratch and becomes stable after $2 0 0 \mathrm { k }$ iterations. In contrast, NeuS cannot extract the reasonable surface from SDF networks in the beginning and starts to become stable after $2 5 0 \mathrm { k }$ iterations. This demonstrates that our proposed explicit SDF optimization also improves the efficiency of neural surfaces learning by volume rendering, reducing the training time from around 16 hours to around 10 hours.
+
+Limitation. We show failure cases of our method on scenes with strong specular highlights and transparent objects. Fig. 7(a) shows our reconstructed surfaces on the scene with strong specular highlights, DTU scan77. In this case, the strong specular highlights lead to large view-dependent effects, making the multi-view photometric consistency loss unable to reliably measure multi-view geometry constraints. Thus, our method cannot produce satisfactory surfaces in this case. In addition, Fig. 7(b) shows our reconstructed surfaces on the scene with transparent objects [13]. As proposed in Sec. 3.1, we assume the target objects are all opaque and solid. For transparent objects, the proposed bias between rendered colors and implicit geometry is invalid. Furthermore, the geometric loss we proposed may not work well, just like the photometric consistency used in traditional reconstruction methods.
+
+![](images/99ec3e33b7a24f38900cd11c343f1137e1b9f4c05021d17d11436c245638805c.jpg)  
+Figure 6: Convergence speed.
+
+![](images/1b534d2462c2d1abfe4c3b537e35bbf0cc1db2b68d97a654007530e4ecc586e8.jpg)  
+Figure 7: Failure cases.
+
+# 5 Conclusion
+
+We have proposed Geo-Neus, a new method to perform neural implicit surfaces learning by enforcing explicit SDF optimization. In our paper, we first provide the theoretical analysis that there exists a gap between volume rendering integration and neural SDF learning. With this theoretical support, we propose to explicitly optimize neural SDF learning by introducing two multi-view geometry constraints: sparse 3D points in structure from motion and photometric consistency in multi-view stereo. In this way, Geo-Neus produces high-quality surface reconstruction in both complex thin structures and large smooth regions. Therefore, it outperforms the state-of-the-arts by a large margin, including both traditional and neural implicit surfaces learning methods. We note that although our method greatly improves reconstruction quality, its efficiency is still limited. In the future, it will be interesting to explore accelerating neural implicit surfaces learning by volume rendering through super-fast per-scene radiance field optimization methods [34, 24]. We don’t see an immediate negative societal impact of our work, but accurate 3D models may be used from malevolence.
+
+Acknowledgments This work was in part supported by the National Natural Science Foundation of China under Grants 62176096 and 61991412, the Data Science and Artificial Intelligence Research Center (DSAIR), School of Computer Science and Engineering, Nanyang Technological University and the A\*Star Center for Frontier AI Research (CFAR).
+
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+
+# Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes] See Section 4.3.   
+(c) Did you discuss any potential negative societal impacts of your work? [Yes] See Section 5.   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you are including theoretical results...
+
+(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Section 3.1.   
+(b) Did you include complete proofs of all theoretical results? [Yes] See Section 3.1.
+
+3. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [No] We plan to release the code completely but have not yet with submission.
+
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Section 4.1.   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [No]   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See Section 4.1.
+
+4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] See Section 4.1.   
+(b) Did you mention the license of the assets? [Yes] See Section 4.1.   
+(c) Did you include any new assets either in the supplemental material or as a URL? [No]   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [N/A]   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
+
+5. If you used crowdsourcing or conducted research with human subjects...
+
+(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]   
+(b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A]   
+(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]

parse/dev/MR7XubKUFB/MR7XubKUFB.md

@@ -0,0 +1,445 @@
+# ADVERSARIAL RETRIEVER-RANKER FOR DENSE TEXT RETRIEVAL
+
+Hang Zhang1∗, Yeyun Gong2†, Yelong Shen3, Jiancheng $\mathbf { L } \mathbf { v } ^ { 1 }$ , Nan Duan2, Weizhu Chen3
+
+1College of Computer Science, Sichuan University,   
+2Microsoft Research Asia, 3Microsoft Azure AI   
+hangzhang scu@foxmail.com,{yegong,yelong.shen}@microsoft.com,   
+lvjiancheng@scu.edu.cn, {nanduan,wzchen}@microsoft.com
+
+# ABSTRACT
+
+Current dense text retrieval models face two typical challenges. First, they adopt a siamese dual-encoder architecture to encode queries and documents independently for fast indexing and searching, while neglecting the finer-grained termwise interactions. This results in a sub-optimal recall performance. Second, their model training highly relies on a negative sampling technique to build up the negative documents in their contrastive losses. To address these challenges, we present Adversarial Retriever-Ranker (AR2), which consists of a dual-encoder retriever plus a cross-encoder ranker. The two models are jointly optimized according to a minimax adversarial objective: the retriever learns to retrieve negative documents to cheat the ranker, while the ranker learns to rank a collection of candidates including both the ground-truth and the retrieved ones, as well as providing progressive direct feedback to the dual-encoder retriever. Through this adversarial game, the retriever gradually produces harder negative documents to train a better ranker, whereas the cross-encoder ranker provides progressive feedback to improve retriever. We evaluate AR2 on three benchmarks. Experimental results show that AR2 consistently and significantly outperforms existing dense retriever methods and achieves new state-of-the-art results on all of them. This includes the improvements on Natural Questions $\mathbf { R } @ 5$ to $7 7 . 9 \%$ $( + 2 . 1 \% )$ , TriviaQA $\mathbf { R } @ 5$ to $7 8 . { \bar { 2 } } \%$ $( + 1 . 4 \% )$ , and MS-MARCO MRR $@ 1 0$ to $3 9 . 5 \%$ $( + 1 . 3 \% )$ . Code and models are available at https://github.com/microsoft/AR2.
+
+# 1 INTRODUCTION
+
+Dense text retrieval (Lee et al., 2019; Karpukhin et al., 2020) has achieved great successes in a wide variety of both research and industrial areas, such as search engines (Brickley et al., 2019; Shen et al., 2014), recommendation system (Hu et al., 2020), open-domain question answering (Guo et al., 2018; Liu et al., 2020), etc. A typical dense retrieval model adopts a dual-encoder (Huang et al., 2013) architecture to encode queries and documents into low-dimensional embedding vectors, with the relevance between query and document being measured by the similarity between embeddings. In real-world dense text retrieval applications, it pre-computes all the embedding vectors of documents in the corpus, and leverages the approximate nearest neighbor (ANN) (Johnson et al., 2019) technique for efficiency. To train a dense retriever, contrastive loss with negative samples is widely applied in the literature (Xiong et al., 2021; Karpukhin et al., 2020). During training, the model utilizes a negative sampling method to obtain negative documents for a given querydocument pair, and then minimizes the contrastive loss which relies on both the positive document and the sampled negative ones (Shen et al., 2014; Chen et al., 2017; Radford et al., 2021).
+
+Recent studies on contrastive learning (Xiong et al., 2021; Karpukhin et al., 2020) show that the iterative “hard-negative” sampling technique can significantly improve the performance compared with “random-negative” sampling approach, as it can pick more representative negative samples to … …learn a more discriminative retriever. In the work (Qu et al., 2021), it suggests leveraging crossquery documentencoder model to heuristically filter “hard-negative” samples to further improve performance and shows the importance of sampling technique in the contrastive learning.
+
+![](images/5e5bf19d07f1949b33be18db2543d959a08b45a74baf60171568fd5b53de55ff.jpg)  
+Figure 1: Illustration of two modules in AR2. (a) Retriever: query and document are encoded independently by a dual-encoder. (b) Ranker: concatenated, jointly encoded by a cross-encoder.
+
+On the other hand, the model architecture of dual-encoders enables the encoding of queries and documents independently which is essential for document indexing and fast retrieval. However, this ignores the modeling of finer-grained interactions between queries and documents which could be a sub-optimal solution in terms of retrieval accuracy.
+
+Motivated by these phenomena, we propose an Adversarial Retriever-Ranker (AR2) framework. The intuitive idea of AR2 is inspired by the “retriever-ranker” architecture in the classical information retrieval systems. AR2 consists of two modules: a dual-encoder model served as the retrieval module in Figure 1a and a cross-encoder model served as the ranker module in Figure 1b. The crossencoder model takes the concatenation of a query and document as input text, and can generate more accurate relevance scores compared with the dual-encoder model, since it can fully explore the interactions between the query and document through a self-attention mechanism using a conventional transformer model (Vaswani et al., 2017; Guo et al., 2020). Instead of training “retriever-ranker” modules independently in some IR systems (Manning et al., 2008; Mitra & Craswell, 2017), AR2 constructs a unified minimax game for training the retriever and ranker models interactively, as shown in Figure 2.
+
+In particular, AR2 adopts a minimax objective from the adversarial game (Goodfellow et al., 2014) where the retrieval model is optimized to produce relevant documents to fool the ranker model, whereas the ranker model learns to distinguish the ground-truth relevant document and retrieved ones by its opponent retrieval model. Within the adversarial “retriever-ranker” training framework, the retrieval model receives the smooth training signals from the ranker model which helps alleviate the harmful effects of “false-negative” issues. For example, a “false-negative” example which is rated as high-relevance by the ranker model, will also be granted with high probability by retrieval model in order to fool the ranker, meanwhile the ranker model with better generalization capability is more resistant to label noises compared to the retrieval model.
+
+In the empirical studies of AR2, we further introduce a distillation regularization approach to help stabilize/improve the training of the retriever. Intuitively, the retriever would converge to sharp conditionalprobabilities over documents given a query within the adversarial training framework, i.e., high retrieval probabilities for the top relevant documents and near-zero retrieval ones for the rest. However, it is not a desirable property as it might impede exploring different documents during training. Thus, we incorporate the distillation loss between the retriever and ranker models as a smooth term for further improvement.
+
+![](images/85c68087bda71924e2c7993414684ed5eed03fe0c65d0dff0374f0a4db869bcb.jpg)  
+Figure 2: Illustration of the AR2 training pipeline. $q , d ,$ , and $\mathbb { D } _ { q } ^ { - }$ represent the query, positive document, and retrieved documents, respectively.
+
+In experiments, we evaluate AR2 on three widely used benchmarks for dense text retrieval: Natural Questions, Trivia QA and MS-MARCO. Experimental results show that AR2 achieves state-of-theart performance on all these datasets. Meanwhile, we provide a comprehensive ablation study to demonstrate the advantage of different AR2 components.
+
+# 2 PRELIMINARIES
+
+Dense Text Retrieval: We mainly consider a contrastive-learning paradigm for dense text retrieval in this work, where the training set consists of a collection of text pairs. $C = \{ ( q _ { 1 } , d _ { 1 } ) , . . . , ( q _ { n } , d _ { n } ) \}$ . In the scenario of open-domain question answering, a text pair $( q , d )$ refers to a question and a corresponding document which contains the answer. A typical dense retrieval model adopts a dual encoder architecture, where questions and documents are represented as dense vectors separately and the relevance score $s _ { \theta } ( q , d )$ between them is measured by the similarity between their embeddings:
+
+$$
+s _ { \theta } ( q , d ) = \langle E ( q ; \theta ) , E ( d ; \theta ) ) \rangle
+$$
+
+where $E ( \cdot ; \theta )$ denotes the encoder module parameterized with $\theta$ , and $\langle \cdot \rangle$ is the similarity function, e.g., inner-product, Euclidean distance. Based on the embeddings, existing solutions generally leverage on-the-shelf fast ANN-search (Johnson et al., 2019) for efficiency.
+
+A conventional contrastive-learning algorithm could be applied for training the dual encoders (Shen et al., 2014; Chen et al., 2017; Liu et al., 2020). For example, given a training instance $( q , d )$ , we select $n$ negative irrelevant documents $( d _ { 1 } ^ { - } , . . . , d _ { n } ^ { - } )$ (denoted as $\mathbb { D } _ { q } ^ { - }$ ) to optimize the loss function of the negative log likelihood of the positive document:
+
+$$
+L _ { \theta } ( q , d , \mathbb { D } _ { q } ^ { - } ) = - \mathrm { l o g } \frac { e ^ { \tau s _ { \theta } ( q , d ) } } { e ^ { \tau s _ { \theta } ( q , d ) } + \sum _ { i = 1 } ^ { n } e ^ { \tau s _ { \theta } ( q , d _ { i } ^ { - } ) } }
+$$
+
+where $\tau$ is a hyper-parameter to control the temperature. Previous works (Shen et al., 2014; Chen et al., 2017; Liu et al., 2020) present an effective strategy on negative document sampling, called “InBatch Negatives” where negative documents are randomly sampled from a collection of documents which are within the same mini-batch as question-document training pairs.
+
+Recently, some studies e.g., ANCE (Xiong et al., 2021) and Condenser (Gao & Callan, 2021b), have shown that selecting “hard-negatives” in the training can significantly improve the retrieval performance in open-domain question answering. For example, instead of sampling negative document randomly, “hard-negatives” are iteratively retrieved through previous checkpoints of the dual encoder model. However, a more recent work RocketQA (Qu et al., 2021) continues to point out that the retrieved “hard-negatives” could potential be “false-negatives” in some cases, which might limit the performance.
+
+Generative Adversarial Network: GANs have been widely studied for generating the realisticlooking images in computation vision (Goodfellow et al., 2014; Brock et al., 2018). In the past few years, the idea of GANs has been applied in information retrieval (Wang et al., 2017). For example, IRGAN (Wang et al., 2017), proposes a minimax retrieval framework which constructs two types of IR models: a generative retrieval model and a discriminative retrieval model. The two IR models are optimized through a minimax game: the generative retrieval model generates relevant documents that look like ground-truth relevant documents to fool the discriminative retrieval model, whereas the discriminative retrieval model learns to draw a clear distinction between the groundtruth relevant documents and the generated ones made by its opponent generative retrieval model. The minimax objective is formulated as:
+
+$$
+\begin{array} { r } { J ^ { G ^ { * } , D ^ { * } } = \operatorname* { m i n } _ { \theta } \operatorname* { m a x } _ { \phi } \mathrm { E } _ { d \sim p _ { \mathrm { t w e } } ( \cdot \vert q ) } \left[ \log D _ { \phi } ( d , q ) \right] + \mathrm { E } _ { d ^ { - } \sim G _ { \theta } ( \cdot \vert q ) } \left[ \log \left( 1 - D _ { \phi } ( d ^ { - } , q ) \right) \right] } \end{array}
+$$
+
+where $G _ { \theta } ( \cdot | q )$ and $D _ { \phi } ( d ^ { - } , q )$ denote the generative retrieval model and discriminative retrieval model in IRGAN, respectively. It is worth noting the original IRGAN model doesn’t work for dense retrieval tasks as it doesn’t contain the dual-encoder model for document indexing or fast retrieval.
+
+# 3 METHOD
+
+In this section, we introduce the proposed adversarial retriever-ranker (AR2) approach. It consists of two modules: the dual-encoder retriever module $G _ { \theta }$ as in Figure 1a, and the cross-encoder ranker module $D _ { \phi }$ as in Figure 1b. $G _ { \theta }$ and $D _ { \phi }$ computes the relevance score between question and document as follows:
+
+$$
+\begin{array} { r l } & { G _ { \theta } ( q , d ) = E _ { \theta } ( q ) ^ { T } E _ { \theta } ( d ) } \\ & { D _ { \phi } ( q , d ) = \mathbf { w _ { \phi } } ^ { T } E _ { \phi } \left( [ q , d ] \right) } \end{array}
+$$
+
+where $E _ { \theta } ( \cdot )$ and $E _ { \phi } ( \cdot )$ are language model encoders which can be initialized with any pre-trained language model, $\mathbf { w } _ { \phi }$ is the linear projector in $D _ { \phi }$ , and $[ q , d ]$ is the concatenation of question and document.
+
+In AR2, the retriever and ranker modules are optimized jointly through a contrastive minimax objective:
+
+$$
+J ^ { G ^ { * } , D ^ { * } } = \operatorname* { m i n } _ { \theta } \mathrm { m a x } _ { \phi } { \bf E } _ { \mathbb { D } _ { q } ^ { - } \sim G _ { \theta } ( q , \cdot ) } \left[ \log p _ { \phi } ( d | q ; \mathbb { D } _ { q } ) \right]
+$$
+
+where $\mathbb { D } _ { q } ^ { - } \colon \{ d _ { i } ^ { - } \} _ { i = 1 } ^ { n }$ is the set of $n$ negative documents sampled by $G _ { \theta } ( \boldsymbol { q } , \cdot )$ given $q$ , and $p _ { \phi } ( d | q ; \mathbb { D } _ { q } )$ denotes the probability of selecting the ground-truth document $d$ from the document set $\mathbb { D } _ { q }$ $\mathbb { D } _ { q } =$ $\{ d \} \cup \mathbb { D } _ { q } ^ { - } )$ by the ranker module $D _ { \phi }$ ;
+
+$$
+p _ { \phi } ( d | q ; \mathbb { D } _ { q } ) = \frac { e ^ { \tau D _ { \phi } ( q , d ) } } { \sum _ { d ^ { \prime } \in \mathbb { D } _ { q } } e ^ { \tau D _ { \phi } ( q , d ^ { \prime } ) } }
+$$
+
+According to the objective function (Eqn. 5), the dual-encoder retrieval model $G _ { \theta } ( \boldsymbol { q } , \cdot )$ would try to sample the high-relevant documents to fool the ranker model, whereas the ranker model $D _ { \phi } ( q , \cdot )$ is optimized to draw distinctions between ground-truth passage and the ones sampled by $G _ { \theta } ( q , \cdot )$ . We present the illustration of the AR2 framework in Figure 2. In order to optimize the minimax objective function, we adopt a conventional iterative-learning mechanism to optimize the retriever and ranker modules coordinately.
+
+# 3.1 TRAINING THE RANKER $D _ { \phi }$
+
+Given the fixed retriever $G _ { \theta }$ , the ranker model $D _ { \phi }$ is updated by maximizing the log likelihood of selecting ground-truth $d$ from set $\mathbb { D } _ { q }$ given a query $q$ :
+
+$$
+\begin{array} { r } { \phi ^ { * } = \mathrm { a r g m a x } _ { \phi } \log p _ { \phi } ( d | q ; \mathbb { D } _ { q } ) } \end{array}
+$$
+
+where $\mathbb { D } _ { q }$ consists of ground-truth document $d$ and negative document set $\mathbb { D } _ { q } ^ { - }$ . $\mathbb { D } _ { q } ^ { - }$ is sampled by $G _ { \theta }$ according to Eqn. 5. In experiments, we first retrieve top-100 negative documents, and then randomly sample $n$ examples from them to obtain $\mathbb { D } _ { q } ^ { - }$ .
+
+# 3.2 TRAINING RETRIEVER $G _ { \theta }$
+
+With fixing the ranker $D _ { \phi }$ , the model parameters $\theta ^ { * }$ for the retriever $G _ { \theta }$ is optimized by minimizing the expectation of log likelihood of function. In particular, by isolating $\theta$ from the minimax function (Eqn. 5), the objective for the retriever can be written as:
+
+$$
+\theta ^ { * } = \operatorname * { a r g m i n } _ { \theta } J ^ { \theta } = \mathbf { E } _ { \mathbb { D } _ { q } ^ { - } \sim G _ { \theta } ( q , \cdot ) } \left[ \log p _ { \phi } ( d | q ; \mathbb { D } _ { q } ) \right]
+$$
+
+However, it is intractable to optimize $\theta$ directly through Eqn. 8, as the computation of probability $\mathbb { D } _ { q } ^ { - } \sim G _ { \theta } ( q , \cdot )$ does not follow a close form. Thus, we seek to minimize an alternative upper-bound of the loss criteria:
+
+$$
+J ^ { \theta } \leq \hat { J } ^ { \theta } = \mathbf { E } _ { d ^ { - } \sim p _ { \theta } ( \cdot | q ; \mathbb { D } _ { q } ^ { - } ) } \left[ \log p _ { \phi } ( d | q ; \{ d , d ^ { - } \} ) \right]
+$$
+
+The detailed deviation of Eqn. 9 is provided in the Appendix A.1. Therefore, the gradient of parameter $\theta$ can be computed as the derivative of ${ \hat { J } } ^ { \theta }$ with respect to $\theta$ :
+
+$$
+\nabla _ { \theta } \hat { J } ^ { \theta } = \mathbf { E } _ { d ^ { - } \sim p _ { \theta } ( \cdot | q ; \mathbb { D } _ { q } ^ { - } ) } \nabla _ { \theta } \log p _ { \theta } ( d ^ { - } | q ; \mathbb { D } _ { q } ^ { - } ) \left[ \log p _ { \phi } ( d | q ; \{ d , d ^ { - } \} ) \right]
+$$
+
+Require: Retriever $G _ { \theta }$ ; Ranker $D _ { \phi }$ ; Document pool $\mathbb { D }$ ; Training dataset $C$ .   
+1: Initialize the retriever $G _ { \theta }$ and the ranker $D _ { \phi }$ with pre-trained language models.   
+2: Train the warm-up retriever $G _ { \theta } ^ { 0 }$ on training dataset $C$ .   
+3: Build ANN index on $\mathbb { D }$   
+4: Retrieve negative samples on $\mathbb { D }$ .   
+5: Train the warm-up ranker $D _ { \theta } ^ { 0 }$   
+6: while AR2 has not converged do   
+7: for Retriever training step do   
+8: Sample $n$ documents $\{ d _ { i } ^ { - } \} _ { n }$ from ANN index.   
+9: Update parameters of the retriever $G _ { \theta }$ .   
+10: end for   
+11: Refresh ANN Index.   
+12: for Ranker training step do   
+13: Sample $n$ hard negatives $\{ d _ { i } ^ { - } \} _ { n }$ from ANN index.   
+14: Update parameters of the ranker $D _ { \phi }$ .   
+15: end for   
+16: end while
+
+Here, the same approach is applied to obtain set $\mathbb { D } _ { q } ^ { - }$ as in Eqn. 7.
+
+Regularization: we further introduce a distillation regularization term in $G _ { \theta }$ ’s training, which encourages the retriever model to distill from the ranker model.
+
+$$
+J _ { \mathcal { R } } ^ { \theta } = H ( p _ { \phi } ( \cdot | q ; \mathbb { D } ) , p _ { \theta } ( \cdot | q ; \mathbb { D } ) )
+$$
+
+$H ( \cdot )$ is the cross entropy function. $p _ { \phi } ( \cdot | q ; \mathbb { D } )$ and $p _ { \theta } ( \cdot | q ; \mathbb { D } )$ denote the conditional probabilities of document in the whole corpus $\mathbb { D }$ by the ranker and the retriever model, respectively. In practice, we also limit the sampling space over documents to a fixed set, i.e., $\mathbb { D } _ { q } = { \bar { \{ d \} } } \cup { \bar { \mathbb { D } } } _ { q } ^ { - }$ . Thus the regularization loss for the retriever model can be rewritten as:
+
+$$
+J _ { \mathcal { R } } ^ { \theta } = H \left( p _ { \phi } ( \cdot | q ; \mathbb { D } _ { q } ) , p _ { \theta } ( \cdot | q ; \mathbb { D } _ { q } ) \right)
+$$
+
+# 3.3 INDEX REFRESH
+
+During each training iteration of retriever and ranker models in AR2, we refresh the document index to keep the retrieved document set updated. To build the document index, we take the document encoder from the retrieval model to compute the embeddings $E ( d ; \theta )$ for every document $d$ from the corpus: $d \in C$ , and then build the inner-product based ANN search index with FAISS tool.
+
+In summary, Algorithm 1 shows the full implementation details of the proposed AR2.
+
+# 4 EXPERIMENTS
+
+# 4.1 DATASETS
+
+We conduct experiments on three popular benchmarks: Natural Questions (Kwiatkowski et al., 2019), Trivia QA (Joshi et al., 2017), and MS-MARCO Passage Ranking (Nguyen et al., 2016).
+
+Natural Questions (NQ) collects real questions from the Google search engine and each question is paired with an answer span and golden passages from the Wikipedia pages. In NQ, the goal of the retrieval stage is to find positive passages from a large passage pool. We report Recall of top- $k$ $( \mathbb { R } ^ { \circledcirc \mathrm { k } ) }$ , which represents the proportion of top k retrieved passages that contain the answers.
+
+Trivia QA is a reading comprehension corpus authored by trivia enthusiasts. Each sample is a hquestion, answer, evidencei triple. In the retrieval stage, the goal is to find passages that contain the answer. We also use Recall of top- $k$ as the evaluation metric for Trivia QA.
+
+MS-MARCO Passage Ranking is widely used in information retrieval. It collects real questions from the Bing search engine. Each question is paired with several web documents. Following previous works (Ren et al., 2021; Qu et al., 2021), we report MRR $@ 1 0$ , $\mathrm { R @ 5 0 }$ , ${ \textrm { R @ 1 k } }$ on the dev set. Mean Reciprocal Rank (MRR) is the mean of Reciprocal Rank(RR) across questions, calculated as the reciprocal of the rank where the first relevant document was retrieved.
+
+Table 1: The comparison of the first-stage retrieval performance on Natural Questions test set, Trivia QA test set, and MS-MARCO dev set. The results of the first two blocks are from published papers. If the results are not provided, we mark them as “-”.   
+
+<table><tr><td></td><td colspan="3">Natural Questions</td><td colspan="3">Trivia QA</td><td colspan="3">MS-MARCO</td></tr><tr><td></td><td>R@5</td><td>R@20</td><td>R@100</td><td>R@5</td><td>R@20</td><td>R@100</td><td>MRR@10</td><td>R@50</td><td>R@1k</td></tr><tr><td>BM25 (Yang et al.,2017)</td><td>-</td><td>59.1</td><td>73.7</td><td>-</td><td>66.9</td><td>76.7</td><td>18.7</td><td>59.2</td><td>85.7</td></tr><tr><td>GAR (Mao et al., 2021a)</td><td>60.9</td><td>74.4</td><td>85.3</td><td>73.1</td><td>80.4</td><td>85.7</td><td>-</td><td>=</td><td></td></tr><tr><td>doc2query (Nogueira et al.,2019b)</td><td></td><td>=</td><td>=</td><td></td><td></td><td>1</td><td>21.5</td><td>64.4</td><td>89.1</td></tr><tr><td>DeepCT (Dai&amp; Callan,2019)</td><td>=</td><td>=</td><td>-</td><td>=</td><td></td><td>-</td><td>24.3</td><td>69.0</td><td>91.0</td></tr><tr><td>docTTTTTquery (Nogueira et al.,2019a)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>27.7</td><td>75.6</td><td>94.7</td></tr><tr><td>DPR (Karpukhin et al.,2020)</td><td>-</td><td>78.4</td><td>85.3</td><td>-</td><td>79.3</td><td>84.9</td><td>-</td><td>-</td><td></td></tr><tr><td>ANCE (Xiong et al.,2021)</td><td>-</td><td>81.9</td><td>87.5</td><td></td><td>80.3</td><td>85.3</td><td>33.0</td><td>-</td><td>95.9</td></tr><tr><td>RDR(Yang&amp; Seo,2020)</td><td>=</td><td>82.8</td><td>88.2</td><td>=</td><td>82.5</td><td>87.3</td><td></td><td>-</td><td></td></tr><tr><td>ColBERT(Khattab &amp; Zaharia,2020)</td><td>=</td><td>-</td><td>1</td><td>=</td><td>-</td><td>-</td><td>36.0</td><td>82.9</td><td>96.8</td></tr><tr><td>RocketQA (Qu et al.,2021)</td><td>74.0</td><td>82.7</td><td>88.5</td><td>=</td><td></td><td>-</td><td>37.0</td><td>85.5</td><td>97.9</td></tr><tr><td>COIL (Gao et al.,2021)</td><td>-</td><td>1</td><td>-</td><td>=</td><td></td><td></td><td>35.5</td><td>-</td><td>96.3</td></tr><tr><td>ME-BERT(Luan et al.,2021)</td><td>=</td><td>-</td><td>=</td><td>-</td><td>-</td><td>-</td><td>33.8</td><td>1</td><td>-</td></tr><tr><td>Joint Top-k(Sachan et al.,2021a)</td><td>72.1</td><td>81.8</td><td>87.8</td><td>74.1</td><td>81.3</td><td>86.3</td><td>-</td><td></td><td>=</td></tr><tr><td>Individual Top-k (Sachan et al.,2021a)</td><td>75.0</td><td>84.0</td><td>89.2</td><td>76.8</td><td>83.1</td><td>87.0</td><td></td><td>-</td><td>-</td></tr><tr><td>PAIR (Ren et al., 2021) DPR-PAQ (Oguz et al., 2021)</td><td>74.9</td><td>83.5</td><td>89.1</td><td>-</td><td></td><td>1</td><td>37.9</td><td>86.4</td><td>98.2</td></tr><tr><td>-BERTbase</td><td>74.5</td><td>83.7</td><td>88.6</td><td>=</td><td>=</td><td>=</td><td>31.4</td><td>=</td><td>=</td></tr><tr><td>-RoBERTabase</td><td>74.2</td><td>84.0</td><td>89.2</td><td></td><td></td><td>=</td><td>31.1</td><td>=</td><td>=</td></tr><tr><td>Condenser(Gao &amp; Callan,2021b)</td><td>-</td><td>83.2</td><td>88.4</td><td>-</td><td>81.9</td><td>86.2</td><td>36.6</td><td></td><td>97.4</td></tr><tr><td>coCondenser (Gao &amp; Callan,2021a)</td><td>75.8</td><td>84.3</td><td>89.0</td><td>76.8</td><td>83.2</td><td>87.3</td><td>38.2</td><td>-</td><td>98.4</td></tr><tr><td>AR2-G0</td><td>69.7</td><td>80.8</td><td>87.1</td><td>74.4</td><td>81.7</td><td>86.6</td><td>34.8</td><td>84.2</td><td>98.0</td></tr><tr><td>AR2-G</td><td>77.9</td><td>86.0</td><td>90.1</td><td>78.2</td><td>84.4</td><td>87.9</td><td>39.5</td><td>87.8</td><td>98.6</td></tr></table>
+
+# 4.2 IMPLEMENTATION DETAILS
+
+First step, we follow the experiments in Sachan et al. (2021b) and Gao & Callan (2021a) to continuous pre-training the ERNIE-2.0-base model (Sun et al., 2020) with Inverse Cloze Task (ICT) training (Lee et al., 2019) for NQ and TriviaQA datasets, and coCondenser training (Gao & Callan, 2021a) for MS-MARCO dataset.
+
+Second step, we follow the experiment settings of DPR (Karpukhin et al., 2020) to train a warm-up dual-encoder retrieval model $\mathbf { \dot { G } ^ { 0 } }$ . It is initialized with the continuous pretrained ERNIE-2.0-based model we obtained in step one. Then we train a warm-up cross-encoder model $\mathbf { D ^ { 0 } }$ initialized with the ERNIE-2.0-Large. $\hat { \mathbf { D } } ^ { \mathbf { 0 } }$ learns to rank the Top- $\mathbf { \nabla \cdot k }$ documents selected by $\mathbf { G } ^ { 0 }$ with contrastive learning. The detailed hyper-parameters in training are listed in Appendix A.3.
+
+Third step, we iteratively train the ranker (AR2-D) model initialized with ERNIE-2.0-large and the retriever (AR2-G) initialized with $\mathbf { G } ^ { 0 }$ according to Algorithm 1. The number of training iterations is set to 10. During each iteration of training, the retriever model is scheduled to train with $1 5 0 0 \mathrm { { m i n i } }$ batches, while the ranker model is scheduled to train with 500 mini-batches. The document index is refreshed after each iteration of training. The other hyper-parameters are shown in Appendix A.3.
+
+All the experiments in this work run on 8 NVIDIA Tesla A100 GPUs. The implementation code of AR2 is based on Huggingface Transformers (Wolf et al., 2020) utilizing gradient checkpointing (Chen et al., 2016), Apex1, and gradient accumulation to reduce GPU memory consumption.
+
+# 4.3 RESULTS
+
+Performance of Retriever AR2-G: The comparison of retrieval performance on NQ, Trivia QA, and MS-MARCO are presented in Table 1.
+
+We compare AR2-G with previous state-of-the-art methods, including sparse and dense retrieval models. The top block shows the performance of sparse retrieval methods. BM25 (Yang et al., 2017) is a traditional sparse retriever based on the exact term matching. DeepCT (Dai & Callan, 2019) uses
+
+Table 2: Performance of rankers before and after AR2 training on NQ test set.   
+
+<table><tr><td>Retriever</td><td>Ranker</td><td>R@1</td><td>R@5</td><td>R@10</td></tr><tr><td>AR2-G0</td><td>- AR2-D0 AR2-D</td><td>48.3 60.6 64.2</td><td>69.7 78.7 79.0</td><td>76.2 82.6</td></tr><tr><td>AR2-G</td><td>- AR2-D0 AR2-D</td><td>58.7 61.1 65.6</td><td>77.9 80.1 81.5</td><td>82.6 82.5 84.3 84.9</td></tr></table>
+
+Table 3: Performance of AR2-G on NQ test set with different negative sample size $n$ .   
+
+<table><tr><td></td><td>R@1</td><td>R@5</td><td>R@20</td><td>R@100</td><td>Latency</td></tr><tr><td>n=1</td><td>56.3</td><td>76.4</td><td>85.3</td><td>89.7</td><td>210ms</td></tr><tr><td>n=5</td><td>57.8</td><td>76.9</td><td>85.3</td><td>89.7</td><td>330ms</td></tr><tr><td>n=7</td><td>58.0</td><td>77.2</td><td>85.2</td><td>89.7</td><td>396ms</td></tr><tr><td>n=11</td><td>58.0</td><td>77.1</td><td>85.4</td><td>89.8</td><td>510ms</td></tr><tr><td>n=15</td><td>57.8</td><td>77.3</td><td>85.6</td><td>90.1</td><td>630ms</td></tr></table>
+
+Table 4: Comparison of AR2 and IRGAN.   
+
+<table><tr><td></td><td>R@1</td><td>R@5</td><td>R@20</td><td>R@100</td></tr><tr><td>AR2</td><td>58.7</td><td>77.9</td><td>86.0</td><td>90.1</td></tr><tr><td>IRGAN</td><td>55.2</td><td>75.2</td><td>84.5</td><td>89.2</td></tr></table>
+
+Table 5: Effect of regularization in AR2.   
+
+<table><tr><td></td><td>R@1</td><td>R@5</td><td>R@20</td><td>R@100</td><td>Entropy</td></tr><tr><td>AR2-G</td><td>58.7</td><td>77.9</td><td>86.0</td><td>90.1</td><td>2.10</td></tr><tr><td>-w/oR</td><td>57.8</td><td>77.3</td><td>85.6</td><td>90.1</td><td>1.70</td></tr></table>
+
+BERT to dynamically generate lexical weights to augment BM25 Systems. doc2Query (Nogueira et al., 2019b), docTTTTTQuery (Nogueira et al., 2019a), and GAR (Mao et al., 2021a) use text generation to expand queries or documents to make better use of BM25. The middle block lists the results of strong dense retrieval methods, including DPR (Karpukhin et al., 2020), ANCE (Xiong et al., 2021), RDR (Yang & Seo, 2020), RocketQA (Qu et al., 2021), Joint and Individual Top- $\mathbf { \nabla } \cdot \mathbf { k }$ (Sachan et al., 2021a), PAIR (Ren et al., 2021), DPR-PAQ (Oguz et al., 2021), Condenser (Gao & Callan, ˘ 2021b). coCondenser (Gao & Callan, 2021a), ME-BERT (Luan et al., 2021), CoIL (Gao et al., 2021). These methods improve the performance of dense retrieval by constructing hard negative samples, jointly training the retriever and downstream tasks, pre-training, knowledge distillation, and multi-vector representations.
+
+The bottom block in Table 1 shows the results of proposed AR2 models. AR2- $\mathbf { G } ^ { 0 }$ refers to the warm-up retrieval model in AR2 (details can be found in section 4.2) which leverages the existing continuous pre-training technique for dense text retrieval tasks. i.e., it shows a better performance compared with DPR (Karpukhin et al., 2020) and ANCE (Xiong et al., 2021), etc approaches that do not adopt the continuous pre-training procedure. We also observed that AR2-G: the retrieval model trained with the adversary framework, significantly outperforms the warm-up AR2- $\mathbf { G } ^ { 0 }$ model, and achieves new state-of-the-art performance on all three datasets.
+
+# 4.4 ANALYSIS
+
+In this section, we conduct a set of detailed experiments on analyzing the proposed AR2 training framework to help understand its pros and cons.
+
+Performance of Ranker AR2-D: To evaluate the performance of ranker AR2-D on NQ, we first retrieve the top-100 documents for each query in the test set with the help of dual-encoder AR2- $\mathbf { G }$ model, and then re-rank them with the scores produced by the AR2-D model. The results are shown in Table 2. “-” represents without ranker. ${ \bf A } { \bf R } { \bf \Lambda } ^ { 2 - { \bf D } ^ { 0 } }$ refers to the warm-up ranker model in AR2. The results show that the ranker obtains better performance compared with only using retriever. It suggests that we could use a two-stage ranking strategy to further boost the retrieval performance. Comparing the results of AR2-D and $\mathbf { \Delta } \mathbf { A } \mathbf { R } \mathbf { \hat { \mathbf { \xi } } } \mathbf { - } \mathbf { \bar { D } } ^ { 0 }$ , we further find that the ranker AR2- $\mathbf { D }$ gets a significant gain with adversarial training.
+
+Impact of Negative Sample Size: In the training of AR2, the number of negative documents $n$ would affect both the model performance and training time. In Table 3, we show the performance and the training latency per batch with different negative sample size $n$ . In this setting, we evaluate AR2 without the regularization term. We observe the improvement over $\mathbb { R } \ @ 1$ and $\mathbf { R } @ 5$ by increasing $n$ from 1 to 7, and marginal improvement when keep increasing $n$ from 7 to 15. The latency of training per batch is almost linear increased by improving $n$ .
+
+Comparison with IRGAN: The original IRGAN (Wang et al., 2017) doesn’t work for dense text retrieval tasks as it does not contain the dual-encoder retrieval model for fast document indexing and search. However, it provides an conventional GAN framework for training the generative and discriminative models jointly for IR tasks. To compare the proposed AR2 with IRGAN, we replaced the generative and discriminative models in IRGAN with the retriever and ranker models in AR2, respectively. Therefore, with the configuration of the same model architectures for generator (retriever) and discriminator (ranker), The performance of the retriever is shown in Table 4. We see that AR2 outperforms IRGAN significantly.
+
+![](images/9ed4eebe27b9538efbce9ef46526c7359931f3359b2d736544c9148c38400ece.jpg)  
+Figure 3: NQ $\mathbf { R } @ 5$ on the number of iteration for both the AR2-retriever and the AR2-ranker.
+
+![](images/c0596fd0e5c8521280d2dfd1f94ba2408780e3394bf1e155aaa64797bcf8122d.jpg)  
+Figure 4: The comparison of ANCE and AR2 on NQ test set.
+
+Table 6: The results of the second-stage ranking on Natural Questions test set. Note that we copy the numbers of the first block from the RIDER paper (Mao et al., 2021b).   
+
+<table><tr><td>Retriever</td><td>Ranker</td><td>R@1</td><td>R@5</td><td>R@10</td><td>R@20</td><td>R@50</td><td>R@100</td></tr><tr><td>GAR+ (Mao et al., 2021a)</td><td>1</td><td>46.8</td><td>70.7</td><td>77.0</td><td>81.5</td><td>1</td><td>88.9</td></tr><tr><td>GAR+ (Mao et al., 2021a)</td><td>BERT</td><td>51.4</td><td>67.6</td><td>75.7</td><td>82.4</td><td>1</td><td>88.9</td></tr><tr><td>GAR+ (Mao et al., 2021a)</td><td>BART</td><td>55.2</td><td>73.5</td><td>78.5</td><td>82.2</td><td>1</td><td>88.9</td></tr><tr><td>GAR+ (Mao et al., 2021a)</td><td>RIDER</td><td>53.5</td><td>75.2</td><td>80.0</td><td>83.2</td><td>1</td><td>88.9</td></tr><tr><td>AR2-G</td><td>-</td><td>58.7</td><td>77.9</td><td>82.5</td><td>86.0</td><td>88.5</td><td>90.1</td></tr><tr><td>AR2-G</td><td>AR2-D</td><td>65.6</td><td>81.5</td><td>84.9</td><td>87.2</td><td>89.5</td><td>90.1</td></tr></table>
+
+Effect of Regularization: To study the effectiveness of regularization, we conducted ablation studies by removing the regularization term in the training of retrieval model. In Table 5, $" R "$ refers to the regularization item, it shows that the regularization approach helps to improve the $\mathbf { R } \ @ 1$ and $\mathbf { R } @ 5$ evaluation metrics. In additional, we compute the average entropy of distribution $p _ { \theta } ( \cdot | q , d , \mathbb { D } _ { q } )$ on the NQ test set, where $\mathbb { D } _ { q }$ is the retrieved top-15 documents. The average entropy measures the sharpness of distribution $p _ { \theta } \dot { ( \cdot | } q , d , \mathbb { D } _ { q } )$ . In experiments, the average entropies for with $R$ and w/o $R$ in AR2-G are 2.10 and 1.70 respectively. This indicates that the regularization term could help smooth the prediction of probabilities in the retriever.
+
+Visualization of the Training Procedure: We visualize the changes of $\mathbf { R } @ 5$ during the AR2- $\mathbf { G }$ training. The result is shown in Figure 3. We see that as adversarial iteration increases, the $\mathbf { R } @ 5$ of both AR2-retriever and AR2-ranker also gradually increases. AR2-retriever has the most significant improvement (about $4 . 5 \%$ ) after the first iteration. While the training advances closer to the convergence, the improvement of $\mathbf { R } @ 5$ also gradually slows down. In the end, AR2-retriever is improved by approximately $8 \%$ and AR2-ranker is improved by approximately $3 \%$ .
+
+Adversarial Training versus Iterative Hard-Negative Sampling: To give a fair comparison of AR2 and ANCE (Xiong et al., 2021), we retrain the ANCE model by initializing it with the same warm-up ${ \bf A } { \bf R } 2 – { \bf G } ^ { \bf 0 }$ which leverages the advantage of the continuous pre-training technique. In experiments, ANCE trains the retriever with an iterative hard-negative sampling approach instead of adversarial training in AR2. In Figure 4, we observe that AR2 steadily outperforms ANCE during training in terms of $\mathbf { R } @ 5$ and $\mathrm { R @ 1 0 }$ evaluation metrics with the same model-initialization. It shows that AR2 is a superior training framework compared with ANCE.
+
+Performance of the Pipeline: We evaluate the performance of the retrieve-then-rank pipeline on NQ dataset. The results are shown in Table 6. $\mathrm { G A R ^ { + } }$ is a sparse retriever which ensembles GAR (Mao et al., 2021a) and DPR (Karpukhin et al., 2020). BERT (Nogueira & Cho, 2019), BART (Nogueira et al., 2020), and RIDER (Mao et al., 2021b) are three ranking methods. BERT ranker is a cross-encoder, which makes a binary relevance decision for each query-passage pair.
+
+BART ranker generates relevance labels as target tokens in a seq2seq manner. RIDER re-ranks the retrieved passages based on the lexical overlap with the top predicted answers from the reader. The results show that AR2 pipeline significantly outperforms existing public pipelines.
+
+# 5 RELATED WORK
+
+Text Retrieval: Text retrieval aims to find related documents from a large corpus given a query.   
+Retrieval-then-rank is the widely used pipeline (Huang et al., 2020; Zou et al., 2021).
+
+For the first stage retrieval, early researchers used sparse vector space models, e.g., BM25 (Yang et al., 2017). Recently, some works improve the traditional sparse retriever with neural network, e.g., Dai & Callan (2019) use BERT to dynamically generate term weights, doc2Query (Nogueira et al., 2019b), docTTTTTQuery (Nogueira et al., 2019a), and GAR (Mao et al., 2021a) use text generation to expand queries or documents to make better use of BM25.
+
+Recently, dense retrieval methods have become a new paradigm for the first stage of retrieval. Various methods have been proposed to enhance dense retrieval, e.g., DPR (Karpukhin et al., 2020) and ME-BERT (Luan et al., 2021) use in-batch negatives and construct hard negatives by BM25; ANCE (Xiong et al., 2021), RocketQA (Qu et al., 2021), and ADORE (Zhan et al., 2021) improve the hard negative sampling by iterative replacement, denoising, and dynamic sampling, respectively; PAIR (Ren et al., 2021) leverages passage-centric similarity relation into training object; FID-KD (Izacard & Grave, 2020) and RDR (Yang & Seo, 2020) distill knowledge from reader to retriever; Guu et al. (2020) and Sachan et al. (2021b) enhance retriever by jointly training with downstream tasks. Some researchers focus on the pre-training of dense retrieval, such as ICT (Lee et al., 2019), Condenser (Gao & Callan, 2021b) and Cocondenser (Gao & Callan, 2021a).
+
+For the second stage ranking, previous works typically use cross-encoder based methods. The crossencoder models which capture the token-level interactions between the query and the document (Guo et al., 2016; Xiong et al., 2017), have shown to be more effective. Various methods are proposed to enhance ranker, e.g., Nogueira & Cho (2019) use BERT to make a binary relevance decision for each query-passage pair; Nogueira et al. (2020) adopt BART to generate relevance labels as target tokens in a seq2seq manner; Khattab & Zaharia (2020) and Gao et al. (2020) adopt the lightweight interaction based on the representations of dense retrievers to reduce computation. However, negative samples are statically sampled in these works. In AR2, negative samples for training the ranker will be dynamically adjusted with the progressive retriever.
+
+Generative Adversarial Nets: Generative Adversarial Nets (Goodfellow et al., 2014) have been widely studied in the generation field, i.e., image generation (Brock et al., 2018) and text generation (Yu et al., 2017). With a minimax game, GAN aims to train a generative model to fit the real data distribution under the guidance of a discriminative model. Few works study GAN to text retrieval. A related work is IRGAN (Wang et al., 2017). It proposes a minimax retrieval framework that aims to unify the generative and discriminative retrieval models.
+
+# 6 CONCLUSION
+
+In this paper, we introduce AR2, an adversarial retriever-ranker framework to jointly train the end-toend retrieve-then-rank pipeline. In AR2, the retriever retrieves hard negatives to cheat the ranker, and the ranker learns to rank the collection of positives and hard negatives while providing progressive rewards to the retriever. AR2 can iteratively improve the performance of both the retriever and the ranker because (1) the retriever is guided by the progressive ranker; (2) the ranker learns better through the harder negatives sampled by the progressive retriever. AR2 achieves new state-of-the-art performance on all three competitive benchmarks.
+
+# Acknowledgement
+
+This work is supported by the National Natural Science Fund for Distinguished Young Scholar (Grant No. 61625204), and partially supported by the Key Program of National Science Foundation of China (Grant No. 61836006).
+
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+Jingtao Zhan, Jiaxin Mao, Yiqun Liu, Jiafeng Guo, Min Zhang, and Shaoping Ma. Optimizing dense retrieval model training with hard negatives. In SIGIR, 2021.
+
+Lixin Zou, Shengqiang Zhang, Hengyi Cai, Dehong Ma, Suqi Cheng, Shuaiqiang Wang, Daiting Shi, Zhicong Cheng, and Dawei Yin. Pre-trained language model based ranking in baidu search. In KDD, 2021.
+
+# A APPENDIX
+
+A.1 PROOF
+
+Proof of Eqn. 9: Suppose $d _ { i } ^ { - } \in { \mathbb { D } } _ { q } ^ { - }$ is sampled by $p _ { \theta } ( \cdot | q ; \mathbb { D } _ { q } ^ { - } )$ , thus
+
+$$
+\begin{array} { r l } & { J ^ { \theta } = \mathbf { E } _ { \mathbb { D } _ { q } ^ { - } \sim G _ { \theta } ( q , \cdot ) } \left[ \log p _ { \phi } ( d | q ; \{ d \} \cup \mathbb { D } _ { q } ^ { - } ) \right] } \\ & { \qquad \le \mathbf { E } _ { \mathbb { D } _ { q } ^ { - } \sim G _ { \theta } ( q , \cdot ) } \left( \mathbf { E } _ { d _ { i } ^ { - } \sim p _ { \phi } ( \cdot | q ; \mathbb { D } _ { q } ^ { - } ) } \left[ \log p _ { \phi } ( d | q ; \{ d , d _ { i } ^ { - } \} ) \right] \right) } \end{array}
+$$
+
+where $\mathbb { D } _ { q } ^ { - }$ indicates the set of negative documents sampled by $G _ { \theta } ( q , \cdot )$ . In practice, we approximate $\mathbb { D } _ { q } ^ { - }$ by sampling $n$ documents from the top- $K$ retrieved negative set. Therefore, we could further obtain the following approximately equation in implementation.
+
+$$
+\approx \mathbf { E } _ { d _ { i } ^ { - } \sim p _ { \theta } ( \cdot \vert q ; \mathbb { D } _ { q } ^ { - } ) } \left[ \log p _ { \phi } ( d \vert q ; \{ d , d _ { i } ^ { - } \} ) \right] = \hat { J } ^ { \theta }
+$$
+
+Proof of Eqn. 10:
+
+$$
+\begin{array} { l } { { \nabla _ { \theta } \hat { J } ^ { \theta } = \nabla _ { \theta } \mathbf { E } _ { d _ { i } ^ { - } \sim p _ { \theta } ( \cdot \vert q ; \mathbb { D } _ { q } ^ { - } ) } \left[ \log p _ { \phi } ( d \vert q ; \{ d , d _ { i } ^ { - } \} ) \right] } } \\ { { { { } } } = \displaystyle \sum _ { i } \nabla _ { \theta } p _ { \theta } ( d _ { i } ^ { - } \vert q ; \mathbb { D } _ { q } ^ { - } ) \left[ \log p _ { \phi } ( d \vert q ; \{ d , d _ { i } ^ { - } \} ) \right] } \\ { { { } } } \\ { { { } } = \displaystyle \sum _ { i } p _ { \theta } ( d _ { i } ^ { - } \vert q ; \mathbb { D } _ { q } ^ { - } ) \nabla _ { \theta } \log p _ { \theta } ( d _ { i } ^ { - } \vert q ; \mathbb { D } _ { q } ^ { - } ) \left[ \log p _ { \phi } ( d \vert q ; \{ d , d _ { i } ^ { - } \} ) \right] } \\ { { { } } } \\ { { { } } = \displaystyle \mathbf { E } _ { d _ { i } ^ { - } \sim p _ { \theta } ( \cdot \vert q ; \mathbb { D } _ { q } ^ { - } ) } \nabla _ { \theta } \log p _ { \theta } ( d _ { i } ^ { - } \vert q ; \mathbb { D } _ { q } ^ { - } ) \left[ \log p _ { \phi } ( d \vert q ; \{ d , d _ { i } ^ { - } \} ) \right] }  \end{array}
+$$
+
+# A.2 EFFICIENCY REPORT
+
+We list the time cost of training and inference in Table 7. The evaluation is made with 8 NVIDIA A100 GPUs. The max step of ANCE training is from the ANCE’s open-source website 2.We estimate the overall training time without taking account of the time of continuous pre-training step and warming-up step.
+
+Table 7: Comparison of Efficiency   
+
+<table><tr><td></td><td>DPR</td><td>ANCE</td><td>AR2(n=15)</td><td>AR2(n=1)</td></tr><tr><td>Training Batch Size Max Step</td><td>128 20k 1.8h</td><td>128 136k</td><td>64 20k</td><td>64 20k</td></tr><tr><td>BPfor Retriever BP for Ranker Iteration Number Index Refresh</td><td>1 0 0.5</td><td>11h 1 10</td><td>2.3h 0.75h 10</td><td>1h 0.35h 10</td></tr><tr><td>Overall</td><td>1.85h</td><td>0.5h 16h</td><td>0.5h</td><td>0.5h</td></tr><tr><td>Inference</td><td></td><td></td><td>9.1h</td><td>6.4h</td></tr><tr><td></td><td>20min</td><td></td><td></td><td></td></tr><tr><td>Encoding of Corpus</td><td></td><td>20min</td><td>20min</td><td>20min</td></tr><tr><td>Query Encoding</td><td>40ns</td><td>40ns</td><td>40ns</td><td>40ns</td></tr><tr><td>ANNIndexBuild</td><td>2min</td><td>2min</td><td>2min</td><td></td></tr><tr><td></td><td>2ms</td><td></td><td></td><td>2min</td></tr><tr><td>ANN Retrieval(Top-100)</td><td></td><td>2ms</td><td>2ms</td><td>2ms</td></tr></table>
+
+# A.3 HYPERPARAMETERS
+
+Table 8: Hyperparameters for AR2 training.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=9>Parameter</td><td rowspan=1 colspan=1>NQ    TriviaQA  MS-MARCO</td></tr><tr><td rowspan=1 colspan=1>Default</td><td rowspan=1 colspan=9>Max query lengthMax passage length</td><td rowspan=1 colspan=1>32         32           32128        128          128</td></tr><tr><td rowspan=5 colspan=1>AR2-G0</td><td rowspan=5 colspan=9>Learning rateNegative sizeBatch sizeTemperature TOptimizerSchedulerWarmup proportionTraining epoch</td><td rowspan=1 colspan=1>1e-5       1e-5          1e-4</td></tr><tr><td rowspan=1 colspan=3></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>255       255          127</td></tr><tr><td rowspan=1 colspan=2></td><td rowspan=1 colspan=1></td><td rowspan=3 colspan=1>128        128           641          1            1AdamW   AdamW     AdamWLinear    Linear       Linear0.1        0.1           0.140         40            3</td></tr><tr><td rowspan=1 colspan=2></td></tr><tr><td rowspan=1 colspan=2>Scheduler</td><td rowspan=1 colspan=3>r</td></tr><tr><td rowspan=9 colspan=1>AR2-D0</td><td rowspan=3 colspan=9>Learning rateNegative sizeBatch size</td><td rowspan=1 colspan=1>1e-5       1e-5          1e-5</td></tr><tr><td rowspan=1 colspan=1>15         15            15</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>64         64           256</td></tr><tr><td rowspan=2 colspan=9>Temperature TOptimizer</td><td rowspan=2 colspan=1>1          1             1AdamW  AdamW     AdamW</td></tr><tr><td rowspan=3 colspan=1>AdamW  AdamW     AdamWLinear    Linear       Linear0.1        0.1           0.1</td></tr><tr><td rowspan=1 colspan=9>Scheduler</td><td rowspan=1 colspan=1>Linear    Linear</td></tr><tr><td rowspan=3 colspan=9>Warmup proportionTraining step per iterationMax step</td></tr><tr><td rowspan=1 colspan=1>1500      1500         1500</td></tr><tr><td rowspan=1 colspan=5></td><td rowspan=1 colspan=1>2000      2000         4000</td></tr><tr><td rowspan=8 colspan=1>AR2-G</td><td rowspan=8 colspan=9>Learning rateNegative sizeBatch sizeTemperature TOptimizerSchedulerWarmup proportionTraining step per iterationMax step</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>15         15            15</td></tr><tr><td rowspan=1 colspan=1>64         64            64</td></tr><tr><td rowspan=1 colspan=1>1          1             1AdamW  AdamW     AdamW</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Linear    Linear       Linear</td></tr><tr><td rowspan=1 colspan=1>0.1        0.1           0.1</td></tr><tr><td rowspan=1 colspan=1>1500      1500         1500</td></tr><tr><td rowspan=1 colspan=5></td><td rowspan=1 colspan=1>15000     15000        15000</td></tr><tr><td rowspan=8 colspan=1>AR2-D</td><td rowspan=5 colspan=9>Negative sizeLearning rateBatch sizeTemperature TOptimizerScheduler</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1></td><td></td></tr><tr><td rowspan=1 colspan=1>64         64           64</td></tr><tr><td rowspan=1 colspan=1>1          1            1AdamW  AdamW     AdamW</td></tr><tr><td rowspan=1 colspan=1>Linear    Linear       Linear</td></tr><tr><td rowspan=2 colspan=9>Warmup proportionTraining step per iteration</td><td rowspan=1 colspan=1>0.1        0.1           0.1</td></tr><tr><td rowspan=1 colspan=1>500       500          500</td></tr><tr><td rowspan=1 colspan=9>Max step</td><td rowspan=1 colspan=1>5000      5000         5000</td></tr></table>
+
+# A.4 MODEL CONFIGURATION AND EXPERIMENT SETTINGS
+
+We list the detailed configuration of AR2 and baseline models in Table 9.
+
+Table 9: Model configuration and experiment settings.   
+
+<table><tr><td rowspan=1 colspan=1>Model</td><td rowspan=1 colspan=1>InitialModel</td><td rowspan=1 colspan=1>Parameters</td><td rowspan=1 colspan=1>FurtherPretrain</td><td rowspan=1 colspan=1>AdditionalData</td></tr><tr><td rowspan=1 colspan=1>DPR (Karpukhin et al., 2020)</td><td rowspan=1 colspan=1>BERT-Base</td><td rowspan=1 colspan=1>110M</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1>ANCE (Xiong et al., 2021)</td><td rowspan=1 colspan=1>BERT/RoBERTa-Base</td><td rowspan=1 colspan=1>110M/125M</td><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=1>1</td></tr><tr><td rowspan=1 colspan=1>RocketQA (Qu et al., 2021)</td><td rowspan=1 colspan=1>ERNIE-2.0-BaseERNIE-2.0-Large</td><td rowspan=1 colspan=1>110M330M</td><td rowspan=1 colspan=1>--</td><td rowspan=1 colspan=1>1.7 M</td></tr><tr><td rowspan=1 colspan=1>PAIR (Ren et al., 2021)</td><td rowspan=1 colspan=1>ERNIE-2.0-BaseERNIE-2.0-Large</td><td rowspan=1 colspan=1>110M330M</td><td rowspan=1 colspan=1>--</td><td rowspan=1 colspan=1>1.7 M</td></tr><tr><td rowspan=1 colspan=1>Individual Top-k (Sachan et al., 2021a)</td><td rowspan=1 colspan=1>ERNIE-2.0-BaseT5-Large</td><td rowspan=1 colspan=1>110M739M</td><td rowspan=1 colspan=1>Yes1</td><td rowspan=1 colspan=1>-</td></tr><tr><td rowspan=1 colspan=1>coCondenser (Gao &amp; Callan,2021a)</td><td rowspan=1 colspan=1>BERT-Base</td><td rowspan=1 colspan=1>110M</td><td rowspan=1 colspan=1>Yes</td><td rowspan=1 colspan=1>=</td></tr><tr><td rowspan=1 colspan=1>Our (AR2-G) (Retriever)Our (AR2-D) (Ranker)</td><td rowspan=1 colspan=1>ERNIE-2.0-BaseERNIE-2.0-Large</td><td rowspan=1 colspan=1>110M330M</td><td rowspan=1 colspan=1>Yes-</td><td rowspan=1 colspan=1>==</td></tr></table>
+
+# A.5 ABLATION STUDY ON DIFFERENT INITIAL MODELS
+
+Table 10 shows the results of our method with different initial models. We see that ERNIE-Base as the initial model achieves a little better performance than BERT-Base. And AR2-G using BERTBase as the initial model still achieves better performance than other methods under the same initial model. Meanwhile, ICT pre-training improves the performance of AR2-G.
+
+Table 10: Performance of AR2-G on NQ test set with different initial model   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>Initial Model</td><td rowspan=1 colspan=1>R@1</td><td rowspan=1 colspan=1>R@5</td><td rowspan=1 colspan=2>R@20</td><td rowspan=1 colspan=1>R@100</td></tr><tr><td rowspan=4 colspan=1>DPR (Karpukhin et al., 2020)ANCE (Xiong et al., 2021)RocketQA (Qu et al., 2021)PAIR (Ren et al.,2021)</td><td rowspan=4 colspan=1>BERT-BaseBERT-BaseERNIE-BaseERNIE-Base</td><td rowspan=4 colspan=1>1111</td><td rowspan=1 colspan=1>1</td><td rowspan=1 colspan=2>78.4</td><td rowspan=1 colspan=1>85.3</td></tr><tr><td rowspan=1 colspan=1>-</td><td rowspan=1 colspan=2>81.9</td><td rowspan=1 colspan=1>87.5</td></tr><tr><td rowspan=1 colspan=1>74.0</td><td rowspan=2 colspan=2>82.783.5</td><td rowspan=2 colspan=1>88.589.1</td></tr><tr><td rowspan=1 colspan=1>74.9</td></tr><tr><td rowspan=3 colspan=1>AR2-GAR2-GAR2-G</td><td rowspan=3 colspan=1>BERT-BaseERNIE-BaseERNIE-Base w/ ICT</td><td rowspan=3 colspan=1>56.757.258.7</td><td rowspan=1 colspan=1>76.1</td><td rowspan=1 colspan=2>85.0</td><td rowspan=1 colspan=1>89.3</td></tr><tr><td rowspan=2 colspan=1>76.677.9</td><td rowspan=1 colspan=1>85.3</td><td></td><td rowspan=1 colspan=1>89.8</td></tr><tr><td rowspan=1 colspan=2>86.0</td><td rowspan=1 colspan=1>90.1</td></tr></table>
+
+# A.6 COMPARISON WITH SEVERAL EXISTING APPROACHES
+
+Table 11 shows the comparison of AR2 and several existing retrieval approaches. “Extra Label” refers to whether the answer label is used. AR2 jointly optimizes both the retriever and the ranker according to a principle adversarial objective, which is the key difference with previous works.
+
+Table 11: Comparison with existing approaches   
+
+<table><tr><td>Model</td><td>Extra Label</td><td>Retriever-Ranker/ Retriever-Reader</td><td>Adversarial Objective</td><td>Update Hard Negatives</td></tr><tr><td>FID-KD (Izacard &amp; Grave,2020)</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>RDR(Yang&amp; Seo,2020)</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>RocketQA (Qu et al.,2021)</td><td>No</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>ANCE (Xiong et al.,2021)</td><td>No</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>RIDER (Mao et al., 2021b)</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>AR2</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></table>
+
+# A.7 PERFORMANCE OF THE PIPELINE
+
+Table 12 shows the performance of the retrieve-then-rank pipeline on Trivia QA and MS-MARCO. From the results of Table 6 and Table 12, we find that the ranker AR2-D improves the performance on all three benchmarks including NQ, Trivia QA, and MS-MARCO. Meanwhile, the pipeline based on AR2 achieves state-of-the-art performances on all benchmarks.
+
+Table 12: The results of the second-stage ranking on Trivia QA and MS-MARCO.   
+
+<table><tr><td rowspan="2">Retriever</td><td rowspan="2">Ranker</td><td colspan="3">Trivia QA</td><td rowspan="2">MS-MARCO MRR@10</td></tr><tr><td>R@1</td><td>R@5</td><td>R@10</td><td>R@20</td></tr><tr><td>RepBERT (Zhan et al., 2020)</td><td>RepBERT (Zhan et al.,2020)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>37.7</td></tr><tr><td>ME-HYBIRD (Luan et al., 2021)</td><td>ME-HYBIRD (Luan et al., 2021)</td><td>-</td><td>-</td><td>:</td><td>■</td><td>39.4</td></tr><tr><td>ME-BERT(Luan et al.,2021)</td><td>ME-BERT (Luan et al.,2021)</td><td>-</td><td>-</td><td>■</td><td>■</td><td>39.5</td></tr><tr><td>BM25 (Yang et al.,2017)</td><td>TFR-BERT (Han et al.,2020)</td><td>-</td><td>-</td><td>=</td><td>-</td><td>40.5</td></tr><tr><td>GAR+ (Mao et al.,2021a)</td><td>RIDER (Mao et al.,2021b)</td><td>71.9</td><td>77.5</td><td>79.8</td><td>81.8</td><td>-</td></tr><tr><td>AR2-G</td><td>■</td><td>64.2</td><td>78.2</td><td>81.8</td><td>84.4</td><td>39.5</td></tr><tr><td>AR2-G</td><td>AR2-D</td><td>73.0</td><td>82.1</td><td>84.1</td><td>85.8</td><td>43.2</td></tr></table>
+
+# A.8 PERFORMANCE OF THE LARGE-SIZE MODEL
+
+Table 13 shows the results of AR2-G (Retriever) initialized with ERNIE-2.0-Large (without continuous pre-training (ICT)). All baselines are initialized by large-size model, and DPR-PAQ (Oguz ˘ et al., 2021) utilizes a large external corpus $6 5 \mathrm { m }$ question-answer pairs) to continue pre-training the model; Individual Top-K (Sachan et al., 2021a) utilizes T5-Large model (739M parameters vs 330M parameters ERNIE-2.0-Large) as reader to guide the retriever. Compared with these baseline methods, AR2-G achieves a significant performance improvement, which further demonstrates the effectiveness of AR2-G (Retriever).
+
+Table 13: The performance of large-size models on Natural Questions test set,   
+
+<table><tr><td></td><td>Size</td><td>R@1</td><td>R@5</td><td>R@20</td><td>R@100</td></tr><tr><td>DPR-PAQBERT (Oguz et al., 2021) DPR-PAQRoBERTa (Oguz et al., 2021)</td><td>Large Large</td><td>1 1</td><td>75.3 76.9</td><td>84.4 84.7</td><td>88.9 89.2</td></tr><tr><td>Individual Top-K (Sachan et al., 2021a) AR2-G AR2-G</td><td>Large Base Large</td><td>57.5 58.7 61.1</td><td>76.2 77.9 78.8</td><td>84.8 86.0 86.5</td><td>89.8 90.1 90.4</td></tr></table>

parse/dev/rFbR4Fv-D6-/rFbR4Fv-D6-.md

@@ -0,0 +1,525 @@
+# AUTOMATED SELF-SUPERVISED LEARNING FOR GRAPHS
+
+Wei Jin ∗ Michigan State University jinwei2@msu.edu
+
+Xiaorui Liu Michigan State University xiaorui@msu.edu
+
+Xiaoyu Zhao City University of Hong Kong xy.zhao@cityu.edu.hk
+
+# Yao Ma
+
+Neil Shah   
+Snap Inc.   
+nshah@snap.com
+
+New Jersey Institute of Technology yao.ma@njit.edu
+
+Jiliang Tang Michigan State University tangjili@msu.edu
+
+# ABSTRACT
+
+Graph self-supervised learning has gained increasing attention due to its capacity to learn expressive node representations. Many pretext tasks, or loss functions have been designed from distinct perspectives. However, we observe that different pretext tasks affect downstream tasks differently across datasets, which suggests that searching over pretext tasks is crucial for graph self-supervised learning. Different from existing works focusing on designing single pretext tasks, this work aims to investigate how to automatically leverage multiple pretext tasks effectively. Nevertheless, evaluating representations derived from multiple pretext tasks without direct access to ground truth labels makes this problem challenging. To address this obstacle, we make use of a key principle of many real-world graphs, i.e., homophily, or the principle that “like attracts like,” as the guidance to effectively search various self-supervised pretext tasks. We provide theoretical understanding and empirical evidence to justify the flexibility of homophily in this search task. Then we propose the AUTOSSL framework to automatically search over combinations of various self-supervised tasks. By evaluating the framework on 8 real-world datasets, our experimental results show that AUTOSSL can significantly boost the performance on downstream tasks including node clustering and node classification compared with training under individual tasks.
+
+# 1 INTRODUCTION
+
+Graphs are pivotal data structures describing the relationships between entities in various domains such as social media, biology, transportation and financial systems (Wu et al., 2019b; Battaglia et al., 2018). Due to their prevalence and rich descriptive capacity, pattern mining and discovery on graph data is a prominent research area with powerful implications. As the generalization of deep neural networks on graph data, graph neural networks (GNNs) have proved to be powerful in learning representations for graphs and associated entities (nodes, edges, subgraphs), and they have been employed in various applications such as node classification (Kipf & Welling, 2016a; Velickovi ˇ c´ et al., 2018), node clustering (Pan et al., 2018), recommender systems (Ying et al., 2018) and drug discovery (Duvenaud et al., 2015).
+
+In recent years, the explosive interest in self-supervised learning (SSL) has suggested its great potential in empowering stronger neural networks in an unsupervised manner (Chen et al., 2020; Kolesnikov et al., 2019; Doersch et al., 2015). Many self-supervised methods have also been developed to facilitate graph representation learning (Jin et al., 2020; Xie et al., 2021; Wang et al., 2022) such as DGI (Velickovi ˇ c et al., 2019), P ´ AR/CLU (You et al., 2020) and MVGRL (Hassani & Khasahmadi, 2020). Given graph and node attribute data, they construct pretext tasks, which are called SSL tasks, based on structural and attribute information to provide self-supervision for training graph neural networks without accessing any labeled data. For example, the pretext task of
+
+![](images/e589eafb1c39688767e8fbb4f446e62601e368e39e032ad6949f5c6f51d6f19d.jpg)  
+Figure 1: (a)(b): Performance of 5 SSL tasks ranked best (1) to worst (5) by color on node clustering and classification, showing disparate performance across datasets and tasks. (c): Clustering performance heatmap on Citeseer when combining 2 SSL tasks, PAIRSIM and PAIRDIS, with different weights. (d) AUTOSSL’s search trajectory for task weights, achieving near-ideal performance.
+
+PAR is to predict the graph partitions of nodes. We examine how a variety of SSL tasks including DGI, PAR, CLU, PAIRDIS (Peng et al., 2020) and PAIRSIM (Jin et al., 2020; 2021) perform over 3 datasets. Their node clustering and node classification performance ranks are illustrated in Figure 1a and 1b, respectively. From these figures, we observe that different SSL tasks have distinct downstream performance cross datasets. This observation suggests that the success of SSL tasks strongly depends on the datasets and downstream tasks. Learning representations with a single task naturally leads to ignoring useful information from other tasks. As a result, searching SSL tasks is crucial, which motivates us to study on how to automatically compose a variety of graph self-supervised tasks to learn better node representations.
+
+However, combining multiple different SSL tasks for unlabeled representation learning is immensely challenging. Although promising results have been achieved in multi-task self-supervised learning for computer vision, most of them assign equal weights to SSL tasks (Doersch & Zisserman, 2017; Ren & Lee, 2018; Zamir et al., 2018). Such combination might not always yield better performance than a single task, as different tasks have distinct importance according to specific dataset and downstream tasks. To illustrate this intuition, we combine two SSL tasks, PAIRDIS and PAIRSIM, with varied weights and illustrate the corresponding node clustering performance in Figure 1c. It clearly indicates that different choices of weights yield different performance. To circumvent this problem, we could plausibly search different weights for SSL tasks to optimize downstream tasks. However, to achieve such goal, we have two obstacles. First, the search space is huge, and thus search can be highly expensive. Hence, it is desirable to automatically learn these weights. Second, searching for optimal task weights typically requires guidance from downstream performance, which is naturally missing under the unsupervised setting. Thus, how to design an unsupervised surrogate evaluation measure that can guide the search process is necessary.
+
+It is evident that many real-world graphs such as friendship networks, citation networks, coauthorship networks and co-purchase networks (McPherson et al., 2001; Shchur et al., 2018) satisfy the homophily assumption, i.e., “like attracts like”, or that connected nodes tend to share the same label. This is useful prior knowledge, as it directly relates the label information of downstream tasks to the graph structure. In this work, we explicitly take advantage of this prior knowledge and assume that the predicted labels from good node embeddings should also adhere to homophily. Given the lack of ground-truth labels during SSL, we propose a pseudo-homophily measure to evaluate the quality of the node embeddings trained from specific combinations of SSL task. With pseudohomophily, we are able to design an automated framework for SSL task search, namely AUTOSSL. Our work makes three significant contributions:
+
+(1) To bridge the gap between unsupervised representation and downstream labels, we propose pseudo-homophily to measure the quality of the representation. Moreover, given graphs with high homophily, we theoretically show that pseudo-homophily maximization can help maximize the upper bound of mutual information between pseudo-labels and downstream labels.   
+(2) Based on pseudo-homophily, we propose two strategies to efficiently search SSL tasks, one employing evolution algorithm and the other performing differentiable search via meta-gradient descent. AUTOSSL is able to adjust the task weights during search as shown in Figure 1d.   
+(3) We evaluate the proposed AUTOSSL by composing various individual tasks on 8 real-world datasets. Extensive experiments have demonstrated that AUTOSSL can significantly improve
+
+the performance of individual tasks on node clustering and node classification (e.g., up to $10 . 0 \%$ relative improvement on node clustering).
+
+# 2 BACKGROUND AND RELATED WORK
+
+Graph Neural Networks. Graph neural networks (GNNs) are powerful tools for extracting useful information from graph data (Liu et al., 2021; Wu et al., 2019b; Kipf & Welling, 2016a; Velickovi ˇ c´ et al., 2018; Hamilton et al., 2017; Kipf & Welling, 2016b; Pan et al., 2018; Liu et al., 2020). They aim to learn a mapping function $f _ { \theta }$ parameterized by $\theta$ to map the input graph into a low-dimensional space. Most graph neural networks follow a message passing scheme (Gilmer et al., 2017) where the node representation is obtained by aggregating the representation of its neighbors.
+
+Self-Supervised Learning in GNNs. Graph neural networks have achieved superior performance in various applications; but they also require costly task-dependent labels to learn rich representations. To alleviate the need for the huge amount of labeled data, recent studies have employed self-supervised learning in graph neural networks to provide additional supervision (Jin et al., 2020; Velickovi ˇ c et al., 2019; You et al., 2020; Hassani & Khasahmadi, 2020; Hu et al., 2019; Qiu et al., ´ 2020; Zhu et al., 2020b). Specifically, those SSL methods construct a pre-defined pretext task to assign pseudo-labels for unlabeled nodes/graphs and then train the model on the designed pretext task to learn representations. A recent work JOAO (You et al., 2021) on graph contrastive learning is proposed to automatically select data augmentation and focuses on graph classification task. Another related work is AUX-TS (Han et al., 2021), which also adaptively combines different SSL tasks but the combination happens at the fine-tuning stage and thus requires label information.
+
+Multi-Task Self-Supervised Learning. Our work is also related to multi-task self-supervised learning (Doersch & Zisserman, 2017; Ren & Lee, 2018; Zamir et al., 2018). Most of them assume the tasks with equal weights and perform training under the supervised setting. But our work learns different weights for different tasks and does not require access to labeled data.
+
+Automated Loss Function Search. Tremendous efforts have been paid to automate every aspect of machine learning applications (Yao et al., 2018; Liu et al., 2018; Zhao et al., 2021b), such as feature engineering, model architecture search and loss function search. Among them, our work is highly related to loss function search (Zhao et al., 2021a; Xu et al., 2018; Wang et al., 2020; Li et al., 2019). However, these methods are developed under the supervised setting and not applicable in selfsupervised learning. Another related work, ELo (Piergiovanni et al., 2020), evolves multiple selfsupervised losses based on Zipf distribution matching for action recognition. However, it is designed exclusively for image data and not applicable to non-grid graph-structured data. The problem of self-supervised loss search for graphs remains rarely explored. To bridge the gap, we propose an automated framework for searching SSL losses towards graph data in an unsupervised manner.
+
+# 3 AUTOMATED SELF-SUPERVISED TASK SEARCH WITH AUTOSSL
+
+In this section, we present the proposed framework of automated self-supervised task search, namely AUTOSSL. Given a graph $\mathcal { G }$ , a GNN encoder $f _ { \theta } ( \cdot )$ and a set of $n$ self-supervised losses (tasks) $\{ \ell _ { 1 } , \ell _ { 2 } , \dots , \ell _ { n } \}$ , we aim at learning a set of loss weights $\{ \lambda _ { 1 } , \lambda _ { 2 } , \ldots , \lambda _ { n } \}$ such that $f _ { \theta } ( \cdot )$ trained with the weighted loss combination data. The key challenge is how to $\textstyle \sum _ { i = 1 } ^ { n } \lambda _ { i } \ell _ { i }$ can extract meaningful features from the given graphically define “meaningful features”. If we have the access to the labels of the downstream task, we can define “meaningful features” as the features (node embeddings) that can have high performance on the given downstream task. Then we can simply adopt the downstream performance as the optimization goal and formulate the problem of automated self-supervised task search as follows:
+
+$$
+\operatorname* { m i n } _ { \lambda _ { 1 } , \cdots , \lambda _ { n } } \mathcal { H } ( f _ { \theta ^ { * } } ( \mathcal { G } ) ) , \quad \mathrm { s . t . } \theta ^ { * } = \arg \operatorname* { m i n } _ { \theta } \mathcal { L } ( f _ { \theta } , \{ \lambda _ { i } \} , \{ \ell _ { i } \} ) = \arg \operatorname* { m i n } _ { \theta } \sum _ { i = 1 } ^ { n } \lambda _ { i } \ell _ { i } ( f _ { \theta } ( \mathcal { G } ) ) ,
+$$
+
+where $\mathcal { H }$ denotes the quality measure for the obtained node embeddings, and it can be any metric that evaluates the downstream performance such as cross-entropy loss for the node classification task. However, under the self-supervised setting, we do not have the access to labeled data and thus cannot employ the downstream performance to measure the embedding quality. Instead, we need an unsupervised quality measure $\mathcal { H }$ to evaluate the quality of obtained embeddings. In a nutshell, one challenge of automated self-supervised learning is: how to construct the goal of automated task search without the access to label information of the downstream tasks.
+
+# 3.1 PSEUDO-HOMOPHILY
+
+Most common graphs adhere to the principle of homophily, i.e., “birds of a feather flock together” (McPherson et al., 2001), which suggests that connected nodes often belong to the same class; e.g. connected publications in a citation network often have the same topic, and friends in social networks often share interests (Newman, 2018). Homophily is often calculated as the fraction of intra-class edges in a graph (Zhu et al., 2020a). Formally, it can be defined as follows,
+
+Definition 1 (Homophily). The homophily of a graph $\mathcal { G }$ with node label vector $y$ is given by
+
+$$
+h ( \mathcal { G } , y ) = \frac { 1 } { \vert \mathcal { E } \vert } \sum _ { ( v _ { 1 } , v _ { 2 } ) \in \mathcal { E } } \mathbb { 1 } ( y _ { v _ { 1 } } = y _ { v _ { 2 } } ) ,
+$$
+
+where $y _ { v _ { i } }$ indicates node $v _ { i }$ ’s label and $\mathbb { 1 } ( \cdot )$ is the indicator function.
+
+We calculate the homophily for seven widely used datasets as shown in Appendix A and we find that they all have high homophily, e.g., 0.93 in the Physics dataset. Considering the high homophily in those datasets, intuitively the predicted labels from the extracted node features should also have high homophily. Hence, the prior information of graph homophily in ground truth labels can serve as strong guidance for searching combinations of self-supervised tasks. As mentioned before, in self-supervised tasks, the ground truth labels are not available. Motivated by DeepCluster (Caron et al., 2018) which uses the cluster assignments of learned features as pseudo-labels to train the neural network, we propose to calculate the homophily based on the cluster assignments, which we term as pseudo-homophily. Specifically, we first perform $k$ -means clustering on the obtained node embeddings to get $k$ clusters. Then the cluster results are used as the pseudo labels to calculate homophily based on Eq. (2). Note that though many graphs in the real world have high homophily, there also exist heterophily graphs (Zhu et al., 2020a; Pei et al., 2020) which have low homophily. We include a discussion on the homophily assumption in Appendix D.
+
+Theoretical analysis. In this work, we propose to achieve self-supervised task search via maximizing pseudo-homophily. To understand its rationality, we develop the following theorem to show that pseudo-homophily maximization is related to the upper bound of mutual information between pseudo-labels and ground truth labels.
+
+Theorem 1. Suppose that we are given with a graph $\mathcal { G } = \{ \nu , \varepsilon \}$ , a pseudo label vector $A \ \in$ $\{ 0 , 1 \} ^ { N }$ and a ground truth label vector $B \in \{ 0 , \bar { 1 } \} ^ { N }$ defined on the node set. We denote the homophily of $A$ and $B$ over $\mathcal { G }$ as $h _ { A }$ and $h _ { B }$ , respectively. If the classes in $A$ and $B$ are balanced and $h _ { A } < h _ { B }$ , the following results hold: $( l )$ the mutual information between $A$ and $B _ { i }$ , i.e., $M I ( A , B )$ , has an upper bound $\mathcal { U } _ { A , B }$ , where $\begin{array} { r } { \mathcal { U } _ { A , B } = \frac { 1 } { N } \left[ 2 \Delta \log \left( \frac { 4 } { N } \Delta \right) + 2 ( \frac { N } { 2 } - \Delta ) \log \left( \frac { 4 } { N } ( \frac { N } { 2 } - \Delta ) \right) \right] } \end{array}$ with ∆ = (hB−hA)|E|2d and dmax denoting the largest node degree in the graph; (2) if hA < hA0 < hB, we have $\mathcal { U } _ { A , B } \backslash \mathcal { < } \mathcal { U } _ { A ^ { \prime } , B }$ .
+
+Proof. The detailed proof of this theorem can be found in Appendix B.
+
+The above theorem suggests that a larger difference between pseudo-homophily and real homophily results in a lower upper bound of mutual information between the pseudo-labels and ground truth labels. Thus, maximizing pseudo-homophily is to maximize the upper bound of mutual information between pseudo-labels and ground truth labels, since we assume high homophily of the graph. Notably, while maximizing the upper bound does not guarantee the optimality of the mutual information, we empirically found that it works well in increasing the NMI value in different datasets, showing that it provides the right direction to promote the mutual information.
+
+# 3.2 SEARCH ALGORITHMS
+
+In the last subsection, we have demonstrated the importance of maximizing pseudo-homophily. Thus in the optimization problem of Eq. (1), we can simply set $\mathcal { H }$ to be negative pseudo-homophily. However, the evaluation of a specific task combination involves fitting a model and evaluating its pseudo-homophily, which can be highly expensive. Therefore, another challenge for automated selfsupervised task search is how to design an efficient algorithm. In the following, we introduce the details of the search strategies designed in this work, i.e. AUTOSSL-ES and AUTOSSL-DS.
+
+# 3.2.1 AUTOSSL-ES: EVOLUTIONARY STRATEGY
+
+Evolution algorithms are often used in automated machine learning such as hyperparameter tuning due to their parallelism nature by design (Loshchilov & Hutter, 2016). In this work, we employ the covariance matrix adaptation evolution strategy (CMA-ES) (Hansen et al., 2003), a state-of-theart optimizer for continuous black-box functions, to evolve the combined self-supervised loss. We name this self-supervised task search approach as AUTOSSL-ES. In each iteration of CMA-ES, it samples a set of candidate solutions (i.e., task weights $\{ \lambda _ { i } \} )$ from a multivariate normal distribution and trains the GNN encoder under the combined loss function. The embeddings from the trained encoder are then evaluated by $\mathcal { H }$ . Based on $\mathcal { H }$ , CMA-ES adjusts the normal distribution to give higher probabilities to good samples that can potentially produce a lower value of $\mathcal { H }$ . Note that we constrain $\{ \lambda _ { i } \}$ in [0, 1] and sample 8 candidate combinations for each iteration, which is trivially parallelizable as every candidate combination can be evaluated independently.
+
+# 3.2.2 AUTOSSL-DS: DIFFERENTIABLE SEARCH VIA META-GRADIENT DESCENT
+
+While the aforementioned AUTOSSL-ES is parallelizable, the search cost is still expensive because it requires to evaluate a large population of candidate combinations where every evaluation involves fitting the model in large training epochs. Thus, it is desired to develop gradient-based search methods to accelerate the search process. In this subsection, we introduce the other variant of our proposed framework, AUTOSSL-DS, which performs differentiable search via meta-gradient descent. However, pseudo-homophily is not differentiable as it is based on hard cluster assignments from $k$ -means clustering. Next, we will first present how to make the clustering process differentiable and then introduce how to perform differentiable search.
+
+Soft Clustering. Although $k$ -means clustering assigns hard assignments of data samples to clusters, it can be viewed as a special case of Gaussian mixture model which makes soft assignments based on the posterior probabilities (Bishop, 2006). Given a Gaussian mixture model with centroids $\{ \mathbf { c } _ { 1 } , \mathbf { c } _ { 2 } , \ldots , \mathbf { c } _ { k } \}$ and fixed variances $\sigma ^ { 2 }$ , we can calculate the posterior probability as follows:
+
+$$
+p \left( \mathbf { x } \mid \mathbf { c } _ { i } \right) = \frac { 1 } { \sqrt { 2 \pi \sigma ^ { 2 } } } \exp \left( - \frac { \left\| \mathbf { x } - \mathbf { c } _ { i } \right\| _ { 2 } } { 2 \sigma ^ { 2 } } \right) ,
+$$
+
+where $\mathbf { x }$ is the feature vector of data samples. By Bayes rule and considering an equal prior, i.e., $p ( \mathbf { c } _ { 1 } ) = p ( \mathbf { c } _ { 2 } ) = . . . = p ( \mathbf { c } _ { k } )$ , we can compute the probability of a feature vector $\mathbf { x }$ belonging to a cluster $\mathbf { c } _ { i }$ as:
+
+$$
+p \left( \mathbf { c } _ { i } \mid \mathbf { x } \right) = { \frac { p \left( \mathbf { c } _ { i } \right) p \left( \mathbf { x } \mid \mathbf { c } _ { i } \right) } { \sum _ { j } ^ { k } p \left( \mathbf { c } _ { j } \right) p \left( \mathbf { x } \mid \mathbf { c } _ { j } \right) } } = { \frac { \exp - { \frac { ( \mathbf { x } - \mathbf { c } _ { i } ) ^ { 2 } } { 2 \sigma ^ { 2 } } } } { \sum _ { j = 1 } ^ { k } \exp - { \frac { \left( \mathbf { x } - \mathbf { c } _ { j } \right) ^ { 2 } } { 2 \sigma ^ { 2 } } } } } .
+$$
+
+If $\sigma  0$ , we can obtain the hard assignments as the $k$ -means algorithm. As we can see, the probability of each feature vector belonging to a cluster reduces to computing the distance between them. Then we can construct our homophily loss function as follows:
+
+$$
+{ \mathcal H } ( f _ { \theta ^ { * } } ( \boldsymbol { \mathcal G } ) ) = \frac { 1 } { k | \mathcal { E } | } \sum _ { i = 1 } ^ { k } \sum _ { ( v _ { 1 } , v _ { 2 } ) \in \mathcal E } \ell ( p ( \mathbf { c } _ { i } | \mathbf { x } _ { v _ { 1 } } ) , p ( \mathbf { c } _ { i } | \mathbf { x } _ { v _ { 2 } } ) ) ,
+$$
+
+where $\ell$ is a loss function measuring the difference between the inputs. With soft assignments, the gradient of $\mathcal { H }$ w.r.t. $\theta$ becomes tractable.
+
+Search via Meta Gradient Descent. We now detail the differentiable search process for AUTOSSL-DS. A naive method to tackle bilevel problems is to alternatively optimize the inner and outer problems through gradient descent. However, we cannot perform gradient descent for the outer problem in Eq. (1) where $\mathcal { H }$ is not directly related to $\{ \lambda _ { i } \}$ . To address this issue, we can utilize meta-gradients, i.e., gradients w.r.t. hyperparameters, which have been widely used in solving bi-level problems in meta learning (Finn et al., 2017; Zugner¨ $\&$ G unnemann, 2019). To obtain meta- ¨ gradients, we need to backpropagate through the learning phase of the neural network. Concretely, the meta-gradient of $\mathcal { H }$ with respect to $\{ \lambda _ { i } \}$ is expressed as
+
+$$
+\nabla _ { \{ \lambda _ { i } \} } ^ { \mathrm { m e t a } } : = \nabla _ { \{ \lambda _ { i } \} } \mathcal { H } ( f _ { \theta ^ { * } } ( G ) ) \quad \mathrm { s . t . } \ \theta ^ { * } = \mathrm { o p t } _ { \theta } ( \mathcal { L } ( f _ { \theta } , \{ \lambda _ { i } , \ell _ { i } \} ) ) ,
+$$
+
+where $\operatorname { o p t } _ { \theta }$ stands for the inner optimization that obtains $\theta ^ { * }$ and it is typically multiple steps of gradient descent. As an illustration, we consider $\operatorname { o p t } _ { \theta }$ as $T + 1$ steps of vanilla gradient descent with learning rate $\epsilon$ ,
+
+$$
+\boldsymbol { \theta } _ { t + 1 } = \boldsymbol { \theta } _ { t } - \epsilon \nabla _ { \boldsymbol { \theta } _ { t } } \mathcal { L } \big ( f _ { \boldsymbol { \theta } _ { t } } , \{ \lambda _ { i } , \boldsymbol { \ell } _ { i } \} \big ) .
+$$
+
+By unrolling the training procedure, we can express meta-gradient as
+
+$$
+\begin{array} { r } { \nabla _ { \{ \lambda _ { i } \} } ^ { \mathrm { m e t a } } : = \nabla _ { \{ \lambda _ { i } \} } \mathcal { H } ( f _ { \theta _ { T } } ( G ) ) = \nabla _ { f _ { \theta _ { T } } } \mathcal { H } ( f _ { \theta _ { T } } ( G ) ) \cdot [ \nabla _ { \{ \lambda _ { i } \} } f _ { \theta _ { T } } ( G ) + \nabla _ { \theta _ { T } } f _ { \theta _ { T } } ( G ) \nabla _ { \{ \lambda _ { i } \} } \theta _ { T } ] , } \end{array}
+$$
+
+with $\begin{array} { r l } & { \nabla _ { \{ \lambda _ { i } \} } \theta _ { T } = \nabla _ { \{ \lambda _ { i } \} } \theta _ { T - 1 } - \epsilon \nabla _ { \{ \lambda _ { i } \} } \nabla _ { \theta _ { T - 1 } } \mathcal { L } ( f _ { \theta _ { T - 1 } } , \{ \lambda _ { i } , \ell _ { i } \} ) . \mathrm { S i n c e } \ \nabla _ { \{ \lambda _ { i } \} } f _ { \theta _ { T } } ( G ) = } \\ & { \qquad \nabla _ { \{ \lambda _ { i } \} } ^ { \mathrm { m e t a } } : = \nabla _ { \{ \lambda _ { i } \} } \mathcal { H } ( f _ { \theta _ { T } } ( G ) ) = \nabla _ { f _ { \theta _ { T } } } \mathcal { H } ( f _ { \theta _ { T } } ( G ) ) \cdot \nabla _ { \theta _ { T } } f _ { \theta _ { T } } ( G ) \nabla _ { \{ \lambda _ { i } \} } \theta _ { T } . } \end{array}$ , we have (9)
+
+Note that $\theta _ { T - 1 }$ also depends on the task weights $\{ \lambda _ { i } \}$ (see Eq. (7)). Thus, its derivative w.r.t. the task weights chains back until $\theta _ { 0 }$ . By unrolling all the inner optimization steps, we can obtain the meta-gradient $\nabla _ { \{ \lambda _ { i } \} } ^ { \mathrm { m e t a } }$ and use it to perform gradient descent on $\{ \lambda _ { i } \}$ to reduce $\mathcal { H }$ :
+
+$$
+\{ \lambda _ { i } \}  \{ \lambda _ { i } \} - \eta \nabla _ { \{ \lambda _ { i } \} } ^ { \mathrm { m e t a } } ,
+$$
+
+where $\eta$ is the learning rate for meta-gradient descent (outer optimization).
+
+However, if we use the whole training trajectory $\theta _ { 0 } , \theta _ { 1 } , \ldots , \theta _ { T }$ to calculate the precise metagradient, it would have an extremely high memory footprint since we need to store $\theta _ { 0 } , \theta _ { 1 } , \ldots , \theta _ { T }$ in memory. Thus, inspired by DARTS (Liu et al., 2018), we use an online updating rule where we only perform one step gradient descent on $\theta$ and then update $\{ \lambda _ { i } \}$ in each iteration. During the process, we constrain $\{ \lambda _ { i } \}$ in [0, 1] and dynamically adjust the task weights in a differentiable manner. The detailed algorithm for AUTOSSL-DS is summarized in Appendix C.
+
+# 4 EXPERIMENTAL EVALUATION
+
+In this section, we empirically evaluate the effectiveness of the proposed AUTOSSL on selfsupervised task search on real-world datasets. We aim to answer four questions as follows. Q1: Can AUTOSSL achieve better performance compared to training on individual SSL tasks? Q2: How does AUTOSSL compare to other unsupervised and supervised node representation learning baselines? Q3: Can we observe relations between AUTOSSL’s pseudo-homophily objective and downstream classification performance? and Q4: How do the SSL task weights, pseudo-homophily objective, and downstream performance evolve during AUTOSSL’s training?
+
+# 4.1 EXPERIMENTAL SETTING
+
+Since our goal is to enable automated combination search and discovery of SSL tasks, we use 5 such tasks including 1 contrastive learning method and 4 predictive methods – (1) DGI (Velickovi ˇ c´ et al., 2019): it is a contrastive learning method maximizing the mutual information between graph representation and node representation; (2) CLU (You et al., 2020), it predicts partition labels from Metis graph partition (Karypis & Kumar, 1998); (3) PAR (You et al., 2020), it predicts clustered labels from $k$ -means clustering on node features; (4) PAIRSIM (Jin et al., 2020; 2021), it predicts pairwise feature similarity between node pairs and (5) PAIRDIS (Peng et al., 2020), it predicts shortest path length between node pairs. The proposed AUTOSSL framework automatically learns to jointly leverage the 5 above tasks and carefully mediate their influence. We also note that (1) the recent contrastive learning method, MVGRL (Hassani & Khasahmadi, 2020), needs to deal with a dense diffusion matrix and is prohibitively memory/time-consuming for larger graphs; thus, we only include it as a baseline to compare as shown in Table 2; and (2) the proposed framework is general and it is straightforward to combine other SSL tasks.
+
+We perform experiments on 8 real-world datasets widely used in the literature (Yang et al., 2016; Shchur et al., 2018; Mernyei & Cangea, 2020; Hu et al., 2020), i.e., Physics, CS, Photo, Computers, WikiCS, Citeseer, CoraFull, and ogbn-arxiv. To demonstrate the effectiveness of the proposed framework, we follow (Hassani & Khasahmadi, 2020) and evaluate all methods on two different downstream tasks: node clustering and node classification. For the task of node clustering, we perform $k$ -means clustering on the obtained embeddings. We set the number of clusters to the number of ground truth classes and report the normalized mutual information (NMI) between the cluster results and ground truth labels. Regarding the node classification task, we train a logistic regression model on the obtained node embeddings and report the classification accuracy on test nodes. Note that labels are never used for self-supervised task search. All experiments are performed under 5 different random seeds and results are averaged. Following DGI and MVGRL, we use a simple one-layer GCN (Kipf & Welling, 2016a) as our encoder and set the size of hidden dimensions to 512. We set $2 \sigma ^ { 2 } = 0 . { \dot { 0 } } 0 1$ and use L1 loss in the homophily loss function throughout the experiments. Further details of experimental setup can be found in Appendix A.
+
+# 4.2 PERFORMANCE COMPARISON WITH INDIVIDUAL TASKS
+
+To answer Q1, Table 1 summarizes the results for individual self-supervised tasks and AUTOSSL under the two downstream tasks, i.e., node clustering and node classification. From the table, we make several observations. Obs. 1: individual self-supervised tasks have different node clustering and node classification performance for different datasets. For example, in Photo, DGI achieves the highest classification accuracy while PAR achieves the highest clustering performance; CLU performs better than PAIRDIS in both NMI and ACC on Physics while it cannot outperform PAIRDIS in WikiCS, Citeseer, Computers and CoraFull. This observation suggests the importance of searching suitable SSL tasks to benefit downstream tasks on different datasets. Obs. 2: Most of the time, combinations of SSL tasks searched by AUTOSSL can consistently improve the node clustering and classification performance over the best individual task on the all datasets. For example, the relative improvement over the best individual task on NMI from AUTOSSL-ES is $7 . 3 \%$ for WikiCS and $10 . 0 \%$ for Photo, and its relative improvement on ACC is $1 . 3 \%$ for WikiCS. These results indicate that composing multiple SSL tasks can help the model encode different types of information and avoid overfitting to one single task. Obs. 3: We further note that individual tasks resulted in different pseudo-homophily as shown in the P-H rows of Table 1. Among them, CLU tends to result in a low pseudo-homophily and often performs much worse than other tasks in node clustering task, which supports our theoretical analysis in Section 3.1. It also demonstrates the necessity to increase pseudo-homophily as the two variants of AUTOSSL effectively search tasks that lead to higher pseudo-homophily. Obs. 4: The performance of AUTOSSL-ES and AUTOSSLDS is close when their searched tasks lead to similar pseudo-homophily: the differences in pseudohomophily, NMI and ACC are relative smaller in datasets other than Photo and Computers. It is worth noting that sometimes AUTOSSL-DS can even achieve higher pseudo-homophily than AUTOSSL-ES. This indicates that the online updating rule for $\{ \lambda _ { i } \}$ in AUTOSSL-DS not only can greatly reduce the searching time but also can generate good task combinations. In addition to efficiency, we highlight another major difference between them: AUTOSSL-ES directly finds the best task weights while AUTOSSL-DS adjusts the task weights to generate appropriate gradients to update model parameters. Hence, if we hope to find the best task weights and retrain the model, we should turn to AUTOSSL-ES. More details on their differences can be found in Appendix E.3.
+
+Table 1: Performance comparison of self-supervised tasks (losses) on node clustering and node classification. The NMI rows indicate node clustering performance; ACC rows indicate node classification accuracy $( \% )$ ; P-H stands for pseudo-homophily. AUTOSSL regularly outperforms individual pretext tasks. (Bold: best in all methods; Underline: best in individual tasks). Blue and red numbers indicate the statistically significant improvements over the best individual task, via paired t-test at level 0.05 and 0.1, respectively (same for Table 2 and Table 3).   
+
+<table><tr><td rowspan="2">Dataset</td><td rowspan="2">Metric</td><td colspan="5">Self-Supervised Task</td><td colspan="2">AUTOSSL</td></tr><tr><td>CLU</td><td>PAR</td><td>PAIRSIM</td><td>PAIRDIS</td><td>DGI</td><td>ES</td><td>DS</td></tr><tr><td rowspan="3">WikiCS</td><td>NMI</td><td>0.177±0.02</td><td>0.262±0.02</td><td>0.341±0.01</td><td>0.169±0.04</td><td>0.310±0.02</td><td>0.366±0.01</td><td>0.344±0.02</td></tr><tr><td>ACC</td><td>74.19±0.21</td><td>75.81±0.17</td><td>75.80±0.17</td><td>75.28±0.08</td><td>75.49±0.17</td><td>76.80±0.13</td><td>76.58±0.28</td></tr><tr><td>P-H</td><td>0.549</td><td>0.567</td><td>0.693</td><td>0.463</td><td>0.690</td><td>0.751</td><td>0.749</td></tr><tr><td rowspan="3">Citeseer</td><td>NMI</td><td>0.318±0.00</td><td>0.416±0.00</td><td>0.428±0.01</td><td>0.404±0.01</td><td>0.439±0.00</td><td>0.449±0.01</td><td>0.449±0.01</td></tr><tr><td>ACC</td><td>63.17±0.19</td><td>69.25±0.51</td><td>71.36±0.42</td><td>70.72±0.53</td><td>71.64±0.44</td><td>72.14±0.41</td><td>72.00±0.32</td></tr><tr><td>P-H</td><td>0.787</td><td>0.916</td><td>0.885</td><td>0.901</td><td>0.934</td><td>0.943</td><td>0.934</td></tr><tr><td rowspan="3">Computers</td><td>NMI</td><td>0.171±0.00</td><td>0.433±0.00</td><td>0.387±0.01</td><td>0.300±0.01</td><td>0.318±0.02</td><td>0.447±0.01</td><td>0.448±0.01</td></tr><tr><td>ACC</td><td>75.20±0.20</td><td>87.26±0.15</td><td>82.64±1.15</td><td>85.20±0.41</td><td>83.45±0.54</td><td>87.26±0.64</td><td>88.18±0.43</td></tr><tr><td>P-H</td><td>0.240</td><td>0.471</td><td>0.314</td><td>0.206</td><td>0.298</td><td>0.503</td><td>0.511</td></tr><tr><td rowspan="3">CoraFull</td><td>NMI</td><td>0.128±0.00</td><td>0.498±0.00</td><td>0.409±0.02</td><td>0.406±0.01</td><td>0.462±0.01</td><td>0.506±0.01</td><td>0.500±0.00</td></tr><tr><td>ACC</td><td>44.93±0.53</td><td>57.54±0.32</td><td>56.23±0.59</td><td>58.48±0.80</td><td>60.42±0.39</td><td>61.01±0.50</td><td>61.10±0.68</td></tr><tr><td>P-H</td><td>0.494</td><td>0.887</td><td>0.649</td><td>0.728</td><td>0.888</td><td>0.903</td><td>0.895</td></tr><tr><td rowspan="3">CS</td><td>NMI</td><td>0.658±0.01</td><td>0.767±0.01</td><td>0.749±0.01</td><td>0.635±0.03</td><td>0.747±0.01</td><td>0.772±0.01</td><td>0.771±0.01</td></tr><tr><td>ACC</td><td>88.58±0.27</td><td>92.75±0.12</td><td>92.68±0.09</td><td>89.56±1.01</td><td>90.91±0.51</td><td>93.26±0.16</td><td>93.35±0.09</td></tr><tr><td>P-H</td><td>0.845</td><td>0.882</td><td>0.886</td><td>0.786</td><td>0.883</td><td>0.895</td><td>0.890</td></tr><tr><td rowspan="3">Physics</td><td>NMI</td><td>0.692±0.00</td><td>0.704±0.00</td><td>0.674±0.00</td><td>0.420±0.05</td><td>0.670±0.00</td><td>0.725±0.00</td><td>0.726±0.00</td></tr><tr><td>ACC</td><td>93.60±0.07</td><td>95.07±0.06</td><td>95.05±0.10</td><td>91.69±1.02</td><td>94.03±0.15</td><td>95.57±0.02</td><td>95.13±0.36</td></tr><tr><td>P-H</td><td>0.911</td><td>0.913</td><td>0.905</td><td>0.821</td><td>0.906</td><td>0.921</td><td>0.923</td></tr><tr><td rowspan="3">Photo</td><td>NMI</td><td>0.327±0.00</td><td>0.509±0.01</td><td>0.439±0.04</td><td>0.293±0.08</td><td>0.376±0.03</td><td>0.560±0.04</td><td>0.515±0.03</td></tr><tr><td>ACC</td><td>90.33±0.22</td><td>91.75±0.25</td><td>91.13±0.35</td><td>91.97±0.32</td><td>92.08±0.37</td><td>92.04±0.89</td><td>92.71±0.32</td></tr><tr><td>P-H</td><td>0.434</td><td>0.602</td><td>0.428</td><td>0.327</td><td>0.401</td><td>0.791</td><td>0.616</td></tr><tr><td rowspan="3">ogbn-arxiv</td><td>NMI</td><td>0.305±0.01</td><td>0.410±0.01</td><td>0.379±0.01</td><td>0.314±0.01</td><td>0.319±0.01</td><td>0.424±0.00</td><td>0.417±0.00</td></tr><tr><td>ACC</td><td>66.68±0.34</td><td>67.90±0.10</td><td>67.82±0.20</td><td>67.63±0.13</td><td>67.95±0.56</td><td>68.31±0.05</td><td>69.13±0.04</td></tr><tr><td>P-H</td><td>0.441</td><td>0.660</td><td>0.482</td><td>0.326</td><td>0.390</td><td>0.830</td><td>0.780</td></tr><tr><td rowspan="2">Average Rank</td><td>NMI</td><td>6.3</td><td>3.5</td><td>4.1</td><td>6.5</td><td>4.6</td><td>1.3</td><td>1.5</td></tr><tr><td>ACC</td><td>6.8</td><td>3.9</td><td>4.9</td><td>5.4</td><td>3.9</td><td>1.8</td><td>1.4</td></tr></table>
+
+To answer Q2, we compare AUTOSSL with representative unsupervised and supervised node representation learning baselines. Specifically, for node classification we include 4 unsupervised baselines, i.e., GAE (Kipf & Welling, 2016b), VGAE (Kipf & Welling, 2016b), ARVGA (Pan et al., 2018) and MVGRL, and 2 supervised baselines, i.e. GCN and GAT (Velickovi ˇ c et al., 2018). We also ´ provide the logistic regression performance on raw features and embeddings generated by a randomly initialized encoder, named as Raw-Feat and Random-Init, respectively. Note that the two supervised baselines, GCN and GAT, use label information for node representation learning in an end-to-end manner, while other baselines and AUTOSSL do not leverage label information to learn representations. The average performance and variances are reported in Table 2. From the table, we find that AUTOSSL outperforms unsupervised baselines in all datasets except Citeseer while the performance on Citeseer is still comparable to the state-of-the-art contrastive learning method MVGRL. When compared to supervised baselines, AUTOSSL-DS outperforms GCN and GAT in 4 out of 8 datasets, e.g., a $1 . 7 \%$ relative improvement over GAT on Computers. AUTOSSL-ES also outperforms GCN and GAT in 3/4 out of 8 datasets. In other words, our unsupervised representation learning AUTOSSL can achieve comparable performance with supervised representation learning baselines. In addition, we use the same unsupervised baselines for node clustering and report the results in Table 3. Both AUTOSSL-ES and AUTOSSL-DS show highly competitive clustering performance. For instance, AUTOSSL-ES achieves $2 2 . 2 \%$ and $2 7 . 5 \%$ relative improvement over the second best baseline on Physics and WikiCS; AUTOSSL-DS also achieves $2 2 . 2 \%$ and $1 9 . 8 \%$ relative improvement on these two datasets. These results further validate that composing SSL tasks appropriately can produce expressive and generalizable representations.
+
+Table 2: Node classification accuracy $( \% )$ . The last two rows are supervised baselines. AUTOSSL consistently outperforms alternative self-supervised approaches, and frequently outperforms supervised ones. (Bold/Underline: best/runner-up among self-supervised approaches)   
+
+<table><tr><td>Model</td><td>WikiCs</td><td>Citeseer</td><td>Computers</td><td>CoraFull</td><td>Cs</td><td>Physics</td><td>Photo</td><td>ogbn-arxiv</td><td>Avg. Rank</td></tr><tr><td>Random-Init</td><td>75.07±0.15</td><td>64.06±2.28</td><td>74.42±0.29</td><td>45.07±0.38</td><td>28.57±0.90</td><td>53.33±0.52</td><td>87.01±0.39</td><td>67.55±0.27</td><td>6.0</td></tr><tr><td>Raw-Feat</td><td>72.06±0.03</td><td>61.50±0.00</td><td>74.15±0.48</td><td>37.17±0.30</td><td>87.12±0.42</td><td>92.81±0.24</td><td>79.03±0.37</td><td>51.07±0.00</td><td>7.0</td></tr><tr><td>GAE</td><td>74.85±0.24</td><td>64.76±1.35</td><td>80.25±0.42</td><td>57.85±0.29</td><td>92.35±0.09</td><td>94.66±0.10</td><td>91.51±0.39</td><td>52.57±0.04</td><td>4.1</td></tr><tr><td>VGAE</td><td>74.16±0.16</td><td>67.50±0.42</td><td>81.05±0.41</td><td>53.72±0.30</td><td>92.15±0.16</td><td>94.58±0.17</td><td>88.98±1.05</td><td>52.00±0.19</td><td>4.6</td></tr><tr><td>ARVGA</td><td>71.64±1.03</td><td>46.88±2.15</td><td>67.61±0.92</td><td>45.20±1.33</td><td>87.26±1.07</td><td>93.84±0.13</td><td>77.74±1.16</td><td>31.57±2.96</td><td>7.1</td></tr><tr><td>MvGRL</td><td>75.89±0.12</td><td>72.36±0.49</td><td>84.66±0.62</td><td>60.56±0.33</td><td>90.18±0.19</td><td>94.30±0.20</td><td>92.49±0.40</td><td>0OM</td><td>3.1</td></tr><tr><td>AUTOSSL-ES</td><td>76.80±0.13</td><td>72.14±0.41</td><td>87.26±0.64</td><td>61.01±0.50</td><td>93.26±0.16</td><td>95.57±0.02</td><td>92.04±0.89</td><td>68.31±0.05</td><td>1.9</td></tr><tr><td>AUTOSSL-DS</td><td>76.58±0.28</td><td>72.00±0.32</td><td>88.18±0.43</td><td>61.10±0.68</td><td>93.35±0.09</td><td>95.13±0.36</td><td>92.71±0.32</td><td>69.13±0.04</td><td>1.5</td></tr><tr><td>GCN</td><td>76.42±0.02</td><td>71.26±0.15</td><td>87.53±0.21</td><td>63.77±0.37</td><td>93.04±0.09</td><td>95.66±0.15</td><td>93.09±0.11</td><td>71.74±0.29</td><td>-</td></tr><tr><td>GAT</td><td>77.30±0.01</td><td>71.00±0.62</td><td>86.74±0.69</td><td>63.73±0.43</td><td>92.53±0.19</td><td>95.54±0.08</td><td>92.30±0.28</td><td>71.46±0.34</td><td>-</td></tr></table>
+
+Table 3: Clustering performance (NMI). AUTOSSL embeddings routinely exhibit superior NMI to alternatives. (Bold: best; Underline: runner-up).   
+
+<table><tr><td>Model</td><td>Wikics</td><td>Citeseer</td><td>Computers</td><td>CoraFull</td><td>CS</td><td>Physics</td><td>Photo</td><td>ogbn-arxiv</td><td>Avg. Rank</td></tr><tr><td>Random-Init</td><td>0.107±0.02</td><td>0.354±0.03</td><td>0.155±0.01</td><td>0.318±0.01</td><td>0.716±0.02</td><td>0.551±0.01</td><td>0.246±0.04</td><td>0.306±0.01</td><td>6.4</td></tr><tr><td>Raw-Feat</td><td>0.182±0.00</td><td>0.316±0.00</td><td>0.166±0.00</td><td>0.215±0.00</td><td>0.642±0.00</td><td>0.489±0.00</td><td>0.282±0.00</td><td>0.150±0.01</td><td>7.1</td></tr><tr><td>GAE</td><td>0.243±0.02</td><td>0.313±0.02</td><td>0.441±0.00</td><td>0.485±0.00</td><td>0.731±0.01</td><td>0.545±0.06</td><td>0.616±0.01</td><td>0.325±0.01</td><td>4.3</td></tr><tr><td>VGAE</td><td>0.261±0.01</td><td>0.364±0.01</td><td>0.423±0.00</td><td>0.453±0.01</td><td>0.733±0.00</td><td>0.563±0.02</td><td>0.530±0.04</td><td>0.311±0.01</td><td>4.0</td></tr><tr><td>ARVGA</td><td>0.287±0.02</td><td>0.191±0.02</td><td>0.237±0.01</td><td>0.301±0.01</td><td>0.616±0.03</td><td>0.526±0.05</td><td>0.301±0.01</td><td>0.201±0.01</td><td>6.4</td></tr><tr><td>MvGRL</td><td>0.263±0.01</td><td>0.452±0.01</td><td>0.244±0.00</td><td>0.400±0.01</td><td>0.740±0.01</td><td>0.594±0.00</td><td>0.344±0.04</td><td>OOM</td><td>4.3</td></tr><tr><td>AUTOSSL-ES</td><td>0.366±0.01</td><td>0.449±0.01</td><td>0.447±0.01</td><td>0.506±0.01</td><td>0.772±0.01</td><td>0.725±0.00</td><td>0.560±0.04</td><td>0.424±0.00</td><td>1.6</td></tr><tr><td>AUTOSSL-DS</td><td>0.344±0.02</td><td>0.449±0.01</td><td>0.448±0.01</td><td>0.500±0.00</td><td>0.771±0.01</td><td>0.726±0.00</td><td>0.515±0.03</td><td>0.417±0.00</td><td>2.1</td></tr></table>
+
+# 4.4 RELATION BETWEEN DOWNSTREAM PERFORMANCE AND PSEUDO-HOMOPHILY
+
+In this subsection, we investigate the relation between downstream performance and pseudohomophily and correspondingly answer Q3. Specifically, we use the candidate task weights sampled in the AUTOSSL-ES searching trajectory, and illustrate their node clustering (NMI) and node classification performance (ACC) with respect to their pseudo-homophily. The results on Computers and WikiCS are shown in Figure 2 and results for other datasets are shown in Appendix E.1. We observe that the downstream performance tends to be better if the learned embeddings tend to have higher pseudo-homophily. We also can observe that clustering performance has a clear relation with pseudo-homophily for all datasets. Hence, the results empirically support our theoretical analysis in Section 3.1 that lower pseudo-homophily leads to a lower upper bound of mutual information with ground truth labels. While classification accuracy has a less evident pattern, we can still observe that higher accuracy tends to concentrate on the high pseudo-homophily regions for 5 out of 7 datasets.
+
+![](images/0f44c5b78c22187294c3f0317663445e4b4fba33a4b1c415f473e77bcbabc464.jpg)  
+Figure 2: Relationship between downstream performance and pseudo-homophily.
+
+![](images/05e9a86a0047b55c80e283ce969d1fafc3e2a0d92bb29f900cd6ba6aade8dd87.jpg)  
+Figure 3: Visualization of Task Weights.
+
+![](images/05dd0d84837dced1cd172deea41865a3ec9602f4c2d0b066edfe339179763910.jpg)  
+Figure 4: P-H change of AUTOSSL-ES
+
+4.5 EVOLUTION OF SSL TASK WEIGHTS, PSEUDO-HOMOPHILY AND PERFORMANCE
+
+To answer Q4, we visualize the final task weights searched by AUTOSSL-ES on all datasets through the heatmap in Figure 3a. From the figure, we make three observations. Obs. 1: The searched task weights vary significantly from dataset to dataset. For example, the weights for PAR and DGI are [0.198, 0.980] on Physics while they are [0.955, 0.066] on WikiCS. Obs. 2: In general, Par benefits co-purchase networks, i.e. Photo and Computers; DGI is crucial for citation/coauthorship networks, i.e. Physics, CS, Citeseer, and CoraFull. We conjecture that local structure information (the information that PAR captures) is essential for co-purchase networks while both local and global information (the information that DGI captures) are necessary in citation/coauthorship networks. Obs. 3: AUTOSSL-ES always gives very low weights to CLU, which indicates the pseudo-labels clustered from raw features are not good supervision on the selected datasets.
+
+We also provide the evolution of task weights in AUTOSSL-DS for CoraFull dataset in Figure 3b. The weights of the 5 tasks eventually become stable: CLU and PAIRDIS are assigned with small values while PAIRSIM, DGI and CLU are assigned with large values. Thus, both AUTOSSL-ES and AUTOSSL-DS agree that PAIRDIS and PAR are less important for CoraFull.
+
+We further investigate how pseudo-homophily changes over iterations. For AUTOSSL-ES, we illustrate the mean value of resulted pseudo-homophily in each iteration (round) in Figure 4. We only show the results on CoraFull and Citeseer while similar patterns are exhibited in other datasets. It is clear that AUTOSSL-ES can effectively increase the pseudo-homophily and thus search for better self-supervised task weights. The results for AUTOSSL-DS are deferred to Appendix E.2 due to the page limit.
+
+# 5 CONCLUSION
+
+Graph self-supervised learning has achieved great success in learning expressive node/graph representations. In this work, however, we find that SSL tasks designed for graphs perform differently on different datasets and downstream tasks. Thus, it is worth composing multiple SSL tasks to jointly encode multiple sources of information and produce more generalizable representations. However, without access to labeled data, it poses a great challenge in measuring the quality of the combinations of SSL tasks. To address this issue, we take advantage of graph homophily and propose pseudo-homophily to measure the quality of combinations of SSL tasks. We then theoretically show that maximizing pseudo-homophily can help maximize the upper bound of mutual information between the pseudo-labels and ground truth labels. Based on the pseudo-homophily measure, we develop two automated frameworks AUTOSSL-ES and AUTOSSL-DS to search the task weights efficiently. Extensive experiments have demonstrated that AUTOSSL is able to produce more generalize representations by combining various SSL tasks.
+
+# ACKNOLWEDGEMENT
+
+Wei Jin and Jiliang Tang are supported by the National Science Foundation (NSF) under grant numbers IIS1714741, CNS1815636, IIS1845081, IIS1907704, IIS1928278, IIS1955285, IOS2107215, and IOS2035472, the Army Research Office (ARO) under grant number W911NF-21-1-0198, the Home Depot, Cisco Systems Inc. and SNAP Inc.
+
+# ETHICS STATEMENT
+
+To the best of our knowledge, there are no ethical issues with this paper.
+
+# REPRODUCIBILITY STATEMENT
+
+To ensure reproducibility of our experiments, we provide our source code at https://github.   
+com/ChandlerBang/AutoSSL. The hyper-parameters are described in details in the appendix.   
+We also provide a pseudo-code implementation of our framework in the appendix.
+
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+
+# A EXPERIMENTAL SETUP
+
+Dataset Statistics. We evaluate the proposed framework on seven real-world datasets. The dataset statistics are shown in 4. All datasets can be loaded from PyTorch Geometric (Fey & Lenssen, 2019). When we evaluate the node classification performance, we need to use the training and test data. For WikiCS (Mernyei & Cangea, 2020), ogbn-arxiv (Hu et al., 2020) and Citeseer (Yang et al., 2016), we use the public data splits provided by the authors. For other datasets, we split the nodes into $1 0 \% / 1 0 \% / 8 0 \%$ for training/validation/test.
+
+Table 4: Dataset statistics.   
+
+<table><tr><td>Dataset</td><td>Network Type</td><td>#Nodes</td><td>#Edges</td><td>#Classes</td><td>#Features</td><td>Homophily</td></tr><tr><td>WikiCS</td><td>Reference network</td><td>11,701</td><td>216,123</td><td>10</td><td>300</td><td>0.70</td></tr><tr><td>CS</td><td>Co-authorship network</td><td>18,333</td><td>81,894</td><td>15</td><td>6,805</td><td>0.81</td></tr><tr><td>Physics</td><td>Co-authorship network</td><td>34,493</td><td>247,962</td><td>5</td><td>8,415</td><td>0.93</td></tr><tr><td>Computers</td><td>Co-purchase network</td><td>13,381</td><td>245,778</td><td>10</td><td>767</td><td>0.78</td></tr><tr><td>Photo</td><td>Co-purchase network</td><td>7,487</td><td>119,043</td><td>8</td><td>745</td><td>0.83</td></tr><tr><td>CoraFull</td><td>Citation network</td><td>19,793</td><td>65,311</td><td>70</td><td>8,710</td><td>0.57</td></tr><tr><td>Citeseer</td><td>Citation network</td><td>3,327</td><td>4,732</td><td>6</td><td>3,703</td><td>0.74</td></tr><tr><td>ogbn-arxiv</td><td>Citation network</td><td>169,343</td><td>1,166,243</td><td>40</td><td>128</td><td>0.78</td></tr></table>
+
+Hyper-parameter Settings. When calculating pseudo-homophily, we set the number of clusters to 10 for ogbn-arxiv and Computers, and 5 for other datasets. A small number of clusters can be more efficient but could be less stable. Following DGI (Velickovi ˇ c et al., 2019) and M ´ VGRL (Hassani & Khasahmadi, 2020), we we use a simple one-layer GCN (Kipf & Welling, 2016a) as our encoder. We set the size of hidden dimensions to 512, weight decay to 0, dropout rate to 0. For individual SSL methods and AUTOSSL-ES, we set learning rate to 0.001, use Adam optimizer (Kingma & Ba, 2014), train the models with 1000 epochs and adopt early stopping strategy. For AUTOSSLDS, we train the models with 1000 epochs and choose the model checkpoint that achieves the highest pseudo-homophily. We use Adam optimizer for both inner and outer optimization. The learning rate for outer optimization is set to 0.05. For AUTOSSL-ES, we use a population size of 8 for each round. Due to limited computational resources, we perform 80 rounds for Citeseer, 40 rounds for CS, Computers, CoraFull, Photo, Physics, Computers and WikiCS. We repeat the experiments on 5 different random seeds and report the mean values and variances for downstream performance. To fit DGI into GPU memory on larger datasets and accelerate its training, instead of using all the nodes we sample 2000 positive samples and 2000 negative samples for DGI on all datasets except Citeseer.
+
+Hardware and Software Configurations. We perform experiments on one NVIDIA Tesla K80 GPU and one NVIDIA Tesla V100 GPU. Additionally, we use eight CPUs, with the model name as Intel(R) Xeon(R) Platinum 8260 CPU $\textcircled { a } 2 . 4 0 \mathrm { G H z }$ . The operating system we use is CentOS Linux 7 (Core).
+
+# B PROOF
+
+Theorem 1. Suppose that we are given with a graph $\mathcal { G } = \{ \nu , \varepsilon \}$ , a pseudo label vector $A \in$ $\{ 0 , 1 \} ^ { N }$ and a ground truth label vector $B \in \{ \breve { 0 } , \bar { 1 } \bar  \} ^ { N }$ defined on the node set. We denote the homophily of $A$ and $B$ over $\mathcal { G }$ as $h _ { A }$ and $h _ { B }$ , respectively. If the classes in $A$ and $B$ are balanced and $h _ { A } \mathrm { ~ } / h _ { B }$ , the following results hold: $( l )$ the mutual information between $A$ and $B$ , i.e., $M I ( A , B )$ , has an upper bound $\mathcal { U } _ { A , B }$ , where $\begin{array} { r } { \mathcal { U } _ { A , B } = \frac { 1 } { N } \left[ 2 \Delta \log ( \frac { \check { \mathfrak { q } } } { N } \Delta ) + 2 ( \frac { N } { 2 } - \Delta ) \log \left( \frac { 4 } { N } ( \frac { N } { 2 } - \Delta ) \right) \right] } \end{array}$ with $\begin{array} { r } { \Delta = \frac { ( h _ { B } - h _ { A } ) | \mathcal { E } | } { 2 d _ { m a x } } } \end{array}$ and $d _ { m a x }$ denoting the largest node degree in the graph; (2) if $h _ { A } < h _ { A ^ { \prime } } < h _ { B }$ , we have $\mathcal { U } _ { A , B } < \mathcal { U } _ { A ^ { \prime } , B }$ .
+
+Proof. (1) We start with the proof of the first result. The mutual information between two random variables $X$ and $Y$ is expressed as
+
+$$
+M I ( X , Y ) = \sum _ { y \in \mathcal { Y } } \sum _ { x \in \mathcal { X } } p _ { ( A , B ) } ( x , y ) \log \left( \frac { p _ { ( X , Y ) } ( x , y ) } { p _ { X } ( x ) p _ { Y } ( y ) } \right) .
+$$
+
+Let $\mathbf { \mathcal { A } } _ { i }$ and $B _ { i }$ denote the set of nodes in the $i$ -th class in $A$ and $B$ , respectively. Following the definition in Eq. (11), the mutual information between $A$ and $B$ can be formulated as,
+
+$$
+M I ( A , B ) = \sum _ { i = 0 } ^ { n _ { A } - 1 } \sum _ { j = 0 } ^ { n _ { B } - 1 } \frac { | A _ { i } \cap \mathcal { B } _ { j } | } { N } \log \frac { N | \mathcal { A } _ { i } \cap \mathcal { B } _ { j } | } { | \mathcal { A } _ { i } | | \mathcal { B } _ { j } | } ,
+$$
+
+where $n _ { A } , n _ { B }$ denote the number of classes in $A$ and $B$ . Since here we only consider 2 classes in $A$ and $B$ , we have
+
+$$
+\begin{array} { r l } & { \displaystyle M I ( A , B ) = \frac { \left| \mathcal A _ { 0 } \cap \mathcal B _ { 0 } \right| } { N } \log \frac { N \left| \mathcal A _ { 0 } \cap \mathcal B _ { 0 } \right| } { \left| \mathcal A _ { 0 } \right| \left| \mathcal B _ { 0 } \right| } + \frac { \left| \mathcal A _ { 0 } \cap \mathcal B _ { 1 } \right| } { N } \log \frac { N \left| \mathcal A _ { 0 } \cap \mathcal B _ { 1 } \right| } { \left| \mathcal A _ { 0 } \right| \left| \mathcal B _ { 1 } \right| } } \\ & { \quad \quad \quad \quad + \frac { \left| \mathcal A _ { 1 } \cap \mathcal B _ { 0 } \right| } { N } \log \frac { N \left| \mathcal A _ { 1 } \cap \mathcal B _ { 0 } \right| } { \left| \mathcal A _ { 1 } \right| \left| \mathcal B _ { 0 } \right| } + \frac { \left| \mathcal A _ { 1 } \cap \mathcal B _ { 1 } \right| } { N } \log \frac { N \left| \mathcal A _ { 1 } \cap \mathcal B _ { 1 } \right| } { \left| \mathcal A _ { 1 } \right| \left| \mathcal B _ { 1 } \right| } . } \end{array}
+$$
+
+Let $| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 0 } | = x , | \mathcal { A } _ { 0 } | = a$ and $| B _ { 0 } | = b$ . We then have
+
+$$
+\left\{ \begin{array} { l l } { \left| \mathcal { A } _ { 0 } \right| + \left| \mathcal { A } _ { 1 } \right| = N \Rightarrow \left| \mathcal { A } _ { 1 } \right| = N - a , } \\ { \left| \mathcal { B } _ { 0 } \right| + \left| \mathcal { B } _ { 1 } \right| = N \Rightarrow \left| \mathcal { B } _ { 1 } \right| = N - b , } \\ { \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 0 } \right| + \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 1 } \right| = \left| \mathcal { A } _ { 0 } \right| \Rightarrow \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 1 } \right| = a - x , } \\ { \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 0 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 0 } \right| = \left| \mathcal { B } _ { 0 } \right| \Rightarrow \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 0 } \right| = b - x , } \\ { \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 1 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 1 } \right| = \left| \mathcal { B } _ { 1 } \right| \Rightarrow \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 1 } \right| = N - b - a + x . } \end{array} \right.
+$$
+
+With the equations above, we rewrite $M I ( A , B )$ as follows,
+
+$$
+\begin{array} { c } { { M I ( A , B ) = \displaystyle \frac { 1 } { N } [ x \log \displaystyle \frac { N x } { a b } + ( a - x ) \log \displaystyle \frac { N ( a - x ) } { a ( N - b ) } } } \\ { { + ( b - x ) \log \displaystyle \frac { N ( b - x ) } { ( N - a ) b } + ( N - b - a + x ) \log \displaystyle \frac { N ( N - b - a + x ) } { ( N - a ) ( N - b ) } ] . } } \end{array}
+$$
+
+Then we rewrite result (1) in the theorem as an optimization problem,
+
+$$
+\operatorname* { m a x } f ( x ) = M I ( A , B )
+$$
+
+with constraints,
+
+$$
+\left\{ \begin{array} { l l } { 0 \leq | A _ { 0 } \cap B _ { 0 } | \leq | A _ { 0 } | \Rightarrow 0 \leq x \leq a , } \\ { 0 \leq | A _ { 0 } \cap B _ { 0 } | \leq | B _ { 0 } | \Rightarrow 0 \leq x \leq b , } \\ { | A _ { 1 } \cap B _ { 1 } | \geq 0 \Rightarrow x \geq a + b - N , } \\ { | A _ { 0 } \cap B _ { 0 } | + | A _ { 1 } \cap B _ { 1 } | \leq N \Rightarrow x \leq \frac { a + b } { 2 } , } \\ { | A _ { 0 } \cap B _ { 1 } | + | A _ { 1 } \cap B _ { 0 } | \leq N \Rightarrow x \geq \frac { a + b - N } { 2 } , } \end{array} \right.
+$$
+
+Note that the equality of $\begin{array} { r } { \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 0 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 1 } \right| \leq N } \end{array}$ holds when $A$ and $B$ are the same. However, $A$ and $B$ have different homophily, which indicates $\left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 0 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 1 } \right|$ cannot reach $N$ (the same for $\left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 1 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 0 } \right| )$ . Let $\mathcal { E } _ { A } , \mathcal { E } _ { B }$ denote the inter-class edges for $A$ and $B$ , respectively. Thus, $\begin{array} { r } { h _ { A } = 1 - \frac { | { \mathcal E } _ { A } | } { | { \mathcal E } | } } \end{array}$ and $\begin{array} { r } { h _ { B } = 1 - \frac { | { \mathcal E } _ { B } | } { | { \mathcal E } | } } \end{array}$ |EB ||E| . Since hA < hB , we have |EA| > |EB |. This indicates that there are at least $\left. \mathcal { E } _ { A } \right. - \left. \mathcal { E } _ { B } \right.$ edges in $A$ connecting nodes that belong to the same ground truth class, as shown in Figure 5.
+
+![](images/7af606b7dd6ad123d70029a07ef6828285e51bc874cd8f06b0bc928c507ebd1a.jpg)  
+Figure 5: Illustration for $\left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 0 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 1 } \right|$ . The two dashed rectangles divide the nodes into $\mathcal { A } _ { 0 }$ and $\mathcal { A } _ { 1 }$ ; red and blue nodes denote nodes in $B _ { 0 }$ and $\boldsymbol { B } _ { 1 }$ , respectively.
+
+Let $d _ { \mathrm { m a x } }$ denote the maximum degree in the graph and we know that at least $\frac { | \mathcal { E } _ { A } | - | \mathcal { E } _ { B } | } { d _ { \operatorname* { m a x } } }$ nodes are “misplaced” in $A$ , e.g., in Figure 5 the red node in $\boldsymbol { \mathcal { A } } _ { 1 }$ should be placed in $A _ { 0 }$ to achieve $| { \mathcal { A } } _ { 0 } \cap B _ { 0 } | +$ |A1 ∩ B1| = N . Let ∆ = |EA|−|EB| = $\begin{array} { r } { \Delta = \frac { | \mathcal { E } _ { A } | - | \mathcal { E } _ { B } | } { 2 d _ { \operatorname* { m a x } } } = \frac { ( h _ { B } - h _ { A } ) | \mathcal { E } | } { 2 d _ { \operatorname* { m a x } } } } \end{array}$ (hB−hA)|E| , and we have |A0 ∩ B0| + |A1 ∩ B1| ≤ N − 2∆ and $\begin{array} { r } { \left| \mathcal { A } _ { 0 } \cap \mathcal { B } _ { 1 } \right| + \left| \mathcal { A } _ { 1 } \cap \mathcal { B } _ { 0 } \right| \le \overline { { N } } - 2 \Delta } \end{array}$ .
+
+With the new constraints, we rewrite the optimization problem as
+
+$$
+\operatorname* { m a x } f ( x ) = M I ( A , B ) \quad { \mathrm { s . t . ~ } } { \left\{ \begin{array} { l l } { 0 \leq x \leq a , } \\ { x \leq b , } \\ { x \geq a + b - N , } \\ { x \leq { \frac { a + b - 2 \Delta } { 2 } } , } \\ { x \geq { \frac { a + b - ( N - 2 \Delta ) } { 2 } } , } \end{array} \right. }
+$$
+
+Further, the derivative of $f ( x )$ is expressed as follows,
+
+$$
+f ^ { \prime } ( x ) = \frac { 1 } { N } \log \frac { x ( N - b - a + x ) } { ( a - x ) ( b - x ) } .
+$$
+
+Let $f ^ { \prime } ( x ) \ > \ 0$ , we have $\begin{array} { l l l } { x } & { > } & { { \frac { a b } { N } } } \end{array}$ ; let $f ^ { \prime } ( x ) \ < \ 0$ , we have $\begin{array} { l l l } { x } & { < } & { { \frac { a b } { N } } } \end{array}$ . Thus, $f ( x )$ is g at . $\begin{array} { r } { [ \operatorname* { m a x } ( 0 , a + b - N , \frac { a + b - ( N - 2 \Delta ) } { 2 } ) , \frac { a b } { N } ] } \end{array}$ and monotonically increasing $\begin{array} { r } { [ \frac { a b } { N } , \operatorname* { m i n } ( a , b , \frac { a + b - 2 \Delta } { 2 } ) ] } \end{array}$
+
+Note that in the theorem we assume the pseudo-labels and ground truth classes are balanced, i.e., $\begin{array} { r } { a = b = \frac { N } { 2 } } \end{array}$ . Then $M I ( A , B )$ becomes,
+
+$$
+M I ( A , B ) = f ( x ) = \frac { 1 } { N } \left[ 2 x \log \frac { 4 } { N } x + 2 ( \frac { N } { 2 } - x ) \log \left( \frac { 4 } { N } ( \frac { N } { 2 } - x ) \right) \right] .
+$$
+
+Hence, $f ( x )$ is monotonically decreasing at $[ \Delta , \frac { N } { 4 } ]$ and monotonically increasing $\begin{array} { r } { [ \frac { N } { 4 } , \frac { N } { 2 } - \Delta ] } \end{array}$ . So the maximum value of $f ( x )$ is at either $x = \Delta$ or $\begin{array} { r } { x = \frac { N } { 2 } - \Delta } \end{array}$ . Further it is easy to know that $\begin{array} { r } { f ( \frac { N } { 4 } - x ) = f ( \frac { N } { 4 } + x ) } \end{array}$ . Then we have $\begin{array} { r } { f ( \Delta ) = f ( \frac { N } { 2 } - \Delta ) } \end{array}$ , and we can get the maximum value of $f ( x )$ as follows,
+
+$$
+\mathcal { U } _ { A , B } = \operatorname* { m a x } f ( x ) = f ( \Delta ) = \frac { 1 } { N } \left[ 2 \Delta \log ( \frac { 4 } { N } \Delta ) + 2 ( \frac { N } { 2 } - \Delta ) \log \left( \frac { 4 } { N } ( \frac { N } { 2 } - \Delta ) \right) \right]
+$$
+
+with $\begin{array} { r } { \Delta \ = \ \frac { ( h _ { B } - h _ { A } ) | \mathcal { E } | } { 2 d _ { \operatorname* { m a x } } } } \end{array}$ . In other words, $M I ( A , B )$ reaches its upper bound when $\vert { \mathcal { A } } _ { 0 } \cap { \mathcal { B } } _ { 0 } \vert =$ $\frac { ( h _ { B } - h _ { A } ) | \varepsilon | } { 2 d _ { \operatorname* { m a x } } }$ or $\begin{array} { r l r } {  { \frac { N } { 2 } - \frac { ( h _ { B } - h _ { A } ) | \mathcal { E } | } { 2 d _ { \operatorname* { m a x } } } } } \end{array}$
+
+aints . Bas $\begin{array} { r } { x \le \frac { a + b - 2 \Delta } { 2 } } \end{array}$ nd sio $\begin{array} { r } { x \ge \frac { a + b - ( N - 2 \Delta ) } { 2 } } \end{array}$ h 8), we have  is monotoni $\frac { a + b - ( N - 2 \Delta ) } { 2 } \leq$ $\begin{array} { r } { \frac { a + b - 2 \Delta } { 2 } \Rightarrow \Delta \leq \frac { N } { 4 } } \end{array}$ N4 ed on the discus n in (1), we know t at f (∆) cally decreasing $[ 0 , \frac { N } { 4 } ]$ $\Delta$ $f ( \Delta )$ $\mathcal { U } _ { A , B }$ Since $\begin{array} { r } { \dot { \Delta } = \frac { ( h _ { B } - h _ { A } ) | \mathcal { E } | } { 2 d _ { \operatorname* { m a x } } } } \end{array}$ , a decrease in $h _ { A }$ will lead to a increase in $\Delta$ . Then we have $\mathcal { U } _ { A , B } < \mathcal { U } _ { A ^ { \prime } , B }$ if $h _ { A } < h _ { A ^ { \prime } } < h _ { B } ^ { -- }$ .
+
+Remark on a more generalized case. We now discuss the case where we do not have assumptions on $a$ and $b$ . As we demonstrated in the above discussion, $f ( x )$ is mono$\begin{array} { r } { [ \operatorname* { m a x } ( 0 , a \ + \ b \ - \ N , \frac { a + b - ( N - 2 \Delta ) } { 2 } ) , \frac { a b } { N } ] } \end{array}$ and monotonically incrhould be one of the valAs our goal is to show that $\begin{array} { r } { [ \frac { a b } { N } , \operatorname* { m i n } ( a , b , \frac { a + b - 2 \Delta } { 2 } ) ] } \end{array}$ $f ( x )$ $\bar { f ( 0 ) } , f ( a + b - \bar { N ) } , f ( \frac { a + b - ( N - 2 \Delta ) } { 2 } ) , f ( a ) , f ( b )$ $f ( \frac { a + b - 2 \Delta } { 2 } )$ $\mathcal { U } _ { A , B }$ would be small with low $h _ { A }$ , to simplify the analysis, we consider a large value of $\Delta$ (or a small value of $h _ { A }$ ) which satisfies $\Delta \ge \frac { 1 } { 2 } | \dot { N } - \mathbf { \bar { \Phi } } ( a + b ) |$ and $\Delta \geq { \frac { 1 } { 2 } } | a - b |$ . This indicates $x$ is bounded by $\big [ \frac { a + b - ( N - 2 \Delta ) } { 2 } , \frac { a + b - 2 \Delta } { 2 } \big ]$ . Then the maximum value of $f ( x )$ , i.e., $\mathcal { U } _ { A , B }$ , is expressed as
+
+$$
+\mathcal { U } _ { A , B } = \operatorname* { m a x } ( f ( \frac { a + b - ( N - 2 \Delta ) } { 2 } ) , f ( \frac { a + b - 2 \Delta } { 2 } ) ) .
+$$
+
+When to smaWhen $\begin{array} { r } { \frac { a + b - ( N - 2 \Delta ) } { 2 } \leq \frac { a b } { N } \leq \frac { a + b - 2 \Delta } { 2 } } \end{array}$ larger  be cl. It d $\Delta$ (or smaller r to the mineases with t $h _ { A }$ ) will la point ncrease d.f $\mathcal { U } _ { A , B }$ $\frac { a + b ^ { - } ( N - 2 \Delta ) } { 2 }$ a+b−2∆ will ose im ab $\textstyle { \frac { a b } { N } }$ $\begin{array} { r } { \frac { a b } { N } \ \leq \ \frac { a + b - ( N - 2 \Delta ) } { 2 } \ \leq \ \frac { a + b - 2 \overline { { \Delta } } } { 2 } } \end{array}$ $\mathcal { U } _ { A , B } ~ = ~ f ( \frac { a + b - 2 \Delta } { 2 } )$ $\Delta$ $h _ { A }$ $\frac { a + b - 2 \Delta } { 2 }$ gets closer to the minises with the increase of point (or the $\textstyle { \frac { a b } { N } }$ . Similarcrease of when). To $\begin{array} { r } { \frac { a + b - ( N - 2 \Delta ) } { 2 } \leq \frac { a + b - 2 \Delta } { 2 } \leq \frac { a b } { N } , \mathcal { U } _ { A , B } } \end{array}$ $\Delta$ $h _ { A }$ sum up, for small $h _ { A } ^ { - }$ , the upper bound of $M I ( A , B )$ , decreases with the decrease of
+
+# C ALGORITHM
+
+The detailed algorithm for AUTOSSL-ES is shown in Algorithm 1. Concretely, for each round (iteration) of AUTOSSL-ES, we sample $K$ sets of task weights, i.e., $K$ different combinations of SSL tasks, from a multivariate normal distribution. Then we train $K$ graph neural networks independently on each set of task weights. Afterwards, we calculate the pseudo-homohily for each network and adjust the mean and variance of the multivariate normal distribution through CMA-ES based on their pseudo-homohily.
+
+The detailed algorithm for AUTOSSL-DS is summarized in Algorithm 2. Specifically, we first update the GNN parameter $\theta$ through one step gradient descent; then we perform $k$ -means clustering to obtain centroids, which are used to calculate the homophily loss $\mathcal { H }$ . Afterwards, we calculate the meta-gradient ∇meta{λ }, update $\{ \lambda _ { i } \}$ through gradient descent and clip $\{ \lambda _ { i } \}$ to $[ 0 , 1 ]$ .
+
+# Algorithm 1: AUTOSSL-ES: AutoSSL with Evolutionary Strategy
+
+for $r$ in $\{ 0 , \ldots , R \}$ do
+
+1. Sample $K$ sets of tasks weights from a multivariate normal distribution 2. Train $K$ networks w.r.t. each set of task weights from scratch 3. Calculate pseudo-homophily P-H of node embeddings from each network 4. Adjust the multivariate normal distribution through CMA-ES based on P-H nd
+
+# Algorithm 2: AUTOSSL-DS: AutoSSL with Differential Search
+
+Initialize self-supervised task weights $\{ \lambda _ { i } \}$ and GNN parameters $\theta$ ;   
+for t in $\{ 0 , \ldots , { \bar { T } } \}$ do 1. $\dot { \theta _ { t + 1 } } = \theta _ { t } - \epsilon \nabla _ { \theta _ { t } } \mathcal { L } ( f _ { \theta _ { t } } , \{ \lambda _ { i } , \ell _ { i } \} )$ 2. Perform $k$ -means clustering on $\dot { f } _ { \theta _ { t } } ( \mathcal { G } )$ and obtain centroids $\{ \mathbf { c } _ { 1 } , \mathbf { c } _ { 2 } , \ldots , \mathbf { c } _ { k } \}$ 3. Calculate $p \left( \mathbf { c } _ { i } \mid \mathbf { x } \right)$ according to Eq. (4) 4. Calculate homophily loss $\mathcal { H }$ according to Eq. (5) 5. $\{ \lambda _ { i } \}  \{ \lambda _ { i } \} - \eta \nabla _ { \{ \lambda _ { i } \} } ^ { \mathrm { m e t a } }$ 6. Clip $\{ \lambda _ { i } \}$ to [0,1]
+
+end
+
+# D DISCUSSIONS ON HOMOPHILY ASSUMPTION
+
+Most of the graphs in our real life satisfy the homophily assumption (McPherson et al., 2001), such as social networks, citation networks, co-purchase networks, etc. Thus, in general, we can treat homophily as a prior knowledge for a majority of real-world graphs. Moreover, it has been shown in (Zhu et al., 2020a; Pei et al., 2020) that most GNNs (such as GCN, GAT, ChebyNet and GraphSage) heavily rely on the homophily assumption and fail to generalize to low-homophily (heterophily) graphs even with label information. Thus, following the design of most GNNs, we focus on the homophily graphs. In addition, to apply our method on heterophily graphs, we can use the graph transformation algorithm (Suresh et al., 2021) to increase the homophily of a given graph. While heterophily graphs also exist in real-world applications, the research of GNNs on heterophily graphs is still at the very early stage even in the cases where the label information is available. Therefore, we will leave the research for heterophily graphs in the unsupervised setting as a future work.
+
+# E ADDITIONAL EXPERIMENTAL RESULTS
+
+# E.1 RELATIONSHIP BETWEEN DOWNSTREAM PERFORMANCE AND PSEUDO-HOMOPHILY
+
+We provide more results on the relation between downstream performance and pseudo-homophily in Figure 6. Observations are already made in Section 4.4.
+
+![](images/00e121677eae83db8d9236610b701b47dfe2f995a1db7ce390fa32a75181337c.jpg)  
+Figure 6: Relationship between downstream performance and pseudo-homophily.
+
+![](images/ddfaf8cd6e011b0fb0cf2793ea9fe292451918f5530e9c4d2568781dab014b0e.jpg)  
+Figure 7: Pseudo-homophily versus NMI/ACC/Loss on Citeseer for AUTOSSL-DS. The vertical dashed line indicates the iteration when pseudo-homophily reaches the maximum value.
+
+# E.2 PSEUDO-HOMOPHILY OVER ITERATIONS
+
+We investigate how pseudo-homophily changes over iterations for AUTOSSL-DS. The changes of pseudo-homophily, NMI, ACC and homophily loss (Eq. (5)) are plotted in Figure 7. From Figure 7a and 7b, we can observe that pseudo-homophily first increases and then becomes stable through iterations. The situation is a bit different for clustering and classification performance: NMI and ACC first increase with the increase of pseudo-homophily and then drop when pseudo-homophily is relatively stable. This indicates that overtraining can hurt downstream performance as the model will have the risk of overfitting on the combined SSL tasks. However, as shown in the figure, if we stop at the iteration when pseudo-homophily reaches the maximum value we can still get a high NMI and ACC. On a separate note, Figure $\mathrm { 7 c }$ shows how the homophily loss used in AUTOSSL-DS changes over iterations. We note that in the first iterations the homophily loss is low but the pseudohomophily is also low. This is because the embeddings in the first few epochs are less separable and would lead to very close soft-assignment of clusters. As shown in the figure, however, the problem is resolved as the embeddings become more distinguishable through iterations. Thus, we argue that the homophily loss in Eq. (5) is still a good proxy in optimizing pseudo-homophily.
+
+# E.3 EFFICIENCY ANALYSIS
+
+# E.3.1 TIME COMPLEXITY ANALYSIS
+
+We analyze the time complexity of the proposed AUTOSSL. Here we call one set of task weights $\{ \lambda _ { i } \}$ as one candidate solution. We denote the time of training one epoch on a given set of SSL tasks as $t _ { o }$ and the evaluation time is $t _ { e }$ . Suppose we need to train $T$ epochs for the network. Then the time for running one single candidate solution is $T t _ { o } + t _ { e }$ ; the time of running $R$ rounds of AUTOSSL-ES should be $R T t _ { o } + R t _ { e }$ . For AUTOSSL-DS, the running time is $T t _ { o } + T t _ { e }$ . As an illustration, in an $L$ -layer GCN with $d$ as the number of hidden dimensions, $t _ { o }$ can be expressed as $O ( L | \mathcal { E } | d + L N d ^ { 2 } )$ and $t _ { e }$ has time complexity of $O ( K I N d )$ with $K$ being the number of clusters and $I$ being the number of iterations for $k$ -means. Hence, we also express the time complexity of AUTOSSL-ES as $O ( R T L | \mathcal { E } | d + R T L N d ^ { 2 } + R K I N d )$ and that of AUTOSSL-DS as $\bar { O } ( T \bar { L } | \mathcal { E } | d + T L N d ^ { 2 } +$ $T K I N d )$ . Both of them linearly increase with the number of nodes $N$ when $\mathcal { E }$ is proportional to $N$ . We note that in AUTOSSL-DS, the complexity of calculating the second-order derivatives in backward propagation has an additional factor of $O ( | \theta | | \{ \lambda _ { i } \} | )$ , which can be reduced to $O ( | \{ \lambda _ { i } \} | )$ with approximated Hessian-vector products. The factor can be neglected as the number of tasks $O ( | \{ \lambda _ { i } \} | )$ is small.
+
+# E.3.2 EMPIRICAL COMPARISON
+
+For empirical comparison, we take Citeseer, Photo, CoraFull as examples to illustrate. As shown in Table 5, we compare the running time of different methods for training 1000 epochs on one NVIDIA-K80 GPU. The column of 5-Tasks indicates the running time of training a combination of 5 SSL tasks, i.e. CLU, PAR, PAIRSIM, PAIRDIS and DGI, for 1000 epochs. Note that we report the running time of AUTOSSL-ES as the multiplication between 500 and the time of 5-Tasks, i.e., running 500 candidate solutions. From the table, we can see that the running time of AUTOSSLES depends on the number of candidate solutions and usually takes a long time to run. However, AUTOSSL-DS significantly reduces the running time of AUTOSSL-ES. It is worth noting the stateof-the-art SSL task, MVGRL, takes a long time to run and suffers from the OOM issue when the dataset gets larger.
+
+Table 5: Comparison of running time for training 1000 epochs on one NVIDIA-K80 GPU (12 GB memory). OOM indicates out-of-memory on this GPU.   
+
+<table><tr><td></td><td>DGI</td><td>MvGRL</td><td>5-Tasks</td><td>AUTOSSL-ES</td><td>AUTOSSL-DS</td></tr><tr><td>Citeseer</td><td>222s</td><td>1220s</td><td>322s</td><td>322s×500</td><td>1222s</td></tr><tr><td>Photo</td><td>177s</td><td>1074s</td><td>507s</td><td>507s×500</td><td>1766s</td></tr><tr><td>CoraFull</td><td>553s</td><td>0OM</td><td>858s</td><td>858s×500</td><td>3584s</td></tr></table>
+
+# F COMPARISON WITH DIFFERENT STRATEGY
+
+In this subsection, we examine how other strategies of assigning task weights affect the quality of learned representations. The results are summarized in Table 6. In this table, “Best SSL” indicates the best performance achieved by the individual tasks; “Random Weight” indicates the performance achieved by randomly assigning task weights; “Equal Weight” indicates the performance achieved by assigning the same task weights (i.e., all 1). The values that outperform “Best SSL” are underlined. From the table, we make two observations. Obs 1. Unlike AUTOSSL, “Random Weight” and “Equal Weight” would hurt both NMI and ACC on some datasets, e.g., Citeseer. This suggests that SSL tasks might conflict with each other and thus harm the downstream performance. Obs 2. In some cases like Physics, “Equal Weight” can also improve both ACC and NMI, which aligns well with our initial motivation that combinations of SSL can help capture multiple sources of information and benefit the downstream performance. The two observations suggest that it is important to design a clever strategy that can automatically compose graph SSL tasks.
+
+# G COMPARISON WITH RANDOM SEARCH
+
+In this subsection, we choose Citeseer to study the difference between random search and evolutionary algorithm (AUTOSSL-ES), and report the result in Table 7. Specifically, the random search method randomly generates 800 sets of tasks weights and we evaluate the pseudo-homophily from the models trained with those task weights. Note that in AUTOSSL-ES we also evaluated 800 sets of tasks weights in total. From the table, we can see that random search is not as efficient as AUTOSSLES: with the same search cost, the resulted pseudo-homophily of random search is not as high as AUTOSSL-ES and the downstream performance is also inferior. This result suggests that search with evolutionary algorithm can find the optimum faster than random search.
+
+Table 6: Performance comparison of different strategies of assigning task weights. The NMI rows indicate node clustering performance; ACC rows indicate node classification accuracy $( \% )$ ; P-H stands for pseudo-homophily. (Underline: better than “Best SSL”).   
+
+<table><tr><td>Dataset</td><td>Metric</td><td>Best SSL</td><td>Random Weight</td><td>Equal Weight</td><td>AUTOSSL-ES</td><td>AUTOSSL-DS</td></tr><tr><td rowspan="3">Citeseer</td><td>NMI</td><td>0.439±0.00</td><td>0.398±0.01</td><td>0.408±0.00</td><td>0.449±0.01</td><td>0.449±0.01</td></tr><tr><td>ACC</td><td>71.64±0.44</td><td>70.64±0.07</td><td>70.80±0.31</td><td>72.14±0.41</td><td>72.00±0.32</td></tr><tr><td>P-H</td><td>1</td><td>0.897</td><td>0.904</td><td>0.943</td><td>0.934</td></tr><tr><td rowspan="3">Computers</td><td>NMI</td><td>0.433±0.00</td><td>0.341±0.03</td><td>0.290±0.00</td><td>0.447±0.01</td><td>0.448±0.01</td></tr><tr><td>ACC</td><td>87.26±0.15</td><td>86.86±0.25</td><td>87.24±0.38</td><td>87.26±0.64</td><td>88.18±0.43</td></tr><tr><td>P-H</td><td>1</td><td>0.406</td><td>0.378</td><td>0.503</td><td>0.511</td></tr><tr><td rowspan="3">CoraFull</td><td>NMI</td><td>0.498±0.00</td><td>0.458±0.02</td><td>0.493±0.00</td><td>0.506±0.01</td><td>0.500 ±0.00</td></tr><tr><td>ACC</td><td>60.42±0.39</td><td>58.88±0.32</td><td>59.01±0.29</td><td>61.01 ±0.50</td><td>61.10±0.68</td></tr><tr><td>P-H</td><td>1</td><td>0.811</td><td>0.868</td><td>0.903</td><td>0.895</td></tr><tr><td rowspan="3">CS</td><td>NMI</td><td>0.767±0.01</td><td>0.761±0.01</td><td>0.770 2±0.01</td><td>0.772 2±0.01</td><td>0.771 ±0.01</td></tr><tr><td>ACC</td><td>92.75±0.12</td><td>92.88±0.20</td><td>93.22 ±0.12</td><td>93.26 ±0.16</td><td>93.35 2±0.09</td></tr><tr><td>P-H</td><td>一</td><td>0.879</td><td>0.881</td><td>0.895</td><td>0.890</td></tr><tr><td rowspan="3">Photo</td><td>NMI</td><td>0.509±0.01</td><td>0.341±0.02</td><td>0.366±0.02</td><td>0.560±0.04</td><td>0.511 ±0.03</td></tr><tr><td>ACC</td><td>92.08±0.37</td><td>92.04±0.28</td><td>92.54±0.29</td><td>92.04±0.89</td><td>92.71±0.32</td></tr><tr><td>P-H</td><td>1</td><td>0.412</td><td>0.472</td><td>0.791</td><td>0.626</td></tr><tr><td rowspan="3">Physics</td><td>NMI</td><td>0.704±0.00</td><td>0.692±0.00</td><td>0.709 ±0.01</td><td>0.725±0.00</td><td>0.726±0.00</td></tr><tr><td>ACC</td><td>95.07±0.06</td><td>95.09±0.08</td><td>95.39±0.10</td><td>95.57±0.02</td><td>95.13±0.36</td></tr><tr><td>P-H</td><td>1</td><td>0.914</td><td>0.916</td><td>0.921</td><td>0.923</td></tr><tr><td rowspan="3">WikiCS</td><td>NMI</td><td>0.341±0.01</td><td>0.305±0.01</td><td>0.323±0.01</td><td>0.366±0.01</td><td>0.344±0.02</td></tr><tr><td>ACC</td><td>75.81±0.17</td><td>76.29±0.17</td><td>76.49±0.21</td><td>76.80±0.13</td><td>76.58±0.28</td></tr><tr><td>P-H</td><td>1</td><td>0.675</td><td>0.690</td><td>0.751</td><td>0.749</td></tr></table>
+
+Table 7: Comparison with random search. The NMI indicates node clustering performance; ACC indicates node classification accuracy $( \% )$ ; P-H stands for pseudo-homophily.   
+
+<table><tr><td>Dataset</td><td>Metric</td><td>Random Search</td><td>AUTOSSL-ES</td></tr><tr><td rowspan="4">Citeseer</td><td>NMI</td><td>0.443±0.00</td><td>0.449±0.01</td></tr><tr><td>ACC</td><td>71.68±0.55</td><td>72.14±0.41</td></tr><tr><td>P-H</td><td>0.934</td><td>0.943</td></tr><tr><td></td><td></td><td></td></tr></table>
+
+# H BROADER IMPACT
+
+Graph neural networks (GNNs) are commonly used for node and graph representation learning tasks due to their representational power. Such models have also been recently proposed for use in largescale social platforms for tasks including forecasting (Tang et al., 2020a), friend ranking (Sankar et al., 2021) and item recommendation (Ying et al., 2018; Wu et al., 2019a), which impact many end users. Like other machine learning models, GNNs can suffer from typical unfairness issues which may arise due to sensitive attributes, label parity issues, and more (Dai & Wang, 2021). Moreover, GNNs can also suffer from degree-related biases (Tang et al., 2020b). Self-supervised learning (SSL) is often used to learn high-quality representations without supervision from labeled data sources, and is especially useful in low-resource settings or in pre-training/fine-tuning scenarios. Several works have illustrated the potential for representations learned in a self-supervised way to encode bias unintentionally, for example in language modeling (Bender et al., 2021; Zhao et al., 2019), image representation learning (Roberts et al., 2018) and outlier detection (Shekhar et al., 2020).
+
+Our work on automated self-supervised learning with graph neural networks shares the caveats of these two domains in terms of producing inadvertent or biased outcomes. We propose an approach to learn self-supervised representations by utilizing multiple types of pretext tasks in conjunction with one another. While this produces improved performance on standard tasks used for benchmarking representation quality, it does not guarantee that these representations are fair and should be used without typical fairness checks in industrial contexts. However, such concerns are not inherently posed by our proposed ideas, but by the foundations it builds on in GNNs and SSL. We anticipate our ideas will drive further research in more sophisticated and powerful self-supervised graph learning, and do not anticipate direct negative outcomes from this work.

parse/dev/upJ3vrFKaL/upJ3vrFKaL.md

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+# COLLECTING THE PUZZLE PIECES: DISENTANGLEDSELF-DRIVEN HUMAN POSE TRANSFER BY PERMUT-ING TEXTURES
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Human pose transfer aims to synthesize a new view of a person under a given pose. Recent works achieve this via self-reconstruction, which disentangles pose and texture features from the person image, then combines the two features to reconstruct the person. Such feature-level disentanglement is a difficult and illdefined problem that could lead to loss of details and unwanted artifacts. In this paper, we propose a self-driven human pose transfer method that permutes the textures at random, then reconstructs the image with a dual branch attention to achieve image-level disentanglement and detail-preserving texture transfer. We find that compared with feature-level disentanglement, image-level disentanglement is more controllable and reliable. Furthermore, we introduce a dual kernel encoder that gives different sizes of receptive fields in order to reduce the noise caused by permutation and thus recover clothing details while aligning pose and textures. Extensive experiments on DeepFashion and Market-1501 shows that our model improves the quality of generated images in terms of FID, LPIPS and SSIM over other self-driven methods, and even outperforming some fully-supervised methods. A user study also shows that among self-driven approaches, images generated by our method are preferred in $72 \%$ of cases over prior work.
+
+# 1 INTRODUCTION
+
+The goal of human pose transfer is to change the pose of a person while preserving the person’s appearance and clothing textures. It has wide applications such as virtual try-on (Yang et al., 2020b; Cui et al., 2021; Yu et al., 2019), controllable person image manipulation (Cui et al., 2021; Liu et al., 2021) and person re-identification (Zhang et al., 2021b). Recent work has focused on using paired image data (i.e., two images of the same person before and after reposing) (Zhou et al., 2022; Zhang et al., 2022), but collecting such data can be very labor intensive. Although self-driven methods have been proposed to train pose transfer models without paired data (Ma et al., 2021; Song et al., 2019), there still remains two major challenges: how to disentangle texture and pose, and how to preserve texture details across changes in pose. As illustrated in Figure 1a, prior research attempts to achieve the pose and texture disentanglement at a feature level (Ma et al., 2018; Yang et al., 2020a; Ma et al., 2021; Wang et al., 2022). However, without direct supervision from pose-invariant textures, disentangling texture features from the person image while also preserving specific clothing details in the disentangled features is a difficult and ill-defined problem (Locatello et al., 2019). Small imbalances between pose and texture could leave obvious artifacts in the generated images.
+
+In this paper, we propose Pose Transfer by Permuting Textures $( \mathrm { P T ^ { 2 } } )$ , a self-driven pose transfer model using image-level disentanglement to represent detailed clothing patterns in any target pose. As shown in Figure 1b, a key novelty is our input permutation function that disentangles the raw inputs of texture and pose. Our method does not need supervised pose-invariant textures because most pose information has been removed by the permutation. The input permutation function creates a disentangled texture sample space by randomly reordering the texture patches on the person such that the source pose cannot be recovered from the permuted textures. This approach is similar in spirit to self-supervised representation learning methods that use jigsaw puzzle solving to learn a good feature representation (Noroozi & Favaro, 2016; Carlucci et al., 2019), where the pretext task divides the image into large patches and attempts to infer their relative positions by using the inherent geometry information within each patch. However, we differ in that our goal is to sample relevant patches based on the target posture. We make the patch much smaller in order to remove the position information and thus disentangle pose and texture. Furthermore, we mask some of the textures to force the generator to infer occluded and unseen regions, such as t-shirt occluded by crossed arms.
+
+![](images/3706d01db007440f12ea36da9627cdc9ea93e4c468362e3e2106b57386c9a536.jpg)  
+Figure 1: Pose transfer methods trained without supervision extract disentangled texture and pose representations and then learn to reconstruct the original image. (a) Recent work uses separate encoders to disentangle texture and pose (Pumarola et al., 2018; Ma et al., 2018; 2021; Wang et al., 2022). However, pose information may still appear in the texture features, and without supervision, disentangling them is difficult (Locatello et al., 2019). (b) Our approach disentangles textures from pose by permuting the image patches, effectively eliminating pose information, which enables our approach to disentangle pose and texture features better than prior work.
+
+One challenge we face is that the permutation of textures causes loss of shape and relative position information, which has two significant consequences. First, the model cannot recognize different body parts and garments. For example, the generator could use texture from leggings to synthesize a top tank. Second, it makes the length of clothing items unknown because of lack of relative position of clothing pieces. The first issue can be easily solved by combining the person with a human parsing map to give a semantic identifier for each pixel (Ma et al., 2021). Whereas for the second problem, we need an additional sample space in the model that provides relative position information. This inspires us to add a pose branch, where we use the dense pose representation (Guler et al., 2018) as ¨ the sample space to provide position information for each pixel after permuting the textures. Each pixel value in the space indicates the position of that pixel under the texture coordinate system (Guler ¨ et al., 2018). In addition, we find that using different kernel sizes in the convolutional layers of our dual branch attention module provides a better representation for our task.
+
+Our main contributions are:
+
+• We propose Pose Transfer by Permuting Textures $( \mathrm { P T ^ { 2 } } )$ , a self-driven pose transfer model that utilizes input permutation to transfer clothing patterns to the target pose without using paired images for supervision.   
+• The proposed pose branch in $\mathrm { P T ^ { 2 } }$ provides relative geometry information for the permuted textures, which helps recover shape and length after pose transfer. In addition, different kernel sizes are introduced in the branch, which can reduce the noise caused by input permutation and thus preserve clothing details while aligning pose and textures.   
+• Extensive experiments on DeepFashion (Liu et al., 2016) and Market-1501 (Zheng et al., 2015) show that $\mathrm { P \bar { T } ^ { 2 } }$ significantly improves the image quality of self-driven approaches. A user study reports that our method are preferred in $72 \%$ of cases over the state-of-the-art.
+
+# 2 RELATED WORK
+
+Pose transfer with paired images. Methods trained with paired images aim to learn the complex non-rigid deformation of clothing items. In (Zhu et al., 2019; Zhang et al., 2022; Ren et al., 2022; Gao et al., 2020), this transformation is learned via soft attention that aggregates source image features with weighted sampling. Zhang et al. (2021a); Lv et al. (2021) further use semantic parsing maps as guidance to control the style of each body part. The major difficulty in such feature-level attention is that clothing details could be washed out in lower-resolution feature maps. To preserve these details after pose transfer, flow-based methods haven been proposed to approximate a dense flow field from the source to the target person. Han et al. (2019) introduced a pyramid feature network that outputs a pixel-level flow filed. Tang et al. (2021); Ren et al. (2020) further combined soft attention with dense flow to learn more accurate estimations. However, since the learned flow can only copy existing pixels in the source image to the target, it might fail at inferring occluded and unseen parts of the person. Grigorev et al. (2019); Sarkar et al. (2020); Albahar et al. (2021) explored inpainting 2D partial texture to 3D full texture in the UV space, and then projecting it back to the 2D pose. Although these methods can produce high-quality person images, they all require strong supervision from paired data, which might be difficult to collect in some real-world scenarios.
+
+Pose transfer with unpaired images. In a self-driven setting where paired data is absent, it is more difficult to transfer the pose without losing texture details. Without supervision, the generated images tend to have repeated texture patterns and edge blurring (Wang et al., 2022). Prior work has addressed this problem by disentangling the texture and posture at a feature level. Early attempts produced poor quality images for large pose deformations (Pumarola et al., 2018; Esser et al., 2018; Ma et al., 2018). Song et al. (2019) introduced a generated target parsing map to a cycle-GAN pose transfer model, which requires paired segmentation maps for training the human parsing model. Sanyal et al. (2021) presents a 3D based reposing approach with appearance visibility inference. Wang et al. (2022) used part-wise encoder to learn texture features that are less correlated with pose, where global pose information can still be inferred from the texture features. The model in (Ma et al., 2021) first computes region-wise image features, and then takes their mean and variance as the texture features to be integrated with the pose representation. This helps erase the pose information in the texture features, but, as we show, it may miss clothing details. In contrast to these methods, our approach disentangles the texture at an image-level by permutation, and uses a dual kernel encoder with dual branch attention to transfer detailed clothing patterns to the target pose.
+
+# 3 SELF-DRIVEN POSE TRANSFER BY PERMUTING TEXTURES $( \mathrm { P T ^ { 2 } } )$
+
+Let $I _ { s }$ be the source image with posture $P _ { s }$ . Our goal is to synthesize a new view $I _ { t }$ of the same person in $I _ { s }$ and wearing the same clothes in a target posture $P _ { t }$ . Models requiring paired data use the target pose $P _ { t }$ and the target image $I _ { t }$ for training, but our approach needs only information derived from the source image. Specifically, the target pose/image in training is identical to the source pose/image. In inference, replacing the target pose with a different one enables pose transfer.
+
+$\mathrm { P T ^ { 2 } }$ contains a pose transfer network (Sec. 3.1) that synthesizes a new view of the person in its target pose, and a background inpainting network that infers its full background (Sec. 3.2). The generated person and its full background are combined to create the final reconstructed image.
+
+# 3.1 POSE TRANSFER NETWORK
+
+The objective of the pose transfer network is to take the foreground person in the source image and generate a new view of them in a different pose. Figure 2 gives the overall architecture, which contains two branches: a pose branch that learns the geometric transformation function from pose $P _ { s }$ to pose $P _ { t }$ , and a texture branch that learns to transfer the textures of the person $E _ { s }$ to pose $P _ { t }$ . The permuted inputs (Sec. 3.1.1) from the two branches are first encoded with dual kernel encoder (Sec. 3.1.2), and then merged in a dual branch attention module (Sec. 3.1.3) to be decoded into the generated person $\hat { E } _ { d }$ and its segmentation $S$ .
+
+# 3.1.1 INPUT PERMUTATION
+
+Inputs to the Texture Branch. To guide the texture transfer with a posture in a self-driven way, we first need to disentangle the pose and textures in the image. The posture can be derived by a DensePose model (Guler et al., 2018) pretrained on COCO (Lin et al., 2014), which gives a 2D UV ¨ coordinate representation $P _ { s }$ . However, the texture representation should not simply be the source person $E _ { s }$ itself, as it is obviously entangled with posture. To erase the pose information from $E _ { s }$ , we create a texture sample space by dividing the image into $k \times k$ squares, referred to as “patches,” and then shuffling their locations. Intuitively, when the patch size $k$ is sufficiently small, the original posture cannot easily be retrieved from the permutation. Additionaly, $20 \%$ of the patches are masked to encourage the model to learn occluded regions. Formally, let RandMask $( \cdot )$ be the input permuting function. The inputs of the texture attention branch become $[ \tilde { E } _ { s } ; \tilde { M } ] = \mathrm { R a n d M a s k } ( [ E _ { s } ; M ] , m _ { t } )$ , where $[ ; ]$ means concatenation and $m _ { t }$ is the masking rate. We set $m _ { t } = 0 . 2$ in our experiments. The permuted tetxures $[ \tilde { E } _ { s } ; \tilde { M } ]$ are given as inputs to the dual-kernel texture encoder (Sec. 3.1.2).
+
+![](images/303bdb570b4412b24e01bef00cd95562dd32683df6bd9f9d6596ac4a3c269dbe.jpg)  
+Figure 2: The pose transfer network in $\mathrm { P T ^ { 2 } }$ . During training, the target pose $P _ { t }$ is the same as the source pose $P _ { s }$ . The network takes the source person $E _ { s }$ , source parsing map $M$ and source pose $P _ { s }$ as inputs. In the pose branch and texture branch, the inputs are first permuted (Sec. 3.1.1) to create the corresponding sample space, which is encoded with dual kernel encoders (Sec. 3.1.2). Then the encoded features are sampled in a dual branch attention module (Sec. 3.1.3) to be decoded into the generated person $\hat { E } _ { s }$ and its segmentation $S$ . The output of the pose transfer network is combined with the output of the background inpainting network (Sec. 3.2) to produce the final image.
+
+Inputs to the Pose Branch. While prior work only uses a texture branch to transfer texture to the target pose (Pumarola et al., 2018; Ma et al., 2018; 2021; Wang et al., 2022), we propose a pose branch that provides relative geometry information for the permuted textures, which helps recover shape and length after pose transfer. To learn a powerful pose transformation function that supports large pose variations, the source pose in this branch is permuted the same way as the textures. In addition, we mask $50 \%$ of the source pose representation to force the model to learn the inherit symmetry in human body. The inputs to the pose branch become $[ \tilde { P } _ { s } ; \tilde { M } ] = \mathrm { R a n d M a s k } ( [ P _ { s } ; M ] , \stackrel { . . } { m } _ { p } )$ , where $m _ { p } = 0 . 5$ . Note that the inputs of the texture and pose branches are permuted the same way so they are spatially aligned in the dual branch attention module (see Sec. 3.1.3). The permuted pose representations $[ \tilde { P _ { s } } ; \tilde { M } ]$ are given as inputs to the dual-kernel pose encoder (Sec. 3.1.2).
+
+# 3.1.2 DUAL KERNEL ENCODER
+
+Following (Pumarola et al., 2018; Ma et al., 2018; 2021; Wang et al., 2022), we utilize separate encoders to learn both the texture and the pose information. However, in addition to providing permuted inputs from Sec. 3.1.1 to help further disentangle texture from pose, another way our approach differs is that we use multiple kernel sizes in the encoder’s convolutional layers. More formally, the texture/pose encoder learns a multi-dimensional feature map $F \in \mathbb { R } ^ { H \times W \times d }$ from the permuted texture/posture, where each vector $v \in \mathbb { R } ^ { d }$ in the feature map has a certain receptive field in the image. Let $l$ denote the length of the receptive field and $s$ be the stride of $F$ (both are measured by number of pixels in the image). Generally, larger receptive field is capable of learning more diverse features, and thus $l$ is usually much larger than $s$ . However, for a receptive field that crosses the boundary between two permuted image patches, the pixels within the field could be spatially faraway and irrelevant in the original image. In the left picture of Figure 3, the two black squares denote two adjacent receptive fields. While the left square lying within an image patch are seeing a consistent pattern (e.g., face), the right square crossing the boundary are seeing two distinct patterns (e.g., face and shoes). This could introduce high volume of noise to the feature vector $v$ , preventing the model from recognizing true clothing patterns.
+
+![](images/890e385af89e0320c8b5709a4c58db2a8edea42c1eb582bf4a556892ef415682.jpg)  
+Figure 3: Illustration of the receptive field in the large-kernel encoder (left) and small-kernel encoder (right). The kernel size $l$ is reduced to avoid overlap between receptive fields (see Sec. 3.1.2).   
+Figure 4: Dual branch attention module in Sec. 3.1.3. The top flow is PAM and the bottom flow is TAM. Res represents a residual layer. The cross-attention mechanism aligns the permuted texture with the target pose.
+
+To solve the above issue, we introduce an additional pose encoder with reduced kernel size such that $l \ = \ s$ , which can be regarded as a Multi Layer Perceptron over image patches. We select our kernel size such that the kernel does not cross the boundary of the permuted inputs from Sec. 3.1.1. As shown in the right picture of Figure 3, this design avoids the overlap between receptive fields, enabling the convolutional kernel to learn a consistent pattern within its own receptive field. Note that large kernel size is still necessary as it has more parameters and larger receptive filed for learning larger image patterns. Therefore, by combining encoders with a large and small kernel sizes our model is capable of learning more diverse features. The outputs of the dual kernel encoders in both texture branch and pose branch are fed to the dual branch attention module in Sec. 3.1.3.
+
+# 3.1.3 DUAL BRANCH ATTENTION
+
+We use a cross-attention transformer (Tang et al., 2020; Tan et al., 2021; Zhang et al., 2022) to align texture and pose features. Specifically, we use a Pose Attention Module (PAM) for the pose branch and a Texture Attention Module (TAM) for the texture branch. Let $F _ { s } ^ { p l } , F _ { s } ^ { p s }$ represent the output feature map of the large-kernel pose encoder and the small-kernel pose encoder in the pose branch, respectively. Similarly, $F _ { s } ^ { t l } , F _ { s } ^ { t { \bar { s } } }$ are the encoded features from the texture encoders in the texture branch. $T _ { 1 }$ is the feature map of the target pose $P _ { t }$ encoded by the target pose encoder, which is implemented with six convolutional layers. As shown in Figure 4, both PAM and TAM are composed of three cross-attention vision transformers formulated as Attention $\begin{array} { r } { ( Q , K , V ) = \mathrm { s o f t m a x } ( \frac { Q K ^ { \hat { T } } } { \sqrt { d } } ) \cdot V } \end{array}$ . With cross-attention the model can sample textures based on the target pose to generate a person image. In the first two transformer layers, the pose attention in the pose branch is learned from the correlation between the source pose and the target pose, which is computed as:
+
+$$
+Q = W _ { i } ^ { p q } T _ { i } , K = W _ { i } ^ { p k } F _ { s } ^ { p l } , V = W _ { i } ^ { p v } F _ { s } ^ { t l } , i = 1 , 2 .
+$$
+
+Here, $W _ { i } ^ { p q } , W _ { i } ^ { p k } , W _ { i } ^ { p v }$ are learnable projection matrices. Similarly, the texture attention in the texture branch is formulated as the correlation between the texture and the target pose:
+
+$$
+Q = W _ { i } ^ { t q } T _ { i } , K = W _ { i } ^ { t k } F _ { s } ^ { t l } , V = W _ { i } ^ { t v } F _ { s } ^ { t l } , i = 1 , 2 .
+$$
+
+After each transformer layer, a residual layer is appended as in Figure 4. A random noise vector $z$ is injected to the residual layer as the affine transformation parameters of the feature map $T _ { i }$ to prevent mode collapse (Karras et al., 2019).
+
+In the last transformer layer, wby small-kernel encoders (i.e., $F _ { s } ^ { p l } , F _ { s } ^ { t l }$ in the above equations with features produced to reconstruct more detailed information. The $F _ { s } ^ { p s } , F _ { s } ^ { t s } )$   
+output feature map $T$ of the last transformer layer is then fed to the decoder, where $T$ is gradually   
+upsampled to the target person $\hat { E } _ { s }$ and its segmentation mask $S$ .
+
+PAM in the dual branch attention module learns geometric transformation between different postures, and TAM samples the given textures based on the target pose. Fusing the two source of information provides a more accurate match between the given pose and textures. By filling in more clothing details that are learned through small kernels, our pose transfer network can then faithfully recover the appearance of clothing items after pose transfer.
+
+# 3.2 BACKGROUND INPAINTING NETWORK
+
+As in (Dundar et al., 2021; Liu et al., 2021), we use a separate background inpainting network, implemented using UNet (Long et al., 2015), to infer the background pixels of the masked foreground region. However, we found if we only mask out the foreground segmentation $S$ , the model would ignore the unknown background in the mask and reconstruct only known pixels during inference. This is because the background area is always visible in the source image in self-supervised training, so the network does not learn how to infer missing areas. Therefore, we expand the mask to the whole bounding box of the detected person in order to create invisible background areas during training. Let $\hat { B }$ be the inpainted background. Given the generated person $\hat { E } _ { s }$ and its segmentation mask $S$ produced by the pose transfer network, the final reconstructed image is: $\hat { I } _ { s } = \dot { S } \odot \dot { E } _ { s } + ( 1 - S ) \odot \hat { B }$ .
+
+# 3.3 LOSS FUNCTIONS
+
+We train our model using an adversarial loss that can be written as:
+
+$$
+L _ { a d v } = D ( \hat { I } _ { s } ) ^ { 2 } + ( 1 - D ( I _ { s } ) ) ^ { 2 } + D _ { p } ( [ \hat { I } _ { s } ; P _ { s } ] ) ^ { 2 } + ( 1 - D _ { p } ( [ I _ { s } ; P _ { s } ] ) ) ^ { 2 } .
+$$
+
+where $D$ and $D _ { p }$ represent different discriminators. $D$ penalizes the distribution difference between the synthesized image $\hat { I } _ { s }$ and the ground truth $I _ { s }$ . $D _ { p }$ evaluates that if the posture in $\hat { I } _ { s }$ matches the source pose $P _ { s }$ . To ensure correctness of our image generation, we use three different loss functions that capture different desired properties. The first is a simple reconstruction loss,
+
+$$
+L _ { r e c } = | | \hat { I } _ { s } - I _ { s } | | _ { 1 } .
+$$
+
+In addition, we use a perceptual loss (Johnson et al., 2016) that encourages both the ground truth and reconstructed image have similar semantic properties,
+
+$$
+L _ { p e r c } = \sum _ { i } | | \phi ^ { i } ( \hat { I } _ { s } ) - \phi ^ { i } ( I _ { s } ) | | _ { 1 } ,
+$$
+
+where $\phi ^ { i }$ is the ith layer of a VGG model (Simonyan & Zisserman, 2014) pretrained on ImageNet Deng et al. (2009). Finally, we use a style loss that penalizes discrepancies on colors and textures using the Gram matrix $\mathbb { G } ( \cdot )$ of the features,
+
+$$
+L _ { s t y l e } = \sum _ { i } | | \mathbb { G } ( \phi ^ { i } ( \hat { I } _ { s } ) ) - \mathbb { G } ( \phi ^ { i } ( I _ { s } ) ) | | _ { 1 } .
+$$
+
+Thus, our total loss can be written as,
+
+$$
+L _ { t o t a l } = \lambda _ { 1 } L _ { a d v } + \lambda _ { 2 } L _ { r e c } + \lambda _ { 3 } L _ { p e r c } + \lambda _ { 4 } L _ { s t y l e } .
+$$
+
+where $\lambda _ { 1 - 4 }$ are scalar hyperparameters. Additional training details are provided in Appendix A.
+
+# 4 EXPERIMENTS
+
+Datasets. We evaluate our proposed model on two benchmarks: DeepFashion (Liu et al., 2016) and Market1501 (Zheng et al., 2015). DeepFashion contains 52,712 high-quality images with a clean background. Market-1501 has 32,668 low-resolution images with various lighting conditions and a noisy background. Following Zhang et al. (2022); Wang et al. (2022), we select 8,570 test pairs with a resolution of $2 5 6 \times 2 5 6$ on DeepFashion, and 12,000 test pairs with a resolution of $1 2 8 \times 6 4$ on Market-1501. As in prior self-driven methods (Ma et al., 2021; Wang et al., 2022), we use 37,332 training images for DeepFashion and 12,112 training images for Market-1501.
+
+Metrics. Following (Ma et al., 2021; Wang et al., 2022), we use Structural Similarity Index Measure (SSIM) (Wang et al., 2004), Frechet Inception Distance (FID) (Heusel et al., 2017) , Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al., 2018) and Inception Score (IS) (Salimans et al., 2016) to evaluate the quality of the synthesized images. Among these metrics, SSIM measures structural similarity in the pixel space. FID computes Wasserstein-2 distance between two distributions. LPIPS evaluates perceptual similarity in deep network’s feature space. We use the default AlexNet as LPIPS’s backbone. IS assesses the quality of images generated by adversarial training. On Market-1501, we add Masked-SSIM and Masked-LPIPS computed on the target person region to exclude the influence of the irrelevant background.
+
+Table 1: Pose transfer results for $2 5 6 \times 2 5 6$ resolution images on DeepFashion. All results for prior work are taken from the original papers or produced with the author’s source code.   
+
+<table><tr><td>Method</td><td>FID↓</td><td>SSIM↑</td><td>LPIPS↓</td><td>IS↑</td></tr><tr><td>Supervised by paired images</td><td></td><td></td><td></td><td></td></tr><tr><td>PATN (Zhu et al., 2019)</td><td>24.071</td><td>0.770</td><td>0.299</td><td>3.141</td></tr><tr><td>GFLA (Ren et al., 2020)</td><td>10.573</td><td>0.707</td><td>0.234</td><td>3.635</td></tr><tr><td>PISE (Zhang et al., 2021a)</td><td>13.610</td><td>-</td><td>0.206</td><td>1</td></tr><tr><td>SPIG (Lv et al., 2021)</td><td>12.243</td><td>0.782</td><td>0.211</td><td>=</td></tr><tr><td>DPTN (Zhang et al.,2022)</td><td>11.466</td><td>0.778</td><td>0.196</td><td></td></tr><tr><td>CASD (Zhou et al., 2022)</td><td>11.373</td><td>0.725</td><td>0.194</td><td></td></tr><tr><td>NTED (Ren et al., 2022)</td><td>6.786</td><td>0.808</td><td>0.133</td><td>3.264</td></tr><tr><td>No paired images</td><td></td><td></td><td></td><td></td></tr><tr><td>VU-Net (Esser et al.,2018)</td><td>23.580</td><td>0.786</td><td>0.321</td><td>3.087</td></tr><tr><td>E2E (Song et al., 2019)</td><td>29.900</td><td>0.736</td><td>0.238</td><td>3.441</td></tr><tr><td>DPIG (Ma et al., 2018)</td><td>48.200</td><td>0.614</td><td>0.284</td><td>3.228</td></tr><tr><td>MUST (Ma et al.,2021)</td><td>15.902</td><td>0.742</td><td>-</td><td>3.692</td></tr><tr><td>SCM-Net Wang et al. (2022)</td><td>12.180</td><td>0.751</td><td>0.182</td><td>3.632</td></tr><tr><td>PT²(Ours)</td><td>8.338</td><td>0.795</td><td>0.158</td><td>3.469</td></tr></table>
+
+Table 2: Pose transfer results for $1 2 8 \times 6 4$ resolution images on Market-1501. All results for prior work are taken from the original papers or produced with the author’s source code.   
+
+<table><tr><td>Method</td><td>FID↓</td><td>SSIM↑</td><td>M-SSIM↑</td><td>LPIPS↓</td><td>M-LPIPS↓</td><td>IS↑</td></tr><tr><td>Supervised by paired images</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PATN (Zhu et al., 2019)</td><td>22.657</td><td>0.311</td><td>0.811</td><td>0.320</td><td>0.159</td><td></td></tr><tr><td>GFLA (Ren et al.,2020)</td><td>19.751</td><td>0.281</td><td>0.796</td><td>0.282</td><td>0.148</td><td></td></tr><tr><td>SPIG (Lv et al., 2021)</td><td>23.331</td><td>0.315</td><td>0.818</td><td>0.278</td><td>0.139</td><td></td></tr><tr><td>DPTN (Zhang et al., 2022)</td><td>18.995</td><td>0.285</td><td>1</td><td>0.271</td><td>1</td><td></td></tr><tr><td> No paired images</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PT²(Ours)</td><td>17.389</td><td>0.280</td><td>0.820</td><td>0.314</td><td>0.122</td><td>2.789</td></tr></table>
+
+# 4.1 QUANTITATIVE RESULTS
+
+Table 1 compares methods on the pose transfer task using DeepFashion, where our approach outperforms most methods on FID, SSIM, and LPIP by a large margin. For example, we improve FID by 4 points over the state-of-the-art. Notably, our model, which requires no paired training data, also achieves better performance than most supervised methods trained with paired data. Similar behavior is seen on Market-1501 (Table 2), where our self-driven $\mathrm { P T ^ { 2 } }$ gains in Masked-SSIM and Masked-LPIPS over supervised methods. However, we note that we do perform worse according to SSIM and LPIPS, which is computed over the entire image rather than just the target person region.
+
+To investigate the reason behind the discrepancy when we use masked regions for evaluation, we computed the SSIM scores on different body parts of the person. The average scores for background, arms, legs, clothes and head for $\mathrm { P T ^ { 2 } }$ are: 0.237, 0.263, 0.283, 0.323, 0.337, respectively. The lowest SSIM is on the background because the dataset is collected from surveillance videos, where the background can change drastically in different time frames. This violates our assumption that the background does not change, explaining the relatively poor performance. That said, since our goal is pose transfer, the improved performance using M-SSIM and M-LPIPS demonstrates we are more successful than even the supervised methods on Market-1501 at that task.
+
+User Study. To verify the quality of generated images, we also conducted a human evaluation on DeepFashion using Amazon Mechanical Turk. We collected 3 judgements for 50 images (150 total). Each worker was presented 3 pictures: the true image, a $\mathrm { P T ^ { 2 } }$ generated image, and a image generated by a method from prior work. The worker was asked to pick a picture that looks most similar to the true image. Table 3 shows that among self-driven methods, more than $72 \%$ workers believe our method achieves higher fidelity in the generated images. Compared with approaches supervised by paired images, our method achieves comparable performance with an average of over $62 \%$ user preference, demonstrating the effectiveness of our proposed approach.
+
+![](images/630f609496292089e9c22e4a445158b42ae2ba38d7e278fdbe3a3729dc014820.jpg)  
+Figure 5: Qualitative pose transfer results on DeepFashion (left) and Market-1501 (right). We enlarged the area marked with a red bounding box for a better view of clothing details. Examples from prior work are generated with the author’s code and pretrained models. MUST, E2E, and our $\mathrm { P T ^ { 2 } }$ are trained with unpaired data, while the rest are supervised by paired data. These results show our approach transfers the original clothing patterns onto the target pose better than prior work.
+
+Table 3: A/B user preferences on DeepFashion. We report how often our approach was selected as most like the ground truth image. The number that follows $\pm$ is the corresponding standard deviation. We significantly outperform methods trained without paired images. Our results were also preferred over fully supervised methods.   
+
+<table><tr><td></td><td colspan="3"> Supervised by paired images</td><td colspan="2">No paired images</td></tr><tr><td></td><td>PISE</td><td>DPTN</td><td>CASD</td><td>E2E</td><td>MUST</td></tr><tr><td>PT²</td><td>68.7%±3.27</td><td>66.2%±3.35</td><td>53.8%±3.53</td><td>79.7%±2.84</td><td>(Zhang et al.,2021a) (Zhang et al.,2022) (Zhou et al.,2022) (Song et al.,2019) (Ma et al.,2021) 72.6%±3.15</td></tr></table>
+
+# 4.2 QUALITATIVE RESULTS
+
+Pose Transfer. Figure 5 visualizes pose transfer results. We enlarged the area marked with a red bounding box for a better view of clothing details. In the first row (left), our method transferred the arm tattoos to the target pose while other methods either ignored this detail or failed to reconstruct the arm. Similarly, our model learns the color pattern in the second row (left) better than other approaches. This is because the small kernel encoder in our model can capture such detailed texture and thus reconstruct it based on the target pose. On the right side of Figure 5, compared with supervised pose transfer methods, our approach faithfully recovered the shape and color of the dress and shirt in the two examples. More examples, including failure cases, are in Appendix B.
+
+Garment Replacement. With a given parsing map, our approach can also switch the clothing pieces on two persons. Let $I _ { A } = \left( A _ { p o s e } , A _ { c l t } \right)$ be an image of person $A$ wearing clothes $A _ { c l t }$ under posture $A _ { p o s e }$ . To replace $A _ { c l t }$ with $B _ { c l t }$ in $I _ { B } = ( B _ { p o s e } , B _ { c l t } )$ , we first align $A , B$ ’s pose to $A _ { p o s e }$ using the proposed pose transfer method, and then replace $A _ { c l t }$ to $B _ { c l t }$ using their parsing maps. To fix small mis-alignment after copy-paste $B _ { c l t }$ using the parsing map, the image is fed to $\mathrm { P T ^ { 2 } }$ again for a more plausible reconstruction. Due to the shape difference of the source and reference garments (e.g., jeans and shorts), the model could give different ways of combining all the clothing pieces after replacing a specific garment. For example, in Figure 6, for the person in the top second source image, the upper clothes are tucked into the shorts but untucked to the jeans. Similarly, the shorts in the top first source image are occluded by the camel t-shirt and pink jackets, but are visible when combined with other shirts. Overall, Figure 6 shows that the proposed method successfully replaces various types of garments in the given images while preserving their patterns and details.
+
+# 4.3 ABLATION STUDY
+
+We performed an ablation study to evaluate the effectiveness of each component of our model. In Table $4 , w / \theta$ . Input Permuting does not permute the inputs, which results in entangled pose and textures. Input Warping, w/o. Input Permuting uses Thin Plate Spline transformation (TPS) to warp the source image, which can be viewed as a mild way of disentangling the pose and texture at the image-level. w/o. Pose Branch removes the pose branch in our method. w/o. small kernel uses only large kernel in the feature encoders, which should lead to loss of clothing details. w/o. large kernel uses only small kernel in the feature encoders. We train all these ablation models under the same configuration. As shown in Table 4, our complete model $\mathrm { P T ^ { 2 } }$ improves all the metrics, demonstrating the effectiveness of each component.
+
+![](images/d0b0dd4c6e3e1a06f09a713be2a3f23dc1c286ae23be5cde2033cf212a2fdb32.jpg)  
+Figure 6: Examples of garment replacement. The left column is the source image and the top row is reference image. All reference garments are marked with red bounding boxes.
+
+Table 4: Ablations in DeepFashion. Compare with each ablation model, our full model $\mathrm { P T ^ { 2 } }$ that combines all the components improves the overall performance.   
+
+<table><tr><td>Method</td><td>FID↓</td><td>SSIM↑</td><td>LPIPS↓</td><td>IS个</td></tr><tr><td>Input Warping, w/o. Input Permuting</td><td>10.011</td><td>0.781±0.072</td><td>0.178±0.060</td><td>3.579±0.086</td></tr><tr><td>w/o. Input Permuting</td><td>10.279</td><td>0.780±0.069</td><td>0.169±0.059</td><td>3.525±0.095</td></tr><tr><td>w/o. Pose Branch</td><td>11.391</td><td>0.785±0.068</td><td>0.177±0.068</td><td>3.485±0.095</td></tr><tr><td>w/o. small kernel</td><td>8.905</td><td>0.782±0.067</td><td>0.170±0.060</td><td>3.442±0.119</td></tr><tr><td>w/o. large kernel</td><td>9.275</td><td>0.785±0.068</td><td>0.166±0.060</td><td>3.401±0.078</td></tr><tr><td>PT²(Ours)</td><td>8.338</td><td>0.795±0.067</td><td>0.158±0.059</td><td>3.469±0.098</td></tr></table>
+
+# 5 CONLUSION
+
+We propose $\mathrm { P T ^ { 2 } }$ , a self-driven human pose transfer method that permutes the textures at random and then reconstructs the image with dual branch attention to achieve image-level disentanglement and detail-preserving texture transfer. The introduced dual kernel encoder in the model gives different sizes of receptive fields, which can reduce the noise caused by permutation and thus recovers clothing details while aligning pose and texture. Extensive experiments on DeepFashion and Market-1501 shows that our model improves the image quality of self-driven approaches, where a user study shows our images are preferred over prior work in $72 \%$ of cases. Moreover, it obtains comparable objective and subjective results to most pose transfer methods supervised by paired data.
+
+# 6 REPRODUCIBILITY STATEMENT
+
+We include our source code in the Supplementary for other researchers to easily reproduce our results in this paper. The code has a README file with detailed instructions of running and evaluating our model. The training details and all the hyperparameters we used in our approach are provided in Appendix A.
+
+# 7 ETHICS STATEMENT
+
+The proposed method introduces image-level disentanglement of pose and texture, and provides a self-driven framework for the human pose transfer task. The results of this research could be broadly disseminated by exploiting the publicly available source code. The research is beneficial to the research community in that it builds a unified framework for self-driven pose transfer, and gives insights to other exemplar-guided image generation tasks. From the perspective of ethical considerations, our method has the potential to be used as a tool through the spread of misinformation, which echos concerns have been addressed in related machine learning research (Ramesh et al., 2022; Karnouskos, 2020). It is of utmost importance to follow certain policies and regulations against misinformation (Pennycook et al., 2020) when using these AI technologies, as well as highlight the importance of developing methods for detecting misinformation, including for media created using artificial intelligence (e.g., Wang et al. (2020); Tan et al. (2020)).
+
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+
+![](images/8f9fa37bee3fc66c5cf0fbb73132b83b2eee491364c42c4f0fdbd957ba43295b.jpg)  
+Figure 7: Additional pose transfer examples on DeepFashion.
+
+# A TRAINING DETAILS.
+
+We use AdamW optimizer (Loshchilov & Hutter, 2019) for training with $\beta _ { 1 } = 0 . 5 , \beta _ { 2 } = 0 . 9 9 9 .$ . The initial learning rate is set to $1 0 ^ { - 3 }$ and decays to $2 \times 1 0 ^ { - 4 }$ after five starting epochs. The trade-off parameters are set to $\lambda _ { 1 } = 2 . 0 , \lambda _ { 2 } = 5 . 0 , \lambda _ { 3 } = 0 . 5$ , $\lambda _ { 4 } = 1 5 0$ in all experiments. The patch size is $1 6 \times 1 6$ for DeepFashion and $8 \times 8$ for Market-1501. To stabilize the training, we use the EMA strategy Yaz et al. (2019) to average the learned weights of the generator. Our pose representation is predicted by DensePose (Guler et al., 2018) and the parsing maps are obtained from CorrPM ¨ (Zhang et al., 2020). We found that the predicted dense pose in Market-1501 has poor quality as the image resolution is too low $( 1 2 8 \times 6 4 )$ for the DensePose model. Therefore, we use an offline super resolution model Liang et al. (2021) to upsample the Market-1501 images to $5 1 2 \times 2 5 6$ , get dense pose from these images, and then downsample the pose to the original image resolution $( 1 2 8 \times 6 4 )$ for our pose transfer task. We also add human keypoints predicted from OpenPose (Cao et al., 2019) as part of the pose representation to improve the accuracy of predicted posture on Market-1501.
+
+# B DISCUSSIONS
+
+Failure case analysis. Figure 7 provides several successful examples generated by the propsoed method on DeepFashion. However, one limitation of our model is that it relies on the segmentation map and DensePose prediction of the source image to obtain semantic and position information for the permuted textures. Thus, we found the accuracy of human parser and DensePose model greatly affects the transfer results. Figure 8 shows several failed examples due to this type of inaccuracy. In the first row, the coat wrapped around the dress was misrecognized as part of the dress in the parsing map, for which our generated back view incorrectly mixes up their textures. Similarly, the skirt in the second row was classified as shorts in the parsing map. As a result, our generator infers the occluded clothing piece as shorts in the front view. In the last row, the color of skirt is half-black and halfwhite because the skirt piece was not identified in the parsing map. More analysis on ablations. We present some visualized examples in Figure 9 to show the functionality of each component of our model. It’s clear that models with less perturbation of the input texture (i.e., w/o. Input Permuting and Input Warping) fail at large pose changes (e.g., from back view to front full view in the bottom row). Removing the pose branch (w/o. Pose Branch) causes loss of length information, resulting in extended dress in the second row. Without the small-kernel encoder (w/o. small kernel), the ablation model correctly transfers color and shape, but fails to recover complex clothing patterns and details in the third row. Without large kernel (w/o. large kernel), the model can correctly reconstruct clothes with singular color, but is less capable of transferring detailed textures (see the third and fourth row). To see if the large-kernel encoder is learning certain low-level information from permuted patches, we also tried replacing the inputs of the large-kernel encoder with heavily Gaussian blurred image without permutation. From the examples, we can see that images generated by $w .$ blur are much worse compared to the full model. This suggests that features learned by large-kernel encoder from the permuted image might have richer information than Gaussian blurred texture.
+
+![](images/294d67c7c1c181e865d3fb25958e69c9aad11960f1a0f5a572498ae4527c4d1b.jpg)  
+Figure 8: Failure cases in DeepFashion. Many failures are due to incorrect predictions of the source UV map and source parsing map.
+
+![](images/5f033af2f7020a2d905e7f6e9a262b37ccf0c222fb763e3f8c7f9c3d53c9a68c.jpg)  
+Figure 9: Generated images of ablations of our model. Each component of our model improves the transfer of shape information and detailed clothing patterns, resulting in our full model obtaining the best results.
+
+![](images/08b6d34fad50ea24aae456dddcde4a67878ecb6dd799a4fffd843f2bcb7f1f86.jpg)  
+Figure 10: Visualized feature map of the encoded texture features. The feature map is overlaid with the source image. The source image is downsampled to the resolution of the feature map. Each triplet includes a downsampled source image, the feature map from large-kernel encoder, and the feature map from small-kernel encoder. Red indicates higher value and blue means smaller value.
+
+To further explore the differences of texture features learned by the large-kernel encoder and the small-kernel encoder, we sum up the encoded feature maps across all channels in the texture branch, and normalize their values to be in range [0, 1]. Then we downsample the image to the resolution of the feature map and overlay the normalized feature map with the downsampled source image. In Figure 10, each triplet includes the downsampled source image, the feature map from largekernel encoder, and the feature map from small-kernel encoder. Feature map given by large-kernel encoder (middle image in each triplet) appears to be much smoother than that of the small-kernel encoder (right image in each triplet). This suggests that large-kernel encoder might be learning coarse information from the clothing piece (e.g., color and shape), while small-kernel encoder is learning more fine-grained patterns (e.g., stripe and pleat).

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+        "type": "text",
+        "text": "COLLECTING THE PUZZLE PIECES: DISENTANGLEDSELF-DRIVEN HUMAN POSE TRANSFER BY PERMUT-ING TEXTURES",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+            454,
+            261,
+            544,
+            275
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Human pose transfer aims to synthesize a new view of a person under a given pose. Recent works achieve this via self-reconstruction, which disentangles pose and texture features from the person image, then combines the two features to reconstruct the person. Such feature-level disentanglement is a difficult and illdefined problem that could lead to loss of details and unwanted artifacts. In this paper, we propose a self-driven human pose transfer method that permutes the textures at random, then reconstructs the image with a dual branch attention to achieve image-level disentanglement and detail-preserving texture transfer. We find that compared with feature-level disentanglement, image-level disentanglement is more controllable and reliable. Furthermore, we introduce a dual kernel encoder that gives different sizes of receptive fields in order to reduce the noise caused by permutation and thus recover clothing details while aligning pose and textures. Extensive experiments on DeepFashion and Market-1501 shows that our model improves the quality of generated images in terms of FID, LPIPS and SSIM over other self-driven methods, and even outperforming some fully-supervised methods. A user study also shows that among self-driven approaches, images generated by our method are preferred in $72 \\%$ of cases over prior work. ",
+        "bbox": [
+            233,
+            290,
+            764,
+            526
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            553,
+            336,
+            568
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The goal of human pose transfer is to change the pose of a person while preserving the person’s appearance and clothing textures. It has wide applications such as virtual try-on (Yang et al., 2020b; Cui et al., 2021; Yu et al., 2019), controllable person image manipulation (Cui et al., 2021; Liu et al., 2021) and person re-identification (Zhang et al., 2021b). Recent work has focused on using paired image data (i.e., two images of the same person before and after reposing) (Zhou et al., 2022; Zhang et al., 2022), but collecting such data can be very labor intensive. Although self-driven methods have been proposed to train pose transfer models without paired data (Ma et al., 2021; Song et al., 2019), there still remains two major challenges: how to disentangle texture and pose, and how to preserve texture details across changes in pose. As illustrated in Figure 1a, prior research attempts to achieve the pose and texture disentanglement at a feature level (Ma et al., 2018; Yang et al., 2020a; Ma et al., 2021; Wang et al., 2022). However, without direct supervision from pose-invariant textures, disentangling texture features from the person image while also preserving specific clothing details in the disentangled features is a difficult and ill-defined problem (Locatello et al., 2019). Small imbalances between pose and texture could leave obvious artifacts in the generated images. ",
+        "bbox": [
+            174,
+            584,
+            825,
+            777
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we propose Pose Transfer by Permuting Textures $( \\mathrm { P T ^ { 2 } } )$ , a self-driven pose transfer model using image-level disentanglement to represent detailed clothing patterns in any target pose. As shown in Figure 1b, a key novelty is our input permutation function that disentangles the raw inputs of texture and pose. Our method does not need supervised pose-invariant textures because most pose information has been removed by the permutation. The input permutation function creates a disentangled texture sample space by randomly reordering the texture patches on the person such that the source pose cannot be recovered from the permuted textures. This approach is similar in spirit to self-supervised representation learning methods that use jigsaw puzzle solving to learn a good feature representation (Noroozi & Favaro, 2016; Carlucci et al., 2019), where the pretext task divides the image into large patches and attempts to infer their relative positions by using the inherent geometry information within each patch. However, we differ in that our goal is to sample relevant patches based on the target posture. We make the patch much smaller in order to remove the position information and thus disentangle pose and texture. Furthermore, we mask some of the textures to force the generator to infer occluded and unseen regions, such as t-shirt occluded by crossed arms. ",
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+        "type": "image",
+        "img_path": "images/3706d01db007440f12ea36da9627cdc9ea93e4c468362e3e2106b57386c9a536.jpg",
+        "image_caption": [
+            "Figure 1: Pose transfer methods trained without supervision extract disentangled texture and pose representations and then learn to reconstruct the original image. (a) Recent work uses separate encoders to disentangle texture and pose (Pumarola et al., 2018; Ma et al., 2018; 2021; Wang et al., 2022). However, pose information may still appear in the texture features, and without supervision, disentangling them is difficult (Locatello et al., 2019). (b) Our approach disentangles textures from pose by permuting the image patches, effectively eliminating pose information, which enables our approach to disentangle pose and texture features better than prior work. "
+        ],
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+        "type": "text",
+        "text": "One challenge we face is that the permutation of textures causes loss of shape and relative position information, which has two significant consequences. First, the model cannot recognize different body parts and garments. For example, the generator could use texture from leggings to synthesize a top tank. Second, it makes the length of clothing items unknown because of lack of relative position of clothing pieces. The first issue can be easily solved by combining the person with a human parsing map to give a semantic identifier for each pixel (Ma et al., 2021). Whereas for the second problem, we need an additional sample space in the model that provides relative position information. This inspires us to add a pose branch, where we use the dense pose representation (Guler et al., 2018) as ¨ the sample space to provide position information for each pixel after permuting the textures. Each pixel value in the space indicates the position of that pixel under the texture coordinate system (Guler ¨ et al., 2018). In addition, we find that using different kernel sizes in the convolutional layers of our dual branch attention module provides a better representation for our task. ",
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+    {
+        "type": "text",
+        "text": "Our main contributions are: ",
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+    {
+        "type": "text",
+        "text": "• We propose Pose Transfer by Permuting Textures $( \\mathrm { P T ^ { 2 } } )$ , a self-driven pose transfer model that utilizes input permutation to transfer clothing patterns to the target pose without using paired images for supervision.   \n• The proposed pose branch in $\\mathrm { P T ^ { 2 } }$ provides relative geometry information for the permuted textures, which helps recover shape and length after pose transfer. In addition, different kernel sizes are introduced in the branch, which can reduce the noise caused by input permutation and thus preserve clothing details while aligning pose and textures.   \n• Extensive experiments on DeepFashion (Liu et al., 2016) and Market-1501 (Zheng et al., 2015) show that $\\mathrm { P \\bar { T } ^ { 2 } }$ significantly improves the image quality of self-driven approaches. A user study reports that our method are preferred in $72 \\%$ of cases over the state-of-the-art. ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Pose transfer with paired images. Methods trained with paired images aim to learn the complex non-rigid deformation of clothing items. In (Zhu et al., 2019; Zhang et al., 2022; Ren et al., 2022; Gao et al., 2020), this transformation is learned via soft attention that aggregates source image features with weighted sampling. Zhang et al. (2021a); Lv et al. (2021) further use semantic parsing maps as guidance to control the style of each body part. The major difficulty in such feature-level attention is that clothing details could be washed out in lower-resolution feature maps. To preserve these details after pose transfer, flow-based methods haven been proposed to approximate a dense flow field from the source to the target person. Han et al. (2019) introduced a pyramid feature network that outputs a pixel-level flow filed. Tang et al. (2021); Ren et al. (2020) further combined soft attention with dense flow to learn more accurate estimations. However, since the learned flow can only copy existing pixels in the source image to the target, it might fail at inferring occluded and unseen parts of the person. Grigorev et al. (2019); Sarkar et al. (2020); Albahar et al. (2021) explored inpainting 2D partial texture to 3D full texture in the UV space, and then projecting it back to the 2D pose. Although these methods can produce high-quality person images, they all require strong supervision from paired data, which might be difficult to collect in some real-world scenarios. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Pose transfer with unpaired images. In a self-driven setting where paired data is absent, it is more difficult to transfer the pose without losing texture details. Without supervision, the generated images tend to have repeated texture patterns and edge blurring (Wang et al., 2022). Prior work has addressed this problem by disentangling the texture and posture at a feature level. Early attempts produced poor quality images for large pose deformations (Pumarola et al., 2018; Esser et al., 2018; Ma et al., 2018). Song et al. (2019) introduced a generated target parsing map to a cycle-GAN pose transfer model, which requires paired segmentation maps for training the human parsing model. Sanyal et al. (2021) presents a 3D based reposing approach with appearance visibility inference. Wang et al. (2022) used part-wise encoder to learn texture features that are less correlated with pose, where global pose information can still be inferred from the texture features. The model in (Ma et al., 2021) first computes region-wise image features, and then takes their mean and variance as the texture features to be integrated with the pose representation. This helps erase the pose information in the texture features, but, as we show, it may miss clothing details. In contrast to these methods, our approach disentangles the texture at an image-level by permutation, and uses a dual kernel encoder with dual branch attention to transfer detailed clothing patterns to the target pose. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 SELF-DRIVEN POSE TRANSFER BY PERMUTING TEXTURES $( \\mathrm { P T ^ { 2 } } )$ ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Let $I _ { s }$ be the source image with posture $P _ { s }$ . Our goal is to synthesize a new view $I _ { t }$ of the same person in $I _ { s }$ and wearing the same clothes in a target posture $P _ { t }$ . Models requiring paired data use the target pose $P _ { t }$ and the target image $I _ { t }$ for training, but our approach needs only information derived from the source image. Specifically, the target pose/image in training is identical to the source pose/image. In inference, replacing the target pose with a different one enables pose transfer. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "$\\mathrm { P T ^ { 2 } }$ contains a pose transfer network (Sec. 3.1) that synthesizes a new view of the person in its target pose, and a background inpainting network that infers its full background (Sec. 3.2). The generated person and its full background are combined to create the final reconstructed image. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 POSE TRANSFER NETWORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The objective of the pose transfer network is to take the foreground person in the source image and generate a new view of them in a different pose. Figure 2 gives the overall architecture, which contains two branches: a pose branch that learns the geometric transformation function from pose $P _ { s }$ to pose $P _ { t }$ , and a texture branch that learns to transfer the textures of the person $E _ { s }$ to pose $P _ { t }$ . The permuted inputs (Sec. 3.1.1) from the two branches are first encoded with dual kernel encoder (Sec. 3.1.2), and then merged in a dual branch attention module (Sec. 3.1.3) to be decoded into the generated person $\\hat { E } _ { d }$ and its segmentation $S$ . ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1.1 INPUT PERMUTATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Inputs to the Texture Branch. To guide the texture transfer with a posture in a self-driven way, we first need to disentangle the pose and textures in the image. The posture can be derived by a DensePose model (Guler et al., 2018) pretrained on COCO (Lin et al., 2014), which gives a 2D UV ¨ coordinate representation $P _ { s }$ . However, the texture representation should not simply be the source person $E _ { s }$ itself, as it is obviously entangled with posture. To erase the pose information from $E _ { s }$ , we create a texture sample space by dividing the image into $k \\times k$ squares, referred to as “patches,” and then shuffling their locations. Intuitively, when the patch size $k$ is sufficiently small, the original posture cannot easily be retrieved from the permutation. Additionaly, $20 \\%$ of the patches are masked to encourage the model to learn occluded regions. Formally, let RandMask $( \\cdot )$ be the input permuting function. The inputs of the texture attention branch become $[ \\tilde { E } _ { s } ; \\tilde { M } ] = \\mathrm { R a n d M a s k } ( [ E _ { s } ; M ] , m _ { t } )$ , where $[ ; ]$ means concatenation and $m _ { t }$ is the masking rate. We set $m _ { t } = 0 . 2$ in our experiments. The permuted tetxures $[ \\tilde { E } _ { s } ; \\tilde { M } ]$ are given as inputs to the dual-kernel texture encoder (Sec. 3.1.2). ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/303bdb570b4412b24e01bef00cd95562dd32683df6bd9f9d6596ac4a3c269dbe.jpg",
+        "image_caption": [
+            "Figure 2: The pose transfer network in $\\mathrm { P T ^ { 2 } }$ . During training, the target pose $P _ { t }$ is the same as the source pose $P _ { s }$ . The network takes the source person $E _ { s }$ , source parsing map $M$ and source pose $P _ { s }$ as inputs. In the pose branch and texture branch, the inputs are first permuted (Sec. 3.1.1) to create the corresponding sample space, which is encoded with dual kernel encoders (Sec. 3.1.2). Then the encoded features are sampled in a dual branch attention module (Sec. 3.1.3) to be decoded into the generated person $\\hat { E } _ { s }$ and its segmentation $S$ . The output of the pose transfer network is combined with the output of the background inpainting network (Sec. 3.2) to produce the final image. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Inputs to the Pose Branch. While prior work only uses a texture branch to transfer texture to the target pose (Pumarola et al., 2018; Ma et al., 2018; 2021; Wang et al., 2022), we propose a pose branch that provides relative geometry information for the permuted textures, which helps recover shape and length after pose transfer. To learn a powerful pose transformation function that supports large pose variations, the source pose in this branch is permuted the same way as the textures. In addition, we mask $50 \\%$ of the source pose representation to force the model to learn the inherit symmetry in human body. The inputs to the pose branch become $[ \\tilde { P } _ { s } ; \\tilde { M } ] = \\mathrm { R a n d M a s k } ( [ P _ { s } ; M ] , \\stackrel { . . } { m } _ { p } )$ , where $m _ { p } = 0 . 5$ . Note that the inputs of the texture and pose branches are permuted the same way so they are spatially aligned in the dual branch attention module (see Sec. 3.1.3). The permuted pose representations $[ \\tilde { P _ { s } } ; \\tilde { M } ]$ are given as inputs to the dual-kernel pose encoder (Sec. 3.1.2). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1.2 DUAL KERNEL ENCODER ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Following (Pumarola et al., 2018; Ma et al., 2018; 2021; Wang et al., 2022), we utilize separate encoders to learn both the texture and the pose information. However, in addition to providing permuted inputs from Sec. 3.1.1 to help further disentangle texture from pose, another way our approach differs is that we use multiple kernel sizes in the encoder’s convolutional layers. More formally, the texture/pose encoder learns a multi-dimensional feature map $F \\in \\mathbb { R } ^ { H \\times W \\times d }$ from the permuted texture/posture, where each vector $v \\in \\mathbb { R } ^ { d }$ in the feature map has a certain receptive field in the image. Let $l$ denote the length of the receptive field and $s$ be the stride of $F$ (both are measured by number of pixels in the image). Generally, larger receptive field is capable of learning more diverse features, and thus $l$ is usually much larger than $s$ . However, for a receptive field that crosses the boundary between two permuted image patches, the pixels within the field could be spatially faraway and irrelevant in the original image. In the left picture of Figure 3, the two black squares denote two adjacent receptive fields. While the left square lying within an image patch are seeing a consistent pattern (e.g., face), the right square crossing the boundary are seeing two distinct patterns (e.g., face and shoes). This could introduce high volume of noise to the feature vector $v$ , preventing the model from recognizing true clothing patterns. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/890e385af89e0320c8b5709a4c58db2a8edea42c1eb582bf4a556892ef415682.jpg",
+        "image_caption": [
+            "Figure 3: Illustration of the receptive field in the large-kernel encoder (left) and small-kernel encoder (right). The kernel size $l$ is reduced to avoid overlap between receptive fields (see Sec. 3.1.2). ",
+            "Figure 4: Dual branch attention module in Sec. 3.1.3. The top flow is PAM and the bottom flow is TAM. Res represents a residual layer. The cross-attention mechanism aligns the permuted texture with the target pose. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To solve the above issue, we introduce an additional pose encoder with reduced kernel size such that $l \\ = \\ s$ , which can be regarded as a Multi Layer Perceptron over image patches. We select our kernel size such that the kernel does not cross the boundary of the permuted inputs from Sec. 3.1.1. As shown in the right picture of Figure 3, this design avoids the overlap between receptive fields, enabling the convolutional kernel to learn a consistent pattern within its own receptive field. Note that large kernel size is still necessary as it has more parameters and larger receptive filed for learning larger image patterns. Therefore, by combining encoders with a large and small kernel sizes our model is capable of learning more diverse features. The outputs of the dual kernel encoders in both texture branch and pose branch are fed to the dual branch attention module in Sec. 3.1.3. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.1.3 DUAL BRANCH ATTENTION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We use a cross-attention transformer (Tang et al., 2020; Tan et al., 2021; Zhang et al., 2022) to align texture and pose features. Specifically, we use a Pose Attention Module (PAM) for the pose branch and a Texture Attention Module (TAM) for the texture branch. Let $F _ { s } ^ { p l } , F _ { s } ^ { p s }$ represent the output feature map of the large-kernel pose encoder and the small-kernel pose encoder in the pose branch, respectively. Similarly, $F _ { s } ^ { t l } , F _ { s } ^ { t { \\bar { s } } }$ are the encoded features from the texture encoders in the texture branch. $T _ { 1 }$ is the feature map of the target pose $P _ { t }$ encoded by the target pose encoder, which is implemented with six convolutional layers. As shown in Figure 4, both PAM and TAM are composed of three cross-attention vision transformers formulated as Attention $\\begin{array} { r } { ( Q , K , V ) = \\mathrm { s o f t m a x } ( \\frac { Q K ^ { \\hat { T } } } { \\sqrt { d } } ) \\cdot V } \\end{array}$ . With cross-attention the model can sample textures based on the target pose to generate a person image. In the first two transformer layers, the pose attention in the pose branch is learned from the correlation between the source pose and the target pose, which is computed as: ",
+        "bbox": [
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+        "page_idx": 4
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+    {
+        "type": "equation",
+        "img_path": "images/08cb15d9400dde602f18cb68602ce24e8d30c496e9f60f0efdbac47dde647bcc.jpg",
+        "text": "$$\nQ = W _ { i } ^ { p q } T _ { i } , K = W _ { i } ^ { p k } F _ { s } ^ { p l } , V = W _ { i } ^ { p v } F _ { s } ^ { t l } , i = 1 , 2 .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Here, $W _ { i } ^ { p q } , W _ { i } ^ { p k } , W _ { i } ^ { p v }$ are learnable projection matrices. Similarly, the texture attention in the texture branch is formulated as the correlation between the texture and the target pose: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/64f513c3a437971b397d218c36bcf61f801cf3dab242f1475cd24e00fa40cf53.jpg",
+        "text": "$$\nQ = W _ { i } ^ { t q } T _ { i } , K = W _ { i } ^ { t k } F _ { s } ^ { t l } , V = W _ { i } ^ { t v } F _ { s } ^ { t l } , i = 1 , 2 .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            328,
+            702,
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+            722
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "After each transformer layer, a residual layer is appended as in Figure 4. A random noise vector $z$ is injected to the residual layer as the affine transformation parameters of the feature map $T _ { i }$ to prevent mode collapse (Karras et al., 2019). ",
+        "bbox": [
+            176,
+            739,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the last transformer layer, wby small-kernel encoders (i.e., $F _ { s } ^ { p l } , F _ { s } ^ { t l }$ in the above equations with features produced to reconstruct more detailed information. The $F _ { s } ^ { p s } , F _ { s } ^ { t s } )$   \noutput feature map $T$ of the last transformer layer is then fed to the decoder, where $T$ is gradually   \nupsampled to the target person $\\hat { E } _ { s }$ and its segmentation mask $S$ . ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "PAM in the dual branch attention module learns geometric transformation between different postures, and TAM samples the given textures based on the target pose. Fusing the two source of information provides a more accurate match between the given pose and textures. By filling in more clothing details that are learned through small kernels, our pose transfer network can then faithfully recover the appearance of clothing items after pose transfer. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2 BACKGROUND INPAINTING NETWORK",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "As in (Dundar et al., 2021; Liu et al., 2021), we use a separate background inpainting network, implemented using UNet (Long et al., 2015), to infer the background pixels of the masked foreground region. However, we found if we only mask out the foreground segmentation $S$ , the model would ignore the unknown background in the mask and reconstruct only known pixels during inference. This is because the background area is always visible in the source image in self-supervised training, so the network does not learn how to infer missing areas. Therefore, we expand the mask to the whole bounding box of the detected person in order to create invisible background areas during training. Let $\\hat { B }$ be the inpainted background. Given the generated person $\\hat { E } _ { s }$ and its segmentation mask $S$ produced by the pose transfer network, the final reconstructed image is: $\\hat { I } _ { s } = \\dot { S } \\odot \\dot { E } _ { s } + ( 1 - S ) \\odot \\hat { B }$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3.3 LOSS FUNCTIONS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We train our model using an adversarial loss that can be written as: ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/a6b0e87b45e59a3c85875f130f6c462b6e083a17696e279b33183d0fd1455d08.jpg",
+        "text": "$$\nL _ { a d v } = D ( \\hat { I } _ { s } ) ^ { 2 } + ( 1 - D ( I _ { s } ) ) ^ { 2 } + D _ { p } ( [ \\hat { I } _ { s } ; P _ { s } ] ) ^ { 2 } + ( 1 - D _ { p } ( [ I _ { s } ; P _ { s } ] ) ) ^ { 2 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $D$ and $D _ { p }$ represent different discriminators. $D$ penalizes the distribution difference between the synthesized image $\\hat { I } _ { s }$ and the ground truth $I _ { s }$ . $D _ { p }$ evaluates that if the posture in $\\hat { I } _ { s }$ matches the source pose $P _ { s }$ . To ensure correctness of our image generation, we use three different loss functions that capture different desired properties. The first is a simple reconstruction loss, ",
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "equation",
+        "img_path": "images/a99ab5c7793905ccbede912f31060a091cb1fd94f7467dc0b717dda3b0954e66.jpg",
+        "text": "$$\nL _ { r e c } = | | \\hat { I } _ { s } - I _ { s } | | _ { 1 } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In addition, we use a perceptual loss (Johnson et al., 2016) that encourages both the ground truth and reconstructed image have similar semantic properties, ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/cc7a2545ec839453996c650d75d65216a62fef8e225268a0e71fc45cb872565b.jpg",
+        "text": "$$\nL _ { p e r c } = \\sum _ { i } | | \\phi ^ { i } ( \\hat { I } _ { s } ) - \\phi ^ { i } ( I _ { s } ) | | _ { 1 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where $\\phi ^ { i }$ is the ith layer of a VGG model (Simonyan & Zisserman, 2014) pretrained on ImageNet Deng et al. (2009). Finally, we use a style loss that penalizes discrepancies on colors and textures using the Gram matrix $\\mathbb { G } ( \\cdot )$ of the features, ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/f85a29ce89abb51d501722a3aee160b4680fdabb446d4cae90c7d626610ad0e7.jpg",
+        "text": "$$\nL _ { s t y l e } = \\sum _ { i } | | \\mathbb { G } ( \\phi ^ { i } ( \\hat { I } _ { s } ) ) - \\mathbb { G } ( \\phi ^ { i } ( I _ { s } ) ) | | _ { 1 } .\n$$",
+        "text_format": "latex",
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "Thus, our total loss can be written as, ",
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9d62c4dfc2bb8aaaf25c0b0016ea8309b39163f122ed856b8cdba6da101e638a.jpg",
+        "text": "$$\nL _ { t o t a l } = \\lambda _ { 1 } L _ { a d v } + \\lambda _ { 2 } L _ { r e c } + \\lambda _ { 3 } L _ { p e r c } + \\lambda _ { 4 } L _ { s t y l e } .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where $\\lambda _ { 1 - 4 }$ are scalar hyperparameters. Additional training details are provided in Appendix A. ",
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+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Datasets. We evaluate our proposed model on two benchmarks: DeepFashion (Liu et al., 2016) and Market1501 (Zheng et al., 2015). DeepFashion contains 52,712 high-quality images with a clean background. Market-1501 has 32,668 low-resolution images with various lighting conditions and a noisy background. Following Zhang et al. (2022); Wang et al. (2022), we select 8,570 test pairs with a resolution of $2 5 6 \\times 2 5 6$ on DeepFashion, and 12,000 test pairs with a resolution of $1 2 8 \\times 6 4$ on Market-1501. As in prior self-driven methods (Ma et al., 2021; Wang et al., 2022), we use 37,332 training images for DeepFashion and 12,112 training images for Market-1501. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Metrics. Following (Ma et al., 2021; Wang et al., 2022), we use Structural Similarity Index Measure (SSIM) (Wang et al., 2004), Frechet Inception Distance (FID) (Heusel et al., 2017) , Learned Perceptual Image Patch Similarity (LPIPS) (Zhang et al., 2018) and Inception Score (IS) (Salimans et al., 2016) to evaluate the quality of the synthesized images. Among these metrics, SSIM measures structural similarity in the pixel space. FID computes Wasserstein-2 distance between two distributions. LPIPS evaluates perceptual similarity in deep network’s feature space. We use the default AlexNet as LPIPS’s backbone. IS assesses the quality of images generated by adversarial training. On Market-1501, we add Masked-SSIM and Masked-LPIPS computed on the target person region to exclude the influence of the irrelevant background. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/5bdfd0520598abd4b4df234e8fce397485d47fd752f6ea48fc4d05e09645cc76.jpg",
+        "table_caption": [
+            "Table 1: Pose transfer results for $2 5 6 \\times 2 5 6$ resolution images on DeepFashion. All results for prior work are taken from the original papers or produced with the author’s source code. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>FID↓</td><td>SSIM↑</td><td>LPIPS↓</td><td>IS↑</td></tr><tr><td>Supervised by paired images</td><td></td><td></td><td></td><td></td></tr><tr><td>PATN (Zhu et al., 2019)</td><td>24.071</td><td>0.770</td><td>0.299</td><td>3.141</td></tr><tr><td>GFLA (Ren et al., 2020)</td><td>10.573</td><td>0.707</td><td>0.234</td><td>3.635</td></tr><tr><td>PISE (Zhang et al., 2021a)</td><td>13.610</td><td>-</td><td>0.206</td><td>1</td></tr><tr><td>SPIG (Lv et al., 2021)</td><td>12.243</td><td>0.782</td><td>0.211</td><td>=</td></tr><tr><td>DPTN (Zhang et al.,2022)</td><td>11.466</td><td>0.778</td><td>0.196</td><td></td></tr><tr><td>CASD (Zhou et al., 2022)</td><td>11.373</td><td>0.725</td><td>0.194</td><td></td></tr><tr><td>NTED (Ren et al., 2022)</td><td>6.786</td><td>0.808</td><td>0.133</td><td>3.264</td></tr><tr><td>No paired images</td><td></td><td></td><td></td><td></td></tr><tr><td>VU-Net (Esser et al.,2018)</td><td>23.580</td><td>0.786</td><td>0.321</td><td>3.087</td></tr><tr><td>E2E (Song et al., 2019)</td><td>29.900</td><td>0.736</td><td>0.238</td><td>3.441</td></tr><tr><td>DPIG (Ma et al., 2018)</td><td>48.200</td><td>0.614</td><td>0.284</td><td>3.228</td></tr><tr><td>MUST (Ma et al.,2021)</td><td>15.902</td><td>0.742</td><td>-</td><td>3.692</td></tr><tr><td>SCM-Net Wang et al. (2022)</td><td>12.180</td><td>0.751</td><td>0.182</td><td>3.632</td></tr><tr><td>PT²(Ours)</td><td>8.338</td><td>0.795</td><td>0.158</td><td>3.469</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/ab86d464938c83918c6ccd01ef07c8bea675fc0a05fd914d8e54aea78c389b45.jpg",
+        "table_caption": [
+            "Table 2: Pose transfer results for $1 2 8 \\times 6 4$ resolution images on Market-1501. All results for prior work are taken from the original papers or produced with the author’s source code. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>FID↓</td><td>SSIM↑</td><td>M-SSIM↑</td><td>LPIPS↓</td><td>M-LPIPS↓</td><td>IS↑</td></tr><tr><td>Supervised by paired images</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PATN (Zhu et al., 2019)</td><td>22.657</td><td>0.311</td><td>0.811</td><td>0.320</td><td>0.159</td><td></td></tr><tr><td>GFLA (Ren et al.,2020)</td><td>19.751</td><td>0.281</td><td>0.796</td><td>0.282</td><td>0.148</td><td></td></tr><tr><td>SPIG (Lv et al., 2021)</td><td>23.331</td><td>0.315</td><td>0.818</td><td>0.278</td><td>0.139</td><td></td></tr><tr><td>DPTN (Zhang et al., 2022)</td><td>18.995</td><td>0.285</td><td>1</td><td>0.271</td><td>1</td><td></td></tr><tr><td> No paired images</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PT²(Ours)</td><td>17.389</td><td>0.280</td><td>0.820</td><td>0.314</td><td>0.122</td><td>2.789</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "4.1 QUANTITATIVE RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Table 1 compares methods on the pose transfer task using DeepFashion, where our approach outperforms most methods on FID, SSIM, and LPIP by a large margin. For example, we improve FID by 4 points over the state-of-the-art. Notably, our model, which requires no paired training data, also achieves better performance than most supervised methods trained with paired data. Similar behavior is seen on Market-1501 (Table 2), where our self-driven $\\mathrm { P T ^ { 2 } }$ gains in Masked-SSIM and Masked-LPIPS over supervised methods. However, we note that we do perform worse according to SSIM and LPIPS, which is computed over the entire image rather than just the target person region. ",
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+    {
+        "type": "text",
+        "text": "To investigate the reason behind the discrepancy when we use masked regions for evaluation, we computed the SSIM scores on different body parts of the person. The average scores for background, arms, legs, clothes and head for $\\mathrm { P T ^ { 2 } }$ are: 0.237, 0.263, 0.283, 0.323, 0.337, respectively. The lowest SSIM is on the background because the dataset is collected from surveillance videos, where the background can change drastically in different time frames. This violates our assumption that the background does not change, explaining the relatively poor performance. That said, since our goal is pose transfer, the improved performance using M-SSIM and M-LPIPS demonstrates we are more successful than even the supervised methods on Market-1501 at that task. ",
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+    {
+        "type": "text",
+        "text": "User Study. To verify the quality of generated images, we also conducted a human evaluation on DeepFashion using Amazon Mechanical Turk. We collected 3 judgements for 50 images (150 total). Each worker was presented 3 pictures: the true image, a $\\mathrm { P T ^ { 2 } }$ generated image, and a image generated by a method from prior work. The worker was asked to pick a picture that looks most similar to the true image. Table 3 shows that among self-driven methods, more than $72 \\%$ workers believe our method achieves higher fidelity in the generated images. Compared with approaches supervised by paired images, our method achieves comparable performance with an average of over $62 \\%$ user preference, demonstrating the effectiveness of our proposed approach. ",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/630f609496292089e9c22e4a445158b42ae2ba38d7e278fdbe3a3729dc014820.jpg",
+        "image_caption": [
+            "Figure 5: Qualitative pose transfer results on DeepFashion (left) and Market-1501 (right). We enlarged the area marked with a red bounding box for a better view of clothing details. Examples from prior work are generated with the author’s code and pretrained models. MUST, E2E, and our $\\mathrm { P T ^ { 2 } }$ are trained with unpaired data, while the rest are supervised by paired data. These results show our approach transfers the original clothing patterns onto the target pose better than prior work. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/e79bff95d54420d0f731e35c03ec322e6a0dcbf0361fc2814000c9f5d179dd51.jpg",
+        "table_caption": [
+            "Table 3: A/B user preferences on DeepFashion. We report how often our approach was selected as most like the ground truth image. The number that follows $\\pm$ is the corresponding standard deviation. We significantly outperform methods trained without paired images. Our results were also preferred over fully supervised methods. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\"> Supervised by paired images</td><td colspan=\"2\">No paired images</td></tr><tr><td></td><td>PISE</td><td>DPTN</td><td>CASD</td><td>E2E</td><td>MUST</td></tr><tr><td>PT²</td><td>68.7%±3.27</td><td>66.2%±3.35</td><td>53.8%±3.53</td><td>79.7%±2.84</td><td>(Zhang et al.,2021a) (Zhang et al.,2022) (Zhou et al.,2022) (Song et al.,2019) (Ma et al.,2021) 72.6%±3.15</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "4.2 QUALITATIVE RESULTS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Pose Transfer. Figure 5 visualizes pose transfer results. We enlarged the area marked with a red bounding box for a better view of clothing details. In the first row (left), our method transferred the arm tattoos to the target pose while other methods either ignored this detail or failed to reconstruct the arm. Similarly, our model learns the color pattern in the second row (left) better than other approaches. This is because the small kernel encoder in our model can capture such detailed texture and thus reconstruct it based on the target pose. On the right side of Figure 5, compared with supervised pose transfer methods, our approach faithfully recovered the shape and color of the dress and shirt in the two examples. More examples, including failure cases, are in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "Garment Replacement. With a given parsing map, our approach can also switch the clothing pieces on two persons. Let $I _ { A } = \\left( A _ { p o s e } , A _ { c l t } \\right)$ be an image of person $A$ wearing clothes $A _ { c l t }$ under posture $A _ { p o s e }$ . To replace $A _ { c l t }$ with $B _ { c l t }$ in $I _ { B } = ( B _ { p o s e } , B _ { c l t } )$ , we first align $A , B$ ’s pose to $A _ { p o s e }$ using the proposed pose transfer method, and then replace $A _ { c l t }$ to $B _ { c l t }$ using their parsing maps. To fix small mis-alignment after copy-paste $B _ { c l t }$ using the parsing map, the image is fed to $\\mathrm { P T ^ { 2 } }$ again for a more plausible reconstruction. Due to the shape difference of the source and reference garments (e.g., jeans and shorts), the model could give different ways of combining all the clothing pieces after replacing a specific garment. For example, in Figure 6, for the person in the top second source image, the upper clothes are tucked into the shorts but untucked to the jeans. Similarly, the shorts in the top first source image are occluded by the camel t-shirt and pink jackets, but are visible when combined with other shirts. Overall, Figure 6 shows that the proposed method successfully replaces various types of garments in the given images while preserving their patterns and details. ",
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "4.3 ABLATION STUDY ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We performed an ablation study to evaluate the effectiveness of each component of our model. In Table $4 , w / \\theta$ . Input Permuting does not permute the inputs, which results in entangled pose and textures. Input Warping, w/o. Input Permuting uses Thin Plate Spline transformation (TPS) to warp the source image, which can be viewed as a mild way of disentangling the pose and texture at the image-level. w/o. Pose Branch removes the pose branch in our method. w/o. small kernel uses only large kernel in the feature encoders, which should lead to loss of clothing details. w/o. large kernel uses only small kernel in the feature encoders. We train all these ablation models under the same configuration. As shown in Table 4, our complete model $\\mathrm { P T ^ { 2 } }$ improves all the metrics, demonstrating the effectiveness of each component. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/d0b0dd4c6e3e1a06f09a713be2a3f23dc1c286ae23be5cde2033cf212a2fdb32.jpg",
+        "image_caption": [
+            "Figure 6: Examples of garment replacement. The left column is the source image and the top row is reference image. All reference garments are marked with red bounding boxes. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            302,
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/1222e58f947b374546eeea56acc1f12c0120eef033c1323cc49ed2b89810ace3.jpg",
+        "table_caption": [
+            "Table 4: Ablations in DeepFashion. Compare with each ablation model, our full model $\\mathrm { P T ^ { 2 } }$ that combines all the components improves the overall performance. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>FID↓</td><td>SSIM↑</td><td>LPIPS↓</td><td>IS个</td></tr><tr><td>Input Warping, w/o. Input Permuting</td><td>10.011</td><td>0.781±0.072</td><td>0.178±0.060</td><td>3.579±0.086</td></tr><tr><td>w/o. Input Permuting</td><td>10.279</td><td>0.780±0.069</td><td>0.169±0.059</td><td>3.525±0.095</td></tr><tr><td>w/o. Pose Branch</td><td>11.391</td><td>0.785±0.068</td><td>0.177±0.068</td><td>3.485±0.095</td></tr><tr><td>w/o. small kernel</td><td>8.905</td><td>0.782±0.067</td><td>0.170±0.060</td><td>3.442±0.119</td></tr><tr><td>w/o. large kernel</td><td>9.275</td><td>0.785±0.068</td><td>0.166±0.060</td><td>3.401±0.078</td></tr><tr><td>PT²(Ours)</td><td>8.338</td><td>0.795±0.067</td><td>0.158±0.059</td><td>3.469±0.098</td></tr></table>",
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "5 CONLUSION ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We propose $\\mathrm { P T ^ { 2 } }$ , a self-driven human pose transfer method that permutes the textures at random and then reconstructs the image with dual branch attention to achieve image-level disentanglement and detail-preserving texture transfer. The introduced dual kernel encoder in the model gives different sizes of receptive fields, which can reduce the noise caused by permutation and thus recovers clothing details while aligning pose and texture. Extensive experiments on DeepFashion and Market-1501 shows that our model improves the image quality of self-driven approaches, where a user study shows our images are preferred over prior work in $72 \\%$ of cases. Moreover, it obtains comparable objective and subjective results to most pose transfer methods supervised by paired data. ",
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "6 REPRODUCIBILITY STATEMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We include our source code in the Supplementary for other researchers to easily reproduce our results in this paper. The code has a README file with detailed instructions of running and evaluating our model. The training details and all the hyperparameters we used in our approach are provided in Appendix A. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "7 ETHICS STATEMENT ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+    },
+    {
+        "type": "text",
+        "text": "The proposed method introduces image-level disentanglement of pose and texture, and provides a self-driven framework for the human pose transfer task. The results of this research could be broadly disseminated by exploiting the publicly available source code. The research is beneficial to the research community in that it builds a unified framework for self-driven pose transfer, and gives insights to other exemplar-guided image generation tasks. From the perspective of ethical considerations, our method has the potential to be used as a tool through the spread of misinformation, which echos concerns have been addressed in related machine learning research (Ramesh et al., 2022; Karnouskos, 2020). It is of utmost importance to follow certain policies and regulations against misinformation (Pennycook et al., 2020) when using these AI technologies, as well as highlight the importance of developing methods for detecting misinformation, including for media created using artificial intelligence (e.g., Wang et al. (2020); Tan et al. (2020)). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            415,
+            285,
+            429
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Badour Albahar, Jingwan Lu, Jimei Yang, Zhixin Shu, Eli Shechtman, and Jia-Bin Huang. Pose with style: Detail-preserving pose-guided image synthesis with conditional styleGAN. ACM Transactions on Graphics, 2021.   \nZ. Cao, G. Hidalgo Martinez, T. Simon, S. Wei, and Y. A. Sheikh. Openpose: Realtime multi-person 2d pose estimation using part affinity fields. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019.   \nFabio M Carlucci, Antonio D’Innocente, Silvia Bucci, Barbara Caputo, and Tatiana Tommasi. Domain generalization by solving jigsaw puzzles. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019.   \nAiyu Cui, Daniel McKee, and Svetlana Lazebnik. Dressing in order: Recurrent person image generation for pose transfer, virtual try-on and outfit editing. In Proceedings of the IEEE International Conference on Computer Vision, 2021.   \nJia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In IEEE conference on computer vision and pattern recognition, 2009.   \nAysegul Dundar, Kevin J Shih, Animesh Garg, Robert Pottorf, Anrew Tao, and Bryan Catanzaro. Unsupervised disentanglement of pose, appearance and background from images and videos. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(7):3883–3894, 2021.   \nPatrick Esser, Ekaterina Sutter, and Bjorn Ommer. A variational u-net for conditional appearance ¨ and shape generation. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2018.   \nChen Gao, Si Liu, Ran He, Shuicheng Yan, and Bo Li. Recapture as you want. arXiv preprint arXiv:2006.01435, 2020.   \nArtur Grigorev, Artem Sevastopolsky, Alexander Vakhitov, and Victor Lempitsky. Coordinate-based texture inpainting for pose-guided human image generation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2019.   \nRıza Alp Guler, Natalia Neverova, and Iasonas Kokkinos. Densepose: Dense human pose estimation ¨ in the wild. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2018. ",
+        "bbox": [
+            171,
+            428,
+            826,
+            926
+        ],
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+    {
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+        "img_path": "images/8f9fa37bee3fc66c5cf0fbb73132b83b2eee491364c42c4f0fdbd957ba43295b.jpg",
+        "image_caption": [
+            "Figure 7: Additional pose transfer examples on DeepFashion. "
+        ],
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+    {
+        "type": "text",
+        "text": "A TRAINING DETAILS. ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We use AdamW optimizer (Loshchilov & Hutter, 2019) for training with $\\beta _ { 1 } = 0 . 5 , \\beta _ { 2 } = 0 . 9 9 9 .$ . The initial learning rate is set to $1 0 ^ { - 3 }$ and decays to $2 \\times 1 0 ^ { - 4 }$ after five starting epochs. The trade-off parameters are set to $\\lambda _ { 1 } = 2 . 0 , \\lambda _ { 2 } = 5 . 0 , \\lambda _ { 3 } = 0 . 5$ , $\\lambda _ { 4 } = 1 5 0$ in all experiments. The patch size is $1 6 \\times 1 6$ for DeepFashion and $8 \\times 8$ for Market-1501. To stabilize the training, we use the EMA strategy Yaz et al. (2019) to average the learned weights of the generator. Our pose representation is predicted by DensePose (Guler et al., 2018) and the parsing maps are obtained from CorrPM ¨ (Zhang et al., 2020). We found that the predicted dense pose in Market-1501 has poor quality as the image resolution is too low $( 1 2 8 \\times 6 4 )$ for the DensePose model. Therefore, we use an offline super resolution model Liang et al. (2021) to upsample the Market-1501 images to $5 1 2 \\times 2 5 6$ , get dense pose from these images, and then downsample the pose to the original image resolution $( 1 2 8 \\times 6 4 )$ for our pose transfer task. We also add human keypoints predicted from OpenPose (Cao et al., 2019) as part of the pose representation to improve the accuracy of predicted posture on Market-1501. ",
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+    {
+        "type": "text",
+        "text": "B DISCUSSIONS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Failure case analysis. Figure 7 provides several successful examples generated by the propsoed method on DeepFashion. However, one limitation of our model is that it relies on the segmentation map and DensePose prediction of the source image to obtain semantic and position information for the permuted textures. Thus, we found the accuracy of human parser and DensePose model greatly affects the transfer results. Figure 8 shows several failed examples due to this type of inaccuracy. In the first row, the coat wrapped around the dress was misrecognized as part of the dress in the parsing map, for which our generated back view incorrectly mixes up their textures. Similarly, the skirt in the second row was classified as shorts in the parsing map. As a result, our generator infers the occluded clothing piece as shorts in the front view. In the last row, the color of skirt is half-black and halfwhite because the skirt piece was not identified in the parsing map. More analysis on ablations. We present some visualized examples in Figure 9 to show the functionality of each component of our model. It’s clear that models with less perturbation of the input texture (i.e., w/o. Input Permuting and Input Warping) fail at large pose changes (e.g., from back view to front full view in the bottom row). Removing the pose branch (w/o. Pose Branch) causes loss of length information, resulting in extended dress in the second row. Without the small-kernel encoder (w/o. small kernel), the ablation model correctly transfers color and shape, but fails to recover complex clothing patterns and details in the third row. Without large kernel (w/o. large kernel), the model can correctly reconstruct clothes with singular color, but is less capable of transferring detailed textures (see the third and fourth row). To see if the large-kernel encoder is learning certain low-level information from permuted patches, we also tried replacing the inputs of the large-kernel encoder with heavily Gaussian blurred image without permutation. From the examples, we can see that images generated by $w .$ blur are much worse compared to the full model. This suggests that features learned by large-kernel encoder from the permuted image might have richer information than Gaussian blurred texture. ",
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+    {
+        "type": "image",
+        "img_path": "images/294d67c7c1c181e865d3fb25958e69c9aad11960f1a0f5a572498ae4527c4d1b.jpg",
+        "image_caption": [
+            "Figure 8: Failure cases in DeepFashion. Many failures are due to incorrect predictions of the source UV map and source parsing map. "
+        ],
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+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/5f033af2f7020a2d905e7f6e9a262b37ccf0c222fb763e3f8c7f9c3d53c9a68c.jpg",
+        "image_caption": [
+            "Figure 9: Generated images of ablations of our model. Each component of our model improves the transfer of shape information and detailed clothing patterns, resulting in our full model obtaining the best results. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 14
+    },
+    {
+        "type": "image",
+        "img_path": "images/08b6d34fad50ea24aae456dddcde4a67878ecb6dd799a4fffd843f2bcb7f1f86.jpg",
+        "image_caption": [
+            "Figure 10: Visualized feature map of the encoded texture features. The feature map is overlaid with the source image. The source image is downsampled to the resolution of the feature map. Each triplet includes a downsampled source image, the feature map from large-kernel encoder, and the feature map from small-kernel encoder. Red indicates higher value and blue means smaller value. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 15
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 15
+    },
+    {
+        "type": "text",
+        "text": "To further explore the differences of texture features learned by the large-kernel encoder and the small-kernel encoder, we sum up the encoded feature maps across all channels in the texture branch, and normalize their values to be in range [0, 1]. Then we downsample the image to the resolution of the feature map and overlay the normalized feature map with the downsampled source image. In Figure 10, each triplet includes the downsampled source image, the feature map from largekernel encoder, and the feature map from small-kernel encoder. Feature map given by large-kernel encoder (middle image in each triplet) appears to be much smoother than that of the small-kernel encoder (right image in each triplet). This suggests that large-kernel encoder might be learning coarse information from the clothing piece (e.g., color and shape), while small-kernel encoder is learning more fine-grained patterns (e.g., stripe and pleat). ",
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