# embeddings_queue

created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b10ce-6db4-11ee-aa87-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-61", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "by our method for each class across nine different thresholds (Fig. 13). The trend is quite similar to the VOC dataset\nin that our algorithm struggles on the same object classes\n(\u201cchair\u201d, \u201cdining table\u201d, \u201cpotted plant\u201d, \u201cbottle\u201d). Note that\nourAPrfor the \u201cbicycle\u201d class has improved compared to\nthe VOC dataset. This is probably because the VOC dataset\nhas more detailed annotations. In the VOC dataset, each\nspoke of a bicycle\u2019s wheel is often labelled, whilst in SBD,\nthe entire wheel is labelled as a single circle with the \u201cbicycle\u201d label. Therefore, the SBD dataset\u2019s coarser labelling\nmakes it easier for an algorithm to perform well on objects\nwith \ufb01ne details.\nTable 6shows our mean AProver all classes at thresholds ranging from 0.5 to 0.9. Our APrat 0.9 is low compared to the result which we obtained on the VOC dataset.\nThis could be for a number of reasons: As the SBD dataset\nis not as \ufb01nely annotated as the VOC dataset, it might not\nbe suited for measuring the APrat such high thresholds.\nAdditionally, the training data is not as good for training"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b10cf-6db4-11ee-9441-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-62", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "be suited for measuring the APrat such high thresholds.\nAdditionally, the training data is not as good for training\nour system which includes a CRF and is therefore able to\ndelineate sharp boundaries. Finally, as the SBD dataset has\n5732 validation images (compared to the 1449 in VOC), it\nleaves less data for pretraining our initial semantic segmen2http://host.robots.ox.ac.uk:8080/leaderboard/\ndisplaylb.php?challengeid=11&compid=6tation module. This may hinder our network in being able\nto produce precise segmentations.\nTable 6: Comparison of Instance Segmentation performance at multiple APrthesholds on the VOC 2012 Validation Set\nMethodAPr\nAPr\nvol0.5 0.6 0.7 0.8 0.9\nOurs (piecewise) 59.1 51.9 42.1 29.4 12.0 52.3\nOurs (end-to-end ) 62.0 54.0 44.8 32.3 13.8 55.4\nTables 10and11show per-class instance segmentation\nresults on the SBD dataset, at IoU thresholds of 0.7 and\n0.5 respectively. We can only compare results at these two\nthresholds since these are the only thresholds which other"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b10d0-6db4-11ee-b3bc-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-63", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "0.5 respectively. We can only compare results at these two\nthresholds since these are the only thresholds which other\nwork has reported.\nFigure 12: A visualisation of the AProbtained for each of the 20 classes on the VOC dataset, at nine different IoU thresholds.\nThe x-axis represents the IoU threshold, and the y-axis each of the Pascal classes. Therefore, each \u201ccolumn\u201d of this \ufb01gure\ncorresponds to the APrper class at a particular threshold, and is thus an alternate representation to the results tables. Best\nviewed in colour.\nFigure 13: A visualisation of the AProbtained for each of the 20 classes on the SBD dataset, at nine different IoU thresholds.\nThe x-axis represents the IoU threshold, and the y-axis each of the Pascal classes. Therefore, each \u201ccolumn\u201d of this \ufb01gure\ncorresponds to the APrper class at a particular threshold, and is thus an alternate representation to the results tables. Best\nviewed in colour.\nTable 7: Comparison of mean APr, achieved by different published methods, at an IoU threshold of 0.9, for all twenty classes in the VOC dataset.\nMethodMean"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b10d1-6db4-11ee-8e23-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-64", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "Table 7: Comparison of mean APr, achieved by different published methods, at an IoU threshold of 0.9, for all twenty classes in the VOC dataset.\nMethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv\nOur method 25.1 56.6 0.03 36.8 14.4 9.9 39.0 17.2 47.1 1.3 29.0 9.5 47.2 29.8 20.0 14.8 2.3 25.9 23.8 45.7 32.3\nMPA 3-scale [ 37] 18.5 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013\nMPA 1-scale [ 37] 17.3 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013\nArnab et al. [3] 20.1 43.7 0.03 30.0 13.2 11.4 47.3 10.9 34.5 0.7 19.6 12.1 35.6 24.3 13.3 10.7 0.4 20.7 20.9 35.0 17.4"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b10d2-6db4-11ee-9270-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-65", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "PFN [ 33] 15.7 43.9 0.1 24.5 7.8 4.1 32.5 6.3 42.0 0.6 25.7 3.2 31.8 13.4 8.1 5.9 1.6 14.8 14.3 25.0 8.5\nChen et al. [8] 2.6 0.6 0 0.6 0.5 4.9 9.8 1.1 8.3 0.1 1.1 1.2 1.7 0.3 0.8 0.6 0.3 0.8 7.6 4.3 6.2\nSDS [ 19] 0.9 0 0 0.2 0.3 2.0 3.8 0.2 0.9 0.1 0.2 1.5 0 0 0 0.1 0.1 0 2.3 0.2 5.8\nTable 8: Comparison of mean APr, achieved by different published methods, at an IoU threshold of 0.7, for all twenty classes in the VOC dataset.\nMethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3745-6db4-11ee-abd2-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-66", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "MethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv\nOur method 48.6 69.6 1.4 68.2 45.1 25.2 61.1 38.7 72.1 11.2 56.3 30.0 73.3 60.7 64.3 46.8 17.1 49.1 44.6 75.0 62.0\nMPA 3-scale [ 37] 47.4 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013\nMPA 1-scale [ 37] 45.9 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013 \u2013\nArnab et al. [3] 45.4 68.9 0.84 65.1 38.3 26.3 64.7 31.8 72.7 6.7 45.4 32.9 67.9 60.0 63.7 41.1 13.4 43.9 41.1 74.6 48.1"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3746-6db4-11ee-88bb-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-67", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "PFN [ 33] 42.5 68.5 5.6 60.4 34.8 14.9 61.4 19.2 78.6 4.2 51.1 28.2 69.6 60.7 60.5 26.5 9.8 35.1 43.9 71.2 45.6\nChen et al. [8] 27.0 40.8 0.07 40.1 16.2 19.6 56.2 26.5 46.1 2.6 25.2 16.4 36.0 22.1 20.0 22.6 7.7 27.5 19.5 47.7 46.7\nSDS [ 19] 21.3 17.8 0 32.5 7.2 19.2 47.7 22.8 42.3 1.7 18.9 16.9 20.6 14.4 12.0 15.7 5.0 23.7 15.2 40.5 51.4\nTable 9: Comparison of mean APr, achieved by different published methods, at an IoU threshold of 0.5, for all twenty classes in the VOC dataset.\nMethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3747-6db4-11ee-b772-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-68", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "MethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv\nOur method 61.7 80.2 19.3 76.4 69.0 35.3 74.5 50.8 84.5 22.8 70.9 43.3 87.7 71.3 76.2 65.6 37.2 61.3 50.3 90.5 67.2\nMPA 3-scale [ 37] 62.1 79.7 11.5 71.6 54.6 44.7 80.9 62.0 85.4 26.5 64.5 46.6 87.6 71.7 77.9 72.1 48.8 57.4 48.8 78.9 70.8\nMPA 1-scale [ 37] 60.3 79.2 13.4 71.6 59.0 41.5 73.8 52.3 87.3 23.3 61.2 42.5 83.1 70.0 77.0 67.6 50.7 56.0 45.9 80.0 70.5"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3748-6db4-11ee-be75-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-69", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "Arnab et al. [3] 58.4 80.4 7.9 74.4 59.8 32.7 76.6 39.6 84.6 19.3 62.7 44.1 81.0 74.7 72.0 58.6 32.0 59.6 50.5 87.4 68.4\nPFN [ 33] 58.7 76.4 15.6 74.2 54.1 26.3 73.8 31.4 92.1 17.4 73.7 48.1 82.2 81.7 72.0 48.4 23.7 57.7 64.4 88.9 72.3\nChen et al. [8] 46.3 63.6 0.3 61.5 43.9 33.8 67.3 46.9 74.4 8.6 52.3 31.3 63.5 48.8 47.9 48.3 26.3 40.1 33.5 66.7 67.8\nSDS [ 19] 43.8 58.8 0.5 60.1 34.4 29.5 60.6 40.0 73.6 6.5 52.4 31.7 62.0 49.1 45.6 47.9 22.6 43.5 26.9 66.2 66.1"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3749-6db4-11ee-9ec8-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-70", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "Table 10: Comparison of mean APr, achieved by different published methods, at an IoU threshold of 0.7, for all twenty classes in the SBD dataset.\nMethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv\nOur method 44.8 69.0 27.4 52.7 26.4 22.4 70.3 46.0 74.7 9.6 46.8 16.9 71.6 48.4 46.3 40.3 14.8 47.6 36.5 69.7 58.2\nIIS sp, rescore[\n30]43.3 61.9 35.1 44.4 26.4 29.6 74.0 48.7 66.8 10.9 48.4 13.6 64.0 53.0 46.8 33.0 19.0 51.0 23.7 62.2 53.9\nIIS raw [ 30] 38.7 61.8 31.5 42.0 22.0 22.7 72.4 44.8 65.4 7.2 37.6 10.4 60.4 39.6 41.9 32.5 12.0 40.9 19.9 58.8 50.8"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b374a-6db4-11ee-a8bb-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1704.02386-71", "title": "Pixelwise Instance Segmentation with a Dynamically Instantiated Network", "source": "http://arxiv.org/pdf/1704.02386", "start_index": 0, "chroma:document": "Table 11: Comparison of mean APr, achieved by different published methods, at an IoU threshold of 0.5, for all twenty classes in the SBD dataset.\nMethodMean\nAPr(%)aeroplanebike bird boatbottlebus car cat chair cow table dog horse mbikepersonplant sheep sofa train tv\nOur method 62.0 80.3 52.8 68.5 47.4 39.5 79.1 61.5 87.0 28.1 68.3 35.5 86.1 73.9 66.1 63.8 32.9 65.3 50.4 81.4 71.4\nIIS sp, rescore[\n30]63.6 79.2 67.9 70.0 47.9 45.3 81.6 68.8 84.1 30.4 65.5 31.8 83.6 75.5 74.5 66.6 37.7 70.6 44.7 77.7 68.7\nIIS raw [ 30] 60.1 77.3 65.3 65.5 42.5 35.4 80.3 62.2 83.9 27.2 61.6 32.4 82.3 70.9 71.4 63.1 31.3 63.6 44.9 78.3 62.4"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b374b-6db4-11ee-9eda-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-0", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "Object Detection in Video with\nSpatiotemporal Sampling Networks\nGedas Bertasius1, Lorenzo Torresani2, and Jianbo Shi1\n1University of Pennsylvania,2Dartmouth College\nAbstract. We propose a Spatiotemporal Sampling Network (STSN)\nthat uses deformable convolutions across time for object detection in\nvideos. Our STSN performs object detection in a video frame by learning to spatially sample features from the adjacent frames. This naturally\nrenders the approach robust to occlusion or motion blur in individual\nframes. Our framework does not require additional supervision, as it optimizes sampling locations directly with respect to object detection performance. Our STSN outperforms the state-of-the-art on the ImageNet\nVID dataset and compared to prior video object detection methods it\nuses a simpler design, and does not require optical \ufb02ow data for training.\n1 Introduction\nIn recent years, deep convolutional networks have achieved remarkable results\nin many computer vision tasks [1,2,3,4,5,6,7,8], including object detection in images [9,10,11,12,13,14,15,16,17,18,19]. However, directly applying these imagelevel models to object detection in video is di\ufb03cult due to motion blur, video"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b374c-6db4-11ee-af6e-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-1", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "defocus, unusual poses, or object occlusions (see Figure 1). Despite these challenges, it is natural to assume that video object detectors should be more powerful than still image detectors because video contains richer information about\nthe same object instance (e.g., its appearance in di\ufb00erent poses, and from different viewpoints). The key challenge then is designing a model that e\ufb00ectively\nexploits temporal information in videos.\nPrior work [20,21,22,23] has proposed to exploit such temporal information\nin videos by means of various post-processing steps aimed at making object detections coherent across time. However, since temporal coherence is enforced in\na second stage, typically these methods cannot be trained end-to-end. To overcome this limitation, recent work [24] has introduced a \ufb02ow-based aggregation\nnetwork that is trainable end-to-end. It exploits optical \ufb02ow to \ufb01nd correspondences across time and it then aggregates features across temporal correspondences to smooth object detections over adjacent frames. However, one of the\ndownsides of this new model is that in addition to performing object detection,\nit also needs to predict motion. This is disadvantageous due to the following reasons: 1) designing an e\ufb00ective \ufb02ow network architecture is not trivial, 2) training"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b374d-6db4-11ee-8c95-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-2", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "it also needs to predict motion. This is disadvantageous due to the following reasons: 1) designing an e\ufb00ective \ufb02ow network architecture is not trivial, 2) training\nsuch a model requires large amounts of \ufb02ow data, which may be di\ufb03cult and\ncostly to obtain, 3) integrating a \ufb02ow network and a detection network into a\nsingle model may be challenging due to factors such as di\ufb00erent loss functions,\ndi\ufb00ering training procedures for each network, etc. arXiv:1803.05549v2  [cs.CV]  24 Jul 2018\n2 G. Bertasius, L. Torresani, J. Shi\nMotion Blur\nOcclusion\nUnusual Pose\nVideo DefocusChallengingEasierChallengingEasier\nFig.1: An illustration of the common challenges associated with object detection\nin video. These include video defocus, motion blur, occlusions and unusual poses.\nTheboundingboxesdenotetheobjectsthatwewanttodetectintheseexamples.\nTo address these shortcomings, in this work, we introduce a simple, yet effective Spatiotemporal Sampling Network (STSN) that uses deformable convolutions [25] across space and time to leverage temporal information for object"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b374e-6db4-11ee-a96d-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-3", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "detection in video. Our STSN learns to spatially sample useful feature points\nfrom nearby video frames such that object detection accuracy in a given video\nframe is maximized. To achieve this, we train our STSN end-to-end on a large set\nof video frames labeled with bounding boxes. We show that this leads to a better accuracy compared to the state-of-the-art on the ImageNet VID dataset [26],\nwithout requiring complex \ufb02ow network design, or the need to train the network\non large amounts of \ufb02ow data.\n2 Related Work\n2.1 Object Detection in Images\nModernobjectdetectors[9,10,11,12,13,14,15,16,17,18,19]arepredominantlybuilt\non some form of deep CNNs [1,3,5]. One of the earliest deep CNN object detection systems was R-CNN [14], which involved a two-stage pipeline where object\nproposals were extracted in the \ufb01rst stage, and then each proposal was classi\ufb01ed\nusing a CNN. To reduce the computational burden, the methods in [9], and [13]\nleveraged ROI pooling, which led to more e\ufb03cient learning. Furthermore, to\nunify the entire object detection pipeline, Faster R-CNN [12] replaced various"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b374f-6db4-11ee-a9e2-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-4", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "leveraged ROI pooling, which led to more e\ufb03cient learning. Furthermore, to\nunify the entire object detection pipeline, Faster R-CNN [12] replaced various\nregion proposal methods by another network to make the entire system trainable end-to-end. Following this work, several methods [18,19] extended Faster\nR-CNN into a system that runs in real time with small reduction in performance.\nAdditionally, recent work [17] introduced position sensitive ROI pooling, which\nsigni\ufb01cantly improved the detection e\ufb03ciency compared to prior object detection systems. Finally, two recent methods, Mask R-CNN [10], and Deformable\nCNNs [25], improved object detection results even further and they represent\nthe current state-of-the-art in object detection. Whereas Mask-RCNNs use an\nadditional branch that predicts a mask for each region of interest, Deformable\nObject Detection in Video with Spatiotemporal Sampling Networks 3\nCNNs employ deformable convolutions, which allow the network to condition\ndiscriminatively its receptive \ufb01eld on the input, and to also model deformations\nof objects more robustly.\nWhile the aforementioned methods work well on images, they are not designed to exploit temporal relationships in video. Instead, our Spatiotemporal"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3750-6db4-11ee-8905-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-5", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "of objects more robustly.\nWhile the aforementioned methods work well on images, they are not designed to exploit temporal relationships in video. Instead, our Spatiotemporal\nSampling Network (STSN), is speci\ufb01cally designed for a video object detection\ntask. Unlike standard Deformable CNNs [25], which use deformable convolution\nin the spatial domain, our STSN learns to sample features temporally across\ndi\ufb00erent video frames, which leads to improved video object detection accuracy.\n2.2 Object Detection in Videos\nUp until the introduction of the ImageNet VID challenge [26], there were no\nlarge-scalebenchmarksforvideoobjectdetection.Thus,thereareonlyfewmethods that we can compare our work to. T-CNNs [20,21] use a video object detection pipeline that involves predicting optical \ufb02ow \ufb01rst, then propagating imagelevel predictions according to the \ufb02ow, and \ufb01nally using a tracking algorithm to\nselect temporally consistent high con\ufb01dence detections. Seq-NMS [22] constructs\na temporal graph from overlapping bounding box detections across the adjacent\nframes, and then uses dynamic programming to select bounding box sequences\nwith the highest overall detection score. The work of Lee et al. [23] treats a video"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3751-6db4-11ee-b950-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-6", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "frames, and then uses dynamic programming to select bounding box sequences\nwith the highest overall detection score. The work of Lee et al. [23] treats a video\nobject detection task as a multi-object tracking problem. Finally, the method of\nFeichtenhofer et al. [27] proposes a ConvNet architecture that solves detection\nand tracking problems jointly, and then applies a Viterbi algorithm to link the\ndetections across time.\nThe approach most similar to our work is the method of Zhu et al. [24], who\nproposed an end-to-end trainable network that jointly estimates optical \ufb02ow and\nalso detects objects in video. This is accomplished by using the predicted optical\n\ufb02ow to align the features from the adjacent frames. The aggregated features are\nthen fed as input to the detection network.\nOurmethodisbene\ufb01cialoverthemethodsthatuseoptical\ufb02owCNNssuchas\nthemethodofZhuetal.[24].First,wenotethatpretrainedoptical\ufb02owCNNsdo\nnot always generalize to new datasets, which may hinder video object detection\nperformance. In contrast, our method has a learnable spatiotemporal sampling\nmodule that is discriminatively trained from object detection labels, and thus, it"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3752-6db4-11ee-b0b7-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-7", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "performance. In contrast, our method has a learnable spatiotemporal sampling\nmodule that is discriminatively trained from object detection labels, and thus, it\ndoes not su\ufb00er from this issue. Furthermore, our STSN can be trained for video\nobject detection in a single stage end-to-end. In comparison, methods that rely\non optical \ufb02ow require an additional stage to train an optical \ufb02ow CNN, which\nrenders the training procedure more cumbersome and lengthy. For example, we\nnotethatitwouldtakeaboutfourdaystotrainanoptical\ufb02owCNNofFGFA[24]\nfrom scratch and then four additional days to train FGFA [24] for video object\ndetection, making it eight days of total training time. In contrast, our STSN is\ntrained in a single stage in only 4 days. Finally, we point out that our STSN also\nyields a gain \u2014albeit moderate\u2014 in video object detection accuracy.\n4 G. Bertasius, L. Torresani, J. Shi\n3 Background: Deformable Convolution\nBefore describing our method, we \ufb01rst review some background information on\ndeformable convolution [25], which is one of the key components of our STSN.\nLet us \ufb01rst note that a standard 2D convolution is comprised of two steps: 1)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3753-6db4-11ee-92c0-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-8", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "Let us \ufb01rst note that a standard 2D convolution is comprised of two steps: 1)\nsampling locations on a uniformly-spaced grid R, and 2) performing a weighted\nsummation of sampled values using weights w. For example, if we consider a\nstandard 2D convolution with a 3\u00023kernel, and a dilation factor of 1, the grid\nRis de\ufb01ned asR=f(\u00001;\u00001);(\u00001;0);:::; (0;1);(1;1)g. Under a standard 2D\nconvolution, to compute a new value at pixel location p0in the output feature\nmapy, we would perform the following operation on the input feature map x:\ny(p0) =X\npn2Rw(pn)\u0001x(p0+pn);(1)\nInstead, in a deformable 2D convolution, the grid Ris augmented with dataconditioned o\ufb00sets f\u0001pnjn= 1;:::;Ng, whereN=jRj. We can then compute\na deformable convolution as:\ny(p0) =X\npn2Rw(pn)\u0001x(p0+pn+\u0001pn)(2)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3754-6db4-11ee-a416-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-9", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "a deformable convolution as:\ny(p0) =X\npn2Rw(pn)\u0001x(p0+pn+\u0001pn)(2)\nSince the o\ufb00set \u0001pnis typically fractional, the operation above is implemented using bilinear interpolation. Note that the o\ufb00sets are obtained by applying a separate convolutional layer to the activation tensor containing the feature\nmapx.Thisyieldsano\ufb00setmapthathasthesamespatialresolutionastheinput\nfeature map. Also, note that the o\ufb00sets are shared across all feature channels of\na given activation tensor. During training, the weights for the deformable convolution kernel, and the o\ufb00sets kernel are learned jointly by propagating gradients\nthrough the bilinear interpolation operator. We refer the reader to the original\nwork that introduced deformable convolutions [25] for further details.\n4 Spatiotemporal Sampling Network\nOur goal is to design a network architecture that incorporates temporal information for object detection in video.\nLet us denote with Itthe frame at time tin the video. Let us consider one\nof the scenarios depicted in Figure 1, e.g., a setting where Itis blurry, contains\nan object in an unusual pose, or perhaps an occlusion. But let us assume that"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3755-6db4-11ee-ab1d-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-10", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "of the scenarios depicted in Figure 1, e.g., a setting where Itis blurry, contains\nan object in an unusual pose, or perhaps an occlusion. But let us assume that\na nearby frame It+kincludes the same object clearly visible and in a relatively\nstandard pose. If we only had access to It, accurate object detection would be\nvery challenging. However, leveraging information from It+kmay enable more\nrobust detection in the frame It. Thus, the main challenge in this setting is\nincorporating object-level information from the supporting frameIt+kfor an improved object detection accuracy in the reference frameIt. Note that in our\nsystem each frame in the video is treated in turn as a reference frame in order to\nproduce object detection in every frame of the video. Furthermore, in practice\nObject Detection in Video with Spatiotemporal Sampling Networks 5\nReference Frame (time t)\nSupporting Frame (time t+k)\nDef. Conv.OffsetsDef. Conv.Offsets\nSampled Feature Map\nConcat\nFig.2: Our spatiotemporal sampling mechanism, which we use for video object\ndetection. Given the task of detecting objects in a particular video frame (i.e.,\na reference frame), our goal is to incorporate information from a nearby frame\nof the same video (i.e., a supporting frame). First, we extract features from"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3756-6db4-11ee-9322-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-11", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "a reference frame), our goal is to incorporate information from a nearby frame\nof the same video (i.e., a supporting frame). First, we extract features from\nboth frames via a backbone convolutional network (CNN). Next, we concatenate\nthe features from the reference and supporting frames, and feed them through\nmultiple deformable convolutional layers. The last of such layers produces o\ufb00sets\nthat are used to sample informative features from the supporting frame. Our\nspatiotemporal sampling scheme allows us to produce accurate detections even\nif objects in the reference frame appear blurry or occluded.\nwe use 2Ksupporting frames for detection in the reference frame, by taking\ntheKpreceding frames and the Ksubsequent frames as supporting frames, i.e.\nfIt\u0000K;It\u0000(K\u00001);:::;I t\u00001;It+1;:::;I t+(K\u00001);It+Kg. However, for ease of explanation we introduce our STSN by considering a single supporting frame It+k.\nTo e\ufb00ectively integrate temporal information we need two things: 1) powerful\nobject-level features from an image-level network, and 2) an ability to sample\nuseful object-level features from the supporting frames for the reference frame."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3757-6db4-11ee-b9a5-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-12", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "object-level features from an image-level network, and 2) an ability to sample\nuseful object-level features from the supporting frames for the reference frame.\nWeachievetheformerbyemployingastate-of-the-artbackbonenetwork.Forthe\nlatter, we design a spatiotemporal sampling scheme, which we describe below.\nOur STSN can be summarized in four steps. First, a backbone convolutional\nnetwork computes object-level features for each video frame individually. Then,\nspatiotemporal sampling blocks are applied to the object-level feature maps in\norder to sample relevant features from nearby frames conditioned on the input\nreference frame.Next,thesampledfeaturesfromeachvideoframearetemporally\naggregated into a single feature tensor for the reference frame using a per-pixel\nweighted summation. Finally, the feature tensor is provided as input to the\ndetectionnetworktoproduce\ufb01nalobjectdetectionresultsforthegivenreference\nframe. We note that our framework integrates these conceptually-distinct four\nsteps into a single architecture, which we train end-to-end.\n6 G. Bertasius, L. Torresani, J. Shi\nBackbone Architecture. Our backbone network is applied to each frame"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3758-6db4-11ee-9bd6-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-13", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "6 G. Bertasius, L. Torresani, J. Shi\nBackbone Architecture. Our backbone network is applied to each frame\nof the video. As backbone network, we use a Deformable CNN [25] based on\nthe ResNet-101 [5] architecture, which is one of the top-performing object detection systems at the moment. Similarly to [25], our backbone network employs\n6deformable convolutional layers. We also note that even though we use a Deformable CNN architecture, our system can easily integrate other architectures\nand thus it can bene\ufb01t from future improvements in still-image object detection.\nSpatiotemporal Feature Sampling. Our main contribution is the design\nof a spatiotemporal sampling mechanism, which seamlessly integrates temporal\ninformation in a given video. As a \ufb01rst step, we feed the reference frame Itand\nthe supporting frame It+kthrough our image-level backbone network, which\nproduces feature tensors ftandft+k, respectively. Note that ft;ft+k2Rc\u0002h\u0002w\nwherec;h, andware the number of channels, the height, and the width of the\nactivation tensor. The feature tensors ft, andft+kare then concatenated into a"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3759-6db4-11ee-89a6-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-14", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "activation tensor. The feature tensors ft, andft+kare then concatenated into a\nnew feature tensor ft;t+k2R2c\u0002h\u0002w. Note that this tensor ft;t+know has twice\nas many channels as our initial tensors, and that it now contains object-level\ninformation from both the reference and the supporting frame.\nNext, we use the tensor ft;t+kto predict (x;y)location o\ufb00sets, which are\nthen used to sample the supporting tensor ft+k. The sampling mechanism is\nimplementedusingadeformableconvolutionallayer,whichtakes1)thepredicted\no\ufb00sets, and 2) the supporting tensor ft+kas its inputs, and then outputs a\nnewly sampled feature tensor gt;t+k, which can be used for object detection in\nthe reference frame. We use subscript t;t+kto denote the resampled tensor\nbecause, although gis obtained by resampling the supporting tensor, the o\ufb00set\ncomputation uses both the reference as well as the supporting frame. A detailed\nillustration of our spatiotemporal sampling scheme is presented in Figure 2.\nIn practice, our spatiotemporal sampling block has 4deformable convolution"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b375a-6db4-11ee-8814-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-15", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "illustration of our spatiotemporal sampling scheme is presented in Figure 2.\nIn practice, our spatiotemporal sampling block has 4deformable convolution\nlayers (only 2are shown in Figure 2). This means that the initially predicted\no\ufb00setso(1)\nt;t+kand the concatenated temporal features ft;t+kare \ufb01rst used as\ninputs to a deformable convolution layer that outputs a new feature map g(1)\nt;t+k.\nNext, we use g(1)\nt;t+kto predict o\ufb00sets o(2)\nt;t+k, and a new feature map g(2)\nt;t+k. This\ncontinues for 2 more layers until we obtain o\ufb00sets o(4)\nt;t+k, which are then used\nto sample the points out of the supporting feature map ft+k. The \ufb01nal sampled\nfeature map g(4)\nt;t+kis obtained via another deformable convolutional layer that\ntakes as inputs o\ufb00sets o(4)\nt;t+kand the original supporting feature map ft+k.\nOur proposed spatiotemporal sampling mechanism learns, which object-level\nfeatures in the supporting frame are useful for object detection in the reference"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b375b-6db4-11ee-8a04-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-16", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "Our proposed spatiotemporal sampling mechanism learns, which object-level\nfeatures in the supporting frame are useful for object detection in the reference\nframe. Conceptually, it replaces the optical \ufb02ow used in [24] to establish temporal correspondences with a learnable module that is discriminatively trained\nfrom object detection labels. In our experimental section, we show that such a\nsampling scheme allows us to improve video object detection performance over\nthe still-image baseline and the \ufb02ow-based method of Zhu et al. [24] without\ntraining our model on optical \ufb02ow data.\nFeature Aggregation. The spatiotemporal sampling procedure is applied\nfor all the supporting frames in the selected range. Note, that this includes a\nObject Detection in Video with Spatiotemporal Sampling Networks 7\nspecial case, when the reference frame is treated as a supporting frame to itself to\nproduceg(4)\nt;t, which is a feature tensor computed from only the reference frame.\nThe resulting feature tensors have the following form: g(4)\nt;t+k2Rc(4)\u0002h\u0002w.\nThesefeaturetensorsareaggregatedintoanoutputfeaturetensor gagg\nt2Rc(4)\u0002h\u0002w\nfor the reference frame. This tensor captures information from the reference"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b375c-6db4-11ee-91ae-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-17", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "t2Rc(4)\u0002h\u0002w\nfor the reference frame. This tensor captures information from the reference\nframe, itsKpreceding frames and its Ksubsequent frames. The output tensor\nvaluegagg\nt(p)for frametat pixelpis computed as a weighted summation:\ngagg\nt(p) =KX\nk=\u0000Kwt;t+k(p)g(4)\nt;t+k(p) (3)\nInspired by strong results presented in [24], we use their proposed feature\naggregation method where the weights windicate the importance of each supporting frame to the reference frame. To compute the weights w, we attach a\n3-layer subnetwork S(x)to the features g(4)\nt;t+kand then compute their intermediate feature representations S(g(4)\nt;t+k). We then obtain the weights wby applying\nan exponential function on the cosine similarity between each corresponding\nfeature point in a reference frame and a supporting frame:\nwt;t+k(p) = exp \nS(g(4)\nt;t)(p)\u0001S(g(4)\nt;t+k)(p)\njS(g(4)\nt;t)(p)jjS(g(4)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b375d-6db4-11ee-995a-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-18", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "t;t+k)(p)\njS(g(4)\nt;t)(p)jjS(g(4)\nt;t+k)(p)j!\n(4)\nFinally,allweights warefedintothesoftmaxlayer,toensurethattheweights\nsum up to 1at each pixel location p(i.e.,PK\nk=\u0000Kwt;t+k(p) = 18p).\nObject Detection. Finally, the aggregated feature tensor gagg\ntis used as\ninput to the detection network, which outputs the \ufb01nal bounding box predictions\nand their object class probabilities. We describe more details related to the\ndetection network in the next section along with other implementation details.\n4.1 Implementation Details\nFor our experiments we use the MXNet [28] library. Below we provide details\nrelated to our STSN architecture, and our training and inference procedures.\nArchitecture. For our backbone network we adopt a state-of-the-art Deformable CNN [25] based on the ResNet-101 [5] architecture. Our spatiotemporal sampling block consists of four 3\u00023deformable convolutional layers each\nwith 1024output channels. In addition, it also has four 3\u00023convolutional layers"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b375e-6db4-11ee-b6f9-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-19", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "with 1024output channels. In addition, it also has four 3\u00023convolutional layers\npredicting (x;y)o\ufb00sets. To implement a subnetwork S(x)that predicts feature\naggregation weights, we use a sequence of 1\u00021,3\u00023and1\u00021convolutional\nlayers with 512;512and2048output channels respectively. Our detection network is implemented based on the deformable R-FCN design [17,29,25]. When\nfeeding the aggregated feature gagg\ntto the detection network, we split its 1024\nchannels into two parts, and feed the \ufb01rst and the last 512channels to the\nRPN and R-FCN sub-networks respectively. For the RPN, we use 9anchors and\n300proposals for each image. Furthermore, for the R-FCN, we use deformable\nposition-sensitive ROI pooling with 7\u00027groups.\n8 G. Bertasius, L. Torresani, J. Shi\nTraining. Our entire STSN model is fully di\ufb00erentiable, and thus, trainable\nend-to-end. During training, we resize all input images to a shorter side of 600\npixels, and use T= 3frames to train our model (i.e., K= 1). More speci\ufb01cally,"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b375f-6db4-11ee-b165-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-20", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "pixels, and use T= 3frames to train our model (i.e., K= 1). More speci\ufb01cally,\nwe randomly sample one supporting frame before and one supporting frame after\nthe reference frame. We observed that using more supporting frames in training\ndoes not lead to a higher accuracy.\nFor the rest of our training procedure, we follow the protocol outlined in [24].\nSpeci\ufb01cally, we train our model in two stages. First, we pre-train our full model\non the Imagenet DET dataset using the annotations of the 30object classes\nthat overlap with the Imagenet VID dataset. Note that Imagenet DET dataset\ncontains only images, and thus, we cannot sample meaningful supporting frames\nin this case. Therefore, in the case of images, we use the reference frames as our\nsupportingframes.Afterwards,theentiremodelistrainedfor 120Kiterationson\n4Tesla K40 GPUs with each GPU holding a single mini-batch. The learning rate\nis set to 0:001and0:0001for the \ufb01rst 80Kand the last 40Kiterations respectively. Afterwards, we \ufb01netune the entire model on the Imagenet VID dataset\nfor60Kiterations with a learning rate of 0:001and0:0001for the \ufb01rst 40Kand"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3760-6db4-11ee-8c21-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-21", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "for60Kiterations with a learning rate of 0:001and0:0001for the \ufb01rst 40Kand\nthe last 20Kiterations respectively. Note that in the second stage of training\nwe sample the supporting frames randomly within a certain neighborhood of a\nreference frame (as described above).\nInference. During inference, we use T= 27, meaning that we consider\nK= 13supporting frames before and after the reference frame. To avoid GPU\nmemory issues, we \ufb01rst extract features from the backbone network for each\nimage individually, and then cache these features in the memory. Afterwards,\nwe feed all these features into our spatiotemporal sampling block. At the end,\nstandard NMS with a threshold of 0:3is applied to re\ufb01ne the detections. To\nhandle the \ufb01rst and the last K= 13frames in the video \u2014two boundary cases\nthat require sampling the neighboring frames beyond the video start and end,\nwe pad the start of a video with Kcopies of the \ufb01rst frame, and the end of a\nvideo with Kcopies of the last frame.\n5 Experimental Results\nIn this section, we evaluate our approach for video object detection on the ImageNet VID [26] dataset, which has 3;862and555training and testing video"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3761-6db4-11ee-964a-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-22", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "5 Experimental Results\nIn this section, we evaluate our approach for video object detection on the ImageNet VID [26] dataset, which has 3;862and555training and testing video\nclips respectively. Each video is annotated with bounding boxes. The frames\nfrom each video are extracted at 25\u000030fps. The dataset contains 30object\ncategories that are a subset of the 200categories in the ImageNet DET dataset.\n5.1 Quantitative Results\nTo assess the e\ufb00ectiveness of our method we compare it to several relevant baselines, mainly two state-of-the-art methods FGFA [24] and D&T [27]. First, to\nverify that using temporal information from video is bene\ufb01cial, we include a\nstatic image-level variant of our model (SSN) that uses only the reference frame\nObject Detection in Video with Spatiotemporal Sampling Networks 9\nMethods\nD&T [27] Our SSN FGFA [24] Our STSN D&T+ [27] Our STSN+\nNo FlowNet? 3 - 7 3 3 3\nNot Using Flow Data? 3 - 7 3 3 3\nNo Temporal Post-Processing? 3 - 3 3 7 7\nmAP@0.5 75.8 76.0 78.8 78.9 79.8 80.4"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3762-6db4-11ee-898e-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-23", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "No Temporal Post-Processing? 3 - 3 3 7 7\nmAP@0.5 75.8 76.0 78.8 78.9 79.8 80.4\nTable 1: We use the ImageNet VID [26] dataset to compare our STSN to the\nstate-of-the-art FGFA [24] and D&T [27] methods. Note that SSN refers to our\nstatic baseline, which is obtained by using only the reference frame for output\ngeneration (no temporal info). Also note, that D&T+ and STSN+ refer to D&T\nand STSN baselines with temporal post-processing applied on top of the CNN\noutputs. Based on these results, we \ufb01rst point out that unlike FGFA, our STSN\ndoes not rely on the external optical \ufb02ow data, and still yields higher mAP\n(78:9vs78:8). Furthermore, when no temporal post-processing is used, our\nSTSN produces superior performance in comparison to the D&T baseline ( 78:9\nvs75:8). Finally, we demonstrate that if we use a simple Seq-NMS [22] temporal\npost-processing scheme on top of our STSN predictions, we can further improve\nour results and outperform all the other baselines."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3763-6db4-11ee-8b21-00155d3fea2c
encoding: FLOAT32
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{"uid": "1803.05549-24", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "post-processing scheme on top of our STSN predictions, we can further improve\nour results and outperform all the other baselines.\nto make its predictions. Furthermore, we also want to show that our spatiotemporal sampling scheme works as e\ufb00ectively as the optical \ufb02ow network in [24],\nbut without requiring optical \ufb02ow supervision. To do so, we replace the optical\n\ufb02ow network from [24], with our spatiotemporal sampling mechanism. The rest\nof the architecture and the training details are kept the same for both baselines.\nSuch an experimental design allows us to directly compare the e\ufb00ectiveness of\nour spatiotemporal sampling scheme and the optical \ufb02ow network of FGFA [24].\nFinally, we demonstrate that our method performs better than the D&T [27]\nmethod in two scenarios: 1) when we only useCNN-level outputs forvideo object\ndetection, and also 2) when we allow temporal post-processing techniques such\nas Seq-NMS to be applied on top of the CNN outputs. We note that in Table 1,\nD&T [27] and STSN refer to the CNN-level baselines whereas D&T+ [27] and"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3764-6db4-11ee-b6a4-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-25", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "D&T [27] and STSN refer to the CNN-level baselines whereas D&T+ [27] and\nSTSN+ denote these same methods but with temporal post-processing (i.e. SeqNMS[22],object-tubebasedlinking[27],etc)appliedontopoftheCNNoutputs.\nWe present our results in Table 1, where we assess each method according to\nseveral criteria. In the \ufb01rst row of Table 1, we list whether a given method requires integrating a separate \ufb02ow network into its training / prediction pipeline.\nIdeally, we would want to eliminate this step because optical \ufb02ow prediction requiresdesigningahighlycomplex\ufb02ownetworkarchitecture.Wealsolistwhether\na given method requires pre-training on the external optical \ufb02ow data, which we\nwould want to avoid since it makes the whole training pipeline more costly.\nAdditionally, we list, whether a given method uses any external temporal postprocessing steps, which we would want to eliminate because they typically make\nthe training / prediction pipeline disjoint and more complex. Finally, we assess\neach method according to the standard mean average precision (mAP) metric\nat intersection over union (IoU) threshold of 0:5.\n10 G. Bertasius, L. Torresani, J. Shi"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3765-6db4-11ee-b5d9-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-26", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "at intersection over union (IoU) threshold of 0:5.\n10 G. Bertasius, L. Torresani, J. Shi\n0 2 6 10 14 18 22 26 30Number of Supporting Frames7676.57777.57878.579mAP\n-10 -8 -6 -4 -2 0 2 4 6 8 10Time Delta w.r.t Reference Frame0.060.0650.070.0750.080.0850.090.0950.1Weight Magnitude\nFig.3: A \ufb01gure illustrating some of our ablation experiments. Left:we plot mAP\nas a function of the number of supporting frames used by our STSN. From this\nplot, we notice that the video object detection accuracy improves as we use\nmore supporting frames. Right:To understand the contribution of each of the\nsupporting frames, we plot the average weight magnitudes wt;t+k(p)for di\ufb00erent\nvalues ofk. Here,prepresents a point at the center of an object. From this plot,\nwe observe that the largest weights are associated with the supporting frames\nthat are near the reference frame. However, note that even supporting frames\nthat are further away from the reference frame (e.g. k= 9) contribute quite\nsubstantially to the \ufb01nal object detection predictions."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3766-6db4-11ee-b1d5-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-27", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "that are further away from the reference frame (e.g. k= 9) contribute quite\nsubstantially to the \ufb01nal object detection predictions.\nBased on our results in Table 1, we make the following conclusions. First, we\nnotethatourSTSNproducesbetterquantitativeresultsthanthestate-of-the-art\nFGFA method ( 78:9vs78:8). We acknowledge that our accuracy improvement\nover FGFA is moderate. However, we point out that our STSN operates in a\nmuch more challenging setting than FGFA. Unlike FGFA, our STSN does not\nuse any optical \ufb02ow supervision. Instead, it is trained directly for video object\ndetection. The fact that STSN learns temporal correspondences without direct\noptical \ufb02ow supervision, and still outperforms FGFA is quite impressive. Such\nresults also show the bene\ufb01t of discriminative end-to-end training with respect\nto the \ufb01nal video object detection task objective.\nWenextcompareourSTSNtotheD&Tbaseline[27].Wenotethatunlikefor\nthe FGFA [24] baseline, it is much harder to make a direct comparison between"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3767-6db4-11ee-9081-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-28", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "the FGFA [24] baseline, it is much harder to make a direct comparison between\nSTSN and D&T. Whereas our STSN aims to produce powerful spatiotemporal features, the method of D&T [27] is targeted more for smoothing the \ufb01nal\nbounding box predictions across time. Thus, we believe that these two methods\nare complementary, and it would be possible to integrate them together for the\nmodel that produces both: temporally smooth features, as well as temporally\nsmooth bounding box predictions. We also note that our STSN and D&T [27]\nuse slightly di\ufb00erent architectures (both based on ResNet-101 though).\nFirst, we compare STSN and D&T in a setting when no temporal postprocessing(i.e.Seq-NMS[22],object-tubelinking[27],etc)isused,andshowthat\nourSTSNoutperformstheD&Tbaselinebyasubstantialmargin( 78:9vs75:8).\nObject Detection in Video with Spatiotemporal Sampling Networks 11\nThese results indicate, that our STSN is able to learn powerful spatiotemporal\nfeatures, and produce solid video object detection results even without temporal\npost-processing algorithms that link bounding box detections over time."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3768-6db4-11ee-8e95-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-29", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "features, and produce solid video object detection results even without temporal\npost-processing algorithms that link bounding box detections over time.\nAfterwards, we show that integrating a simple temporal post-processing algorithm Seq-NMS [22] further improves our STSN\u2019s results. Such a scheme allows\nus to outperform the D&T+ baseline ( 80:4vs79:8), which uses a similar Viterbi\nbased temporal post-processing scheme.\n5.2 Ablation Studies\nOptimal Number of Supporting Frames. In the left subplot of Figure 3,\nwe also illustrate how the number of supporting frames a\ufb00ects the video object\ndetection accuracy. We notice that the performance keeps increasing as we add\nmore supporting frames, and then plateaus at T= 27.\nIncreasing the Temporal Stride. We also investigate how the temporal\nstridek, at which we sample the supporting frames, a\ufb00ects STSN\u2019s performance.\nWe report that temporal strides of k= 2andk= 4, yield mAP scores of 79:0\nand77:9, respectively. Thus, k= 2yields a slight improvement over our original\n78:9mAP score. However, increasing kto larger values reduces the accuracy.\nFeature Aggregation Weight Analysis. To analyze how much each of"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3769-6db4-11ee-a1a0-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-30", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "78:9mAP score. However, increasing kto larger values reduces the accuracy.\nFeature Aggregation Weight Analysis. To analyze how much each of\nthe supporting frame contributes to the \ufb01nal object detections, we visualize the\naverage weight magnitudes wt;t+k(p)for di\ufb00erent values of k. This visualization\nis presented in the right subplot of Figure 3. We note that in this case, the weight\nmagnitudes correspond to the point p, which is located at the center of an object.\nFrom this plot, we can conclude that the largest contribution comes from the\nsupporting frames that are near the reference frame ( k=\u00001;0;1). However,\nnote that even even supporting frames that are further away from the reference\nframe (e.g. k=\u00009;9) have non-zero weights, and contribute quite substantially\nto the \ufb01nal object detection predictions.\n5.3 Qualitative Results\nTo understand how our STSN exploits temporal information from a given video,\nwe visualize in Figure 4, the average o\ufb00sets predicted by the STSN sampling\nblock. These o\ufb00sets are used by the STSN to decide, which object-level informationfromthesupportingframeshouldbeusedtodetectanobjectinthereference"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b376a-6db4-11ee-b934-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-31", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "frame. The green square in the reference frame depicts a pixel, for which we want\nto compute a convolution output. The red square in the supporting frame represents an average o\ufb00set, which is used to determine which feature points from the\nsupporting frame should be sampled. The yellow arrow indicates object\u2019s motion between the reference frame and the supporting frame. Note that despite\na relatively large motion between the reference and the supporting frames, our\nSTSN samples features from the supporting frame right around the center of the\nobject, which is exactly what we want. Such spatiotemporal sampling allows us\nto detect objects even if they appear blurry or occluded in the reference frame.\n12 G. Bertasius, L. Torresani, J. Shi\nReference Frame (t)Supporting Frame (t+9)\nReference Frame (t)Supporting Frame (t+9)\nFig.4: An illustration of our spatiotemporal sampling scheme (zoom-in for a better view). The green square indicates a point in the reference frame, for which\nwe want to compute a new convolutional output. The red square indicates the\ncorresponding point predicted by our STSN in a supporting frame. The yellow\narrow illustrates the estimated object motion. Although our model is trained\ndiscriminatively for object detection and notfor tracking or motion estimation,"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b376b-6db4-11ee-98f0-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-32", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "arrow illustrates the estimated object motion. Although our model is trained\ndiscriminatively for object detection and notfor tracking or motion estimation,\nour STSN learns to sample from the supporting frame at locations that coincide almost perfectly with the same object. This allows our method to perform\naccurate object detection even if objects in the reference frame are blurry or\noccluded.\nIn addition, based on the results in Figure 4, we observe that even without\nan explicit optical \ufb02ow supervision, our STSN learns to accurately capture the\nmotion of the objects, which is another appealing property of our model. In\nfact, in Figure 5, we illustrate several examples of using our STSN to track\nobjects in a given video. From Figure 5, we observe that despite a relatively\nlarge motion in each sequence, our STSN accurately samples features around\nobjects in every supporting frame. Such results indicate that we may be able\nto use our sampling mechanism for discriminative object tracking. In fact, we\nnote that the commonly used dense optical \ufb02ow methods are often redundant\nbecause most applications do not require \ufb02ow prediction for every single pixel. In\ncomparison, we point out that our STSN captures a more discriminative form of\nmotion, which is learned to exclusively bene\ufb01t a video object detection task. In\nour supplementary material, we include more of such results in the video form."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b376c-6db4-11ee-8c4b-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-33", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "motion, which is learned to exclusively bene\ufb01t a video object detection task. In\nour supplementary material, we include more of such results in the video form.\nIn Figure 6, we also illustrate object detections of the static SSN baseline,\nand those of our full STSN model (zoom-in to see the probabilities and class\npredictions). In all of these cases, we observe that incorporating temporal information helps STSN to correct the mistakes made by the static baseline. For\ninstance, in the third row of Figure 6, a static SSN baseline incorrectly labels\nan object in the reference frame as a bird, which happens due to the occluded\nhead of the lizard. However, STSN \ufb01xes this mistake by looking at the supporting frames, and by sampling around the lizard body and its head (See Row 3,\nColumn 1 in Figure 6). Furthermore, in the last row, a static SSN baseline fails\nto detect one of the bicycles because it is occluded in the reference frame. STSN\n\ufb01xes this error, by sampling around the missed bicycle in the supporting frame\nObject Detection in Video with Spatiotemporal Sampling Networks 13\nReference Frame (t)Supporting Frame (t-9)Supporting Frame (t-4)Supporting Frame (t+4)Supporting Frame (t+9)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b376d-6db4-11ee-a77a-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-34", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "Reference Frame (t)Supporting Frame (t-9)Supporting Frame (t-4)Supporting Frame (t+4)Supporting Frame (t+9)\nFig.5: An illustration of using our spatiotemporal sampling scheme in action.\nThe green square indicates a \ufb01xed object location in the reference frame. The\nred square depicts a location in a supporting frame, from which relevant features\nare sampled. Even without optical \ufb02ow supervision, our STSN learns to track\nthese objects in video. In our supplementary material, we include more of such\nexamples in the video format.\nwhere the bicycle is more clearly visible. Similar behavior also occurs in other\ncases where STSN successfully resolves occlusion and blurriness issues.\n6 Conclusion\nInthiswork,weintroducedtheSpatiotemporalSamplingNetwork(STSN)which\nis a new architecture for object detection in video. Compared to the state-of-theart FGFA [24] method, our model involves a simpler design, it does not require\noptical \ufb02ow computation and it produces higher video object detection accuracy.\nOurmodelisfullydi\ufb00erentiable,andunlikepriorvideoobjectdetectionmethods,\nit does not necessitate optical \ufb02ow training data. This renders our model easy to"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b376e-6db4-11ee-a865-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-35", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "it does not necessitate optical \ufb02ow training data. This renders our model easy to\ntrain end-to-end. Our future work will include experimenting with more complex\ndesign of spatiotemporal sampling blocks.\n7 Acknowledgements\nThis work was funded in part by NSF award CNS-120552. We gratefully acknowledge NVIDIA and Facebook for the donation of GPUs used for portions\nof this work.\n14 G. Bertasius, L. Torresani, J. Shi\nSSN (Static)STSN (Ours)\nSampled Points in the     Supporting Frame\nFig.6: A \ufb01gure illustrating object detection examples where our spatiotemporal\nsampling mechanism helps STSN to correct the mistakes made by a static SSN\nbaseline (please zoom-in to see the class predictions and their probabilities).\nThese mistakes typically occur due to occlusions, blurriness, etc. STSN \ufb01xes\nthese errors by using relevant object level information from supporting frames.\nInColumn 1weillustratethepointsinthesupportingframethatSTSNconsiders\nrelevant when computing the output for a point denoted by the green square in\nColumn 2.\nObject Detection in Video with Spatiotemporal Sampling Networks 15\nReferences"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b376f-6db4-11ee-91d1-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-36", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "relevant when computing the output for a point denoted by the green square in\nColumn 2.\nObject Detection in Video with Spatiotemporal Sampling Networks 15\nReferences\n1. Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classi\ufb01cation with deep\nconvolutional neural networks. In: NIPS. (2012)\n2. Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D.,\nVanhoucke, V., Rabinovich, A.: Going deeper with convolutions. In: Computer\nVision and Pattern Recognition (CVPR). (2015)\n3. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale\nimage recognition. In: ICLR. (2015)\n4. Bertasius, G., Shi, J., Torresani, L.: Deepedge: A multi-scale bifurcated deep\nnetwork for top-down contour detection. In: The IEEE Conference on Computer\nVision and Pattern Recognition (CVPR). (June 2015)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3770-6db4-11ee-8501-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-37", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "network for top-down contour detection. In: The IEEE Conference on Computer\nVision and Pattern Recognition (CVPR). (June 2015)\n5. He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. 2016IEEEConferenceonComputerVisionandPatternRecognition(CVPR)\n(2016) 770\u2013778\n6. Xie,S.,Girshick,R.,Doll\u00e1r,P.,Tu,Z.,He,K.: Aggregatedresidualtransformations\nfor deep neural networks. In: CVPR. (2017)\n7. Toshev, A., Szegedy, C.: Deeppose: Human pose estimation via deep neural networks. In: CVPR. (2014)\n8. Bertasius, G., Torresani, L., Yu, S.X., Shi, J.: Convolutional random walk networks\nfor semantic image segmentation. In: The IEEE Conference on Computer Vision\nand Pattern Recognition (CVPR). (July 2017)\n9. He, K., Zhang, X., Ren, S., Sun, J.: Spatial pyramid pooling in deep convolutional\nnetworks for visual recognition. In Fleet, D., Pajdla, T., Schiele, B., Tuytelaars,"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3771-6db4-11ee-a80e-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-38", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "networks for visual recognition. In Fleet, D., Pajdla, T., Schiele, B., Tuytelaars,\nT., eds.: Computer Vision \u2013 ECCV 2014. (2014)\n10. He, K., Gkioxari, G., Doll\u00e1r, P., Girshick, R.: Mask R-CNN. In: Proceedings of\nthe International Conference on Computer Vision (ICCV). (2017)\n11. Lin, T.Y., Goyal, P., Girshick, R., He, K., Doll\u00e1r, P.: Focal Loss for Dense Object\nDetection. In: Proceedings of the International Conference on Computer Vision\n(ICCV). (2017)\n12. Ren, S., He, K., Girshick, R., Sun, J.: Faster R-CNN: Towards real-time object detection with region proposal networks. In: Neural Information Processing Systems\n(NIPS). (2015)\n13. Girshick, R.: Fast R-CNN. In: Proceedings of the International Conference on\nComputer Vision (ICCV). (2015)\n14. Girshick, R., Donahue, J., Darrell, T., Malik, J.: Rich feature hierarchies for accurate object detection and semantic segmentation. In: Proceedings of the IEEE\nConference on Computer Vision and Pattern Recognition (CVPR). (2014)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3772-6db4-11ee-b6bf-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-39", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "Conference on Computer Vision and Pattern Recognition (CVPR). (2014)\n15. Gupta,S.,Girshick,R.,Arbelaez,P.,Malik,J.: LearningrichfeaturesfromRGB-D\nimages for object detection and segmentation. In: ECCV. (2014)\n16. Liu, W., Anguelov, D., Erhan, D., Szegedy, C., Reed, S., Fu, C.Y., Berg, A.C.:\nSsd: Single shot multibox detector. In: ECCV. (2016)\n17. Dai, J., Li, Y., He, K., Sun, J.: R-fcn: Object detection via region-based fully\nconvolutional networks. In: Advances in Neural Information Processing Systems\n29. Curran Associates, Inc. (2016) 379\u2013387\n18. Redmon,J.,Divvala,S.K.,Girshick,R.B.,Farhadi,A.: Youonlylookonce:Uni\ufb01ed,\nreal-time object detection. In: 2016 IEEE Conference on Computer Vision and\nPattern Recognition, CVPR 2016, Las Vegas, NV, USA, June 27-30, 2016. (2016)\n779\u2013788\n16 G. Bertasius, L. Torresani, J. Shi"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3773-6db4-11ee-a478-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-40", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "779\u2013788\n16 G. Bertasius, L. Torresani, J. Shi\n19. Redmon, J., Farhadi, A.: YOLO9000: better, faster, stronger. In: 2017 IEEE\nConference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu,\nHI, USA, July 21-26, 2017. (2017) 6517\u20136525\n20. Kang, K., Li, H., Yan, J., Zeng, X., Yang, B., Xiao, T., Zhang, C., Wang, Z., Wang,\nR., Wang, X., Ouyang, W.: T-CNN: tubelets with convolutional neural networks\nfor object detection from videos. IEEE TCSVT 2017 (2017)\n21. Kang, K., Ouyang, W., Li, H., Wang, X.: Object detection from video tubelets\nwith convolutional neural networks. CoRR abs/1604.04053 (2016)\n22. Han, W., Khorrami, P., Paine, T.L., Ramachandran, P., Babaeizadeh, M., Shi,\nH., Li, J., Yan, S., Huang, T.S.: Seq-nms for video object detection. CoRR\nabs/1602.08465 (2016)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3774-6db4-11ee-82c5-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-41", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "H., Li, J., Yan, S., Huang, T.S.: Seq-nms for video object detection. CoRR\nabs/1602.08465 (2016)\n23. Lee, B., Erdenee, E., Jin, S., Rhee, P.: Multi-class multi-object tracking using\nchanging point detection. CoRR abs/1608.08434 (2016)\n24. Zhu, X., Wang, Y., Dai, J., Yuan, L., Wei, Y.: Flow-guided feature aggregation for\nvideo object detection. In: International Conference on Computer Vision (ICCV).\n(2017)\n25. Dai, J., Qi, H., Xiong, Y., Li, Y., Zhang, G., Hu, H., Wei, Y.: Deformable convolutional networks. In: 2017 IEEE International Conference on Computer Vision\n(ICCV). Volume 00. (Oct. 2017) 764\u2013773\n26. Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z.,\nKarpathy, A., Khosla, A., Bernstein, M., Berg, A.C., Fei-Fei, L.: ImageNet Large\nScale Visual Recognition Challenge. International Journal of Computer Vision\n(IJCV) 115(3) (2015) 211\u2013252"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3775-6db4-11ee-b7ec-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1803.05549-42", "title": "Object Detection in Video with Spatiotemporal Sampling Networks", "source": "http://arxiv.org/pdf/1803.05549", "start_index": 0, "chroma:document": "Scale Visual Recognition Challenge. International Journal of Computer Vision\n(IJCV) 115(3) (2015) 211\u2013252\n27. Feichtenhofer, C., Pinz, A., Zisserman, A.: Detect to track and track to detect. In:\nInternational Conference on Computer Vision (ICCV). (2017)\n28. Chen, T., Li, M., Li, Y., Lin, M., Wang, N., Wang, M., Xiao, T., Xu, B., Zhang,\nC., Zhang, Z.: Mxnet: A \ufb02exible and e\ufb03cient machine learning library for heterogeneous distributed systems. CoRR abs/1512.01274 (2015)\n29. Zhu, X., Xiong, Y., Dai, J., Yuan, L., Wei, Y.: Deep feature \ufb02ow for video recognition. In: CVPR. (2017)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3776-6db4-11ee-894d-00155d3fea2c
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{"uid": "1806.01261-0", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Relational inductive biases, deep learning, and graph networks\nPeter W. Battaglia1\u0003,Jessica B. Hamrick1,Victor Bapst1,\nAlvaro Sanchez-Gonzalez1,Vinicius Zambaldi1,Mateusz Malinowski1,\nAndrea Tacchetti1,David Raposo1,Adam Santoro1,Ryan Faulkner1,\nCaglar Gulcehre1,Francis Song1,Andrew Ballard1,Justin Gilmer2,\nGeorge Dahl2,Ashish Vaswani2,Kelsey Allen3,Charles Nash4,\nVictoria Langston1,Chris Dyer1,Nicolas Heess1,\nDaan Wierstra1,Pushmeet Kohli1,Matt Botvinick1,\nOriol Vinyals1,Yujia Li1,Razvan Pascanu1\n1DeepMind;2Google Brain;3MIT;4University of Edinburgh\nAbstract\nArti\fcial intelligence (AI) has undergone a renaissance recently, making major progress in\nkey domains such as vision, language, control, and decision-making. This has been due, in\npart, to cheap data and cheap compute resources, which have \ft the natural strengths of deep\nlearning. However, many de\fning characteristics of human intelligence, which developed under"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3777-6db4-11ee-89fa-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-1", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "part, to cheap data and cheap compute resources, which have \ft the natural strengths of deep\nlearning. However, many de\fning characteristics of human intelligence, which developed under\nmuch di\u000berent pressures, remain out of reach for current approaches. In particular, generalizing\nbeyond one's experiences|a hallmark of human intelligence from infancy|remains a formidable\nchallenge for modern AI.\nThe following is part position paper, part review, and part uni\fcation. We argue that\ncombinatorial generalization must be a top priority for AI to achieve human-like abilities, and that\nstructured representations and computations are key to realizing this objective. Just as biology\nuses nature and nurture cooperatively, we reject the false choice between \\hand-engineering\"\nand \\end-to-end\" learning, and instead advocate for an approach which bene\fts from their\ncomplementary strengths. We explore how using relational inductive biases within deep learning\narchitectures can facilitate learning about entities, relations, and rules for composing them. We\npresent a new building block for the AI toolkit with a strong relational inductive bias|the graph\nnetwork |which generalizes and extends various approaches for neural networks that operate\non graphs, and provides a straightforward interface for manipulating structured knowledge and\nproducing structured behaviors. We discuss how graph networks can support relational reasoning"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3778-6db4-11ee-9ca4-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-2", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "on graphs, and provides a straightforward interface for manipulating structured knowledge and\nproducing structured behaviors. We discuss how graph networks can support relational reasoning\nand combinatorial generalization, laying the foundation for more sophisticated, interpretable,\nand \rexible patterns of reasoning. As a companion to this paper, we have also released an\nopen-source software library for building graph networks, with demonstrations of how to use\nthem in practice.\n1 Introduction\nA key signature of human intelligence is the ability to make \\in\fnite use of \fnite means\" (Humboldt,\n1836; Chomsky, 1965), in which a small set of elements (such as words) can be productively\ncomposed in limitless ways (such as into new sentences). This re\rects the principle of combinatorial\ngeneralization , that is, constructing new inferences, predictions, and behaviors from known building\nblocks. Here we explore how to improve modern AI's capacity for combinatorial generalization by\n\u0003Corresponding author: peterbattaglia@google.com\n1arXiv:1806.01261v3  [cs.LG]  17 Oct 2018\nbiasing learning towards structured representations and computations, and in particular, systems\nthat operate on graphs."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3779-6db4-11ee-86fa-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-3", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "biasing learning towards structured representations and computations, and in particular, systems\nthat operate on graphs.\nHumans' capacity for combinatorial generalization depends critically on our cognitive mechanisms for representing structure and reasoning about relations. We represent complex systems as\ncompositions of entities and their interactions1(Navon, 1977; McClelland and Rumelhart, 1981;\nPlaut et al., 1996; Marcus, 2001; Goodwin and Johnson-Laird, 2005; Kemp and Tenenbaum, 2008),\nsuch as judging whether a haphazard stack of objects is stable (Battaglia et al., 2013). We use\nhierarchies to abstract away from \fne-grained di\u000berences, and capture more general commonalities\nbetween representations and behaviors (Botvinick, 2008; Tenenbaum et al., 2011), such as parts of\nan object, objects in a scene, neighborhoods in a town, and towns in a country. We solve novel\nproblems by composing familiar skills and routines (Anderson, 1982), for example traveling to a\nnew location by composing familiar procedures and objectives, such as \\travel by airplane\", \\to\nSan Diego\", \\eat at\", and \\an Indian restaurant\". We draw analogies by aligning the relational\nstructure between two domains and drawing inferences about one based on corresponding knowledge"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b377a-6db4-11ee-9e38-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-4", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "San Diego\", \\eat at\", and \\an Indian restaurant\". We draw analogies by aligning the relational\nstructure between two domains and drawing inferences about one based on corresponding knowledge\nabout the other (Gentner and Markman, 1997; Hummel and Holyoak, 2003).\nKenneth Craik's \\The Nature of Explanation\" (1943), connects the compositional structure of\nthe world to how our internal mental models are organized:\n...[a human mental model] has a similar relation-structure to that of the process it\nimitates. By `relation-structure' I do not mean some obscure non-physical entity which\nattends the model, but the fact that it is a working physical model which works in the\nsame way as the process it parallels... physical reality is built up, apparently, from a few\nfundamental types of units whose properties determine many of the properties of the\nmost complicated phenomena, and this seems to a\u000bord a su\u000ecient explanation of the\nemergence of analogies between mechanisms and similarities of relation-structure among\nthese combinations without the necessity of any theory of objective universals. (Craik,\n1943, page 51-55)\nThat is, the world is compositional, or at least, we understand it in compositional terms. When\nlearning, we either \ft new knowledge into our existing structured representations, or adjust the"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b377b-6db4-11ee-b4af-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-5", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "learning, we either \ft new knowledge into our existing structured representations, or adjust the\nstructure itself to better accommodate (and make use of) the new and the old (Tenenbaum et al.,\n2006; Gri\u000eths et al., 2010; Ullman et al., 2017).\nThe question of how to build arti\fcial systems which exhibit combinatorial generalization has\nbeen at the heart of AI since its origins, and was central to many structured approaches, including\nlogic, grammars, classic planning, graphical models, causal reasoning, Bayesian nonparametrics, and\nprobabilistic programming (Chomsky, 1957; Nilsson and Fikes, 1970; Pearl, 1986, 2009; Russell and\nNorvig, 2009; Hjort et al., 2010; Goodman et al., 2012; Ghahramani, 2015). Entire sub-\felds have\nfocused on explicit entity- and relation-centric learning, such as relational reinforcement learning\n(D\u0014 zeroski et al., 2001) and statistical relational learning (Getoor and Taskar, 2007). A key reason\nwhy structured approaches were so vital to machine learning in previous eras was, in part, because\ndata and computing resources were expensive, and the improved sample complexity a\u000borded by\nstructured approaches' strong inductive biases was very valuable."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b377c-6db4-11ee-a780-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-6", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "data and computing resources were expensive, and the improved sample complexity a\u000borded by\nstructured approaches' strong inductive biases was very valuable.\nIn contrast with past approaches in AI, modern deep learning methods (LeCun et al., 2015;\nSchmidhuber, 2015; Goodfellow et al., 2016) often follow an \\end-to-end\" design philosophy which\nemphasizes minimal a priori representational and computational assumptions, and seeks to avoid\nexplicit structure and \\hand-engineering\". This emphasis has \ft well with|and has perhaps been\na\u000ermed by|the current abundance of cheap data and cheap computing resources, which make\n1Whether this entails a \\language of thought\" (Fodor, 1975) is beyond the scope of this work.\n2\ntrading o\u000b sample e\u000eciency for more \rexible learning a rational choice. The remarkable and rapid\nadvances across many challenging domains, from image classi\fcation (Krizhevsky et al., 2012;\nSzegedy et al., 2017), to natural language processing (Sutskever et al., 2014; Bahdanau et al., 2015),\nto game play (Mnih et al., 2015; Silver et al., 2016; Morav\u0014 c\u0013 \u0010k et al., 2017), are a testament to this"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b377d-6db4-11ee-898a-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-7", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "to game play (Mnih et al., 2015; Silver et al., 2016; Morav\u0014 c\u0013 \u0010k et al., 2017), are a testament to this\nminimalist principle. A prominent example is from language translation, where sequence-to-sequence\napproaches (Sutskever et al., 2014; Bahdanau et al., 2015) have proven very e\u000bective without using\nexplicit parse trees or complex relationships between linguistic entities.\nDespite deep learning's successes, however, important critiques (Marcus, 2001; Shalev-Shwartz\net al., 2017; Lake et al., 2017; Lake and Baroni, 2018; Marcus, 2018a,b; Pearl, 2018; Yuille and\nLiu, 2018) have highlighted key challenges it faces in complex language and scene understanding,\nreasoning about structured data, transferring learning beyond the training conditions, and learning\nfrom small amounts of experience. These challenges demand combinatorial generalization, and so it\nis perhaps not surprising that an approach which eschews compositionality and explicit structure\nstruggles to meet them.\nWhen deep learning's connectionist (Rumelhart et al., 1987) forebears were faced with analogous\ncritiques from structured, symbolic positions (Fodor and Pylyshyn, 1988; Pinker and Prince, 1988),"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b377e-6db4-11ee-a1a8-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-8", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "critiques from structured, symbolic positions (Fodor and Pylyshyn, 1988; Pinker and Prince, 1988),\nthere was a constructive e\u000bort (Bobrow and Hinton, 1990; Marcus, 2001) to address the challenges\ndirectly and carefully. A variety of innovative sub-symbolic approaches for representing and reasoning\nabout structured objects were developed in domains such as analogy-making, linguistic analysis,\nsymbol manipulation, and other forms of relational reasoning (Smolensky, 1990; Hinton, 1990;\nPollack, 1990; Elman, 1991; Plate, 1995; Eliasmith, 2013), as well as more integrative theories for\nhow the mind works (Marcus, 2001). Such work also helped cultivate more recent deep learning\nadvances which use distributed, vector representations to capture rich semantic content in text\n(Mikolov et al., 2013; Pennington et al., 2014), graphs (Narayanan et al., 2016, 2017), algebraic and\nlogical expressions (Allamanis et al., 2017; Evans et al., 2018), and programs (Devlin et al., 2017;\nChen et al., 2018b).\nWe suggest that a key path forward for modern AI is to commit to combinatorial generalization\nas a top priority, and we advocate for integrative approaches to realize this goal. Just as biology does"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b377f-6db4-11ee-91eb-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-9", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "as a top priority, and we advocate for integrative approaches to realize this goal. Just as biology does\nnot choose between nature versus nurture|it uses nature and nurture jointly , to build wholes which\nare greater than the sums of their parts|we, too, reject the notion that structure and \rexibility are\nsomehow at odds or incompatible, and embrace both with the aim of reaping their complementary\nstrengths. In the spirit of numerous recent examples of principled hybrids of structure-based methods\nand deep learning (e.g., Reed and De Freitas, 2016; Garnelo et al., 2016; Ritchie et al., 2016; Wu\net al., 2017; Denil et al., 2017; Hudson and Manning, 2018), we see great promise in synthesizing\nnew techniques by drawing on the full AI toolkit and marrying the best approaches from today\nwith those which were essential during times when data and computation were at a premium.\nRecently, a class of models has arisen at the intersection of deep learning and structured\napproaches, which focuses on approaches for reasoning about explicitly structured data, in particular\ngraphs (e.g. Scarselli et al., 2009b; Bronstein et al., 2017; Gilmer et al., 2017; Wang et al., 2018c; Li\net al., 2018; Kipf et al., 2018; Gulcehre et al., 2018). What these approaches all have in common"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3780-6db4-11ee-8e60-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-10", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "et al., 2018; Kipf et al., 2018; Gulcehre et al., 2018). What these approaches all have in common\nis a capacity for performing computation over discrete entities and the relations between them.\nWhat sets them apart from classical approaches is how the representations and structure of the\nentities and relations|and the corresponding computations|can be learned, relieving the burden\nof needing to specify them in advance. Crucially, these methods carry strong relational inductive\nbiases , in the form of speci\fc architectural assumptions, which guide these approaches towards\nlearning about entities and relations (Mitchell, 1980), which we, joining many others (Spelke et al.,\n1992; Spelke and Kinzler, 2007; Marcus, 2001; Tenenbaum et al., 2011; Lake et al., 2017; Lake and\nBaroni, 2018; Marcus, 2018b), suggest are an essential ingredient for human-like intelligence.\n3\nBox 1: Relational reasoning\nWe de\fne structure as the product of composing a set of known building blocks. \\Structured\nrepresentations\" capture this composition (i.e., the arrangement of the elements) and \\structured\ncomputations\" operate over the elements and their composition as a whole. Relational reasoning,\nthen, involves manipulating structured representations of entities and relations , using rules"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3781-6db4-11ee-a25f-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-11", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "computations\" operate over the elements and their composition as a whole. Relational reasoning,\nthen, involves manipulating structured representations of entities and relations , using rules\nfor how they can be composed. We use these terms to capture notions from cognitive science,\ntheoretical computer science, and AI, as follows:\n\u000eAnentity is an element with attributes, such as a physical object with a size and mass.\n\u000eArelation is a property between entities. Relations between two objects might include\nsame size as ,heavier than , and distance from . Relations can have attributes as\nwell. The relation more than Xtimes heavier than takes an attribute, X, which\ndetermines the relative weight threshold for the relation to be true vs.false . Relations\ncan also be sensitive to the global context. For a stone and a feather, the relation falls\nwith greater acceleration than depends on whether the context is in air vs.in a\nvacuum . Here we focus on pairwise relations between entities.\n\u000eAruleis a function (like a non-binary logical predicate) that maps entities and relations\nto other entities and relations, such as a scale comparison like is entity X large? and\nis entity X heavier than entity Y? . Here we consider rules which take one or two\narguments (unary and binary), and return a unary property value."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3782-6db4-11ee-af5c-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-12", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "is entity X heavier than entity Y? . Here we consider rules which take one or two\narguments (unary and binary), and return a unary property value.\nAs an illustrative example of relational reasoning in machine learning, graphical models (Pearl,\n1988; Koller and Friedman, 2009) can represent complex joint distributions by making explicit\nrandom conditional independences among random variables. Such models have been very\nsuccessful because they capture the sparse structure which underlies many real-world generative\nprocesses and because they support e\u000ecient algorithms for learning and reasoning. For example,\nhidden Markov models constrain latent states to be conditionally independent of others given\nthe state at the previous time step, and observations to be conditionally independent given the\nlatent state at the current time step, which are well-matched to the relational structure of many\nreal-world causal processes. Explicitly expressing the sparse dependencies among variables\nprovides for various e\u000ecient inference and reasoning algorithms, such as message-passing, which\napply a common information propagation procedure across localities within a graphical model,\nresulting in a composable, and partially parallelizable, reasoning procedure which can be applied\nto graphical models of di\u000berent sizes and shape.\nIn the remainder of the paper, we examine various deep learning methods through the lens of"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3783-6db4-11ee-8f92-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-12", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 1180, "chroma:document": "resulting in a composable, and partially parallelizable, reasoning procedure which can be applied\nto graphical models of di\u000berent sizes and shape.\nIn the remainder of the paper, we examine various deep learning methods through the lens of\ntheir relational inductive biases, showing that existing methods often carry relational assumptions"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3784-6db4-11ee-82cc-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-13", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "In the remainder of the paper, we examine various deep learning methods through the lens of\ntheir relational inductive biases, showing that existing methods often carry relational assumptions\nwhich are not always explicit or immediately evident. We then present a general framework for\nentity- and relation-based reasoning|which we term graph networks |for unifying and extending\nexisting methods which operate on graphs, and describe key design principles for building powerful\narchitectures using graph networks as building blocks. We have also released an open-source library\nfor building graph networks, which can be found here: github.com/deepmind/graph nets .\n2 Relational inductive biases\nMany approaches in machine learning and AI which have a capacity for relational reasoning\n4\nBox 2: Inductive biases\nLearning is the process of apprehending useful knowledge by observing and interacting with the\nworld. It involves searching a space of solutions for one expected to provide a better explanation\nof the data or to achieve higher rewards. But in many cases, there are multiple solutions which\nare equally good (Goodman, 1955). An inductive bias allows a learning algorithm to prioritize\none solution (or interpretation) over another, independent of the observed data (Mitchell,\n1980). In a Bayesian model, inductive biases are typically expressed through the choice and\nparameterization of the prior distribution (Gri\u000eths et al., 2010). In other contexts, an inductive"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3785-6db4-11ee-9f6a-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-14", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "parameterization of the prior distribution (Gri\u000eths et al., 2010). In other contexts, an inductive\nbias might be a regularization term (McClelland, 1994) added to avoid over\ftting, or it might\nbe encoded in the architecture of the algorithm itself. Inductive biases often trade \rexibility\nfor improved sample complexity and can be understood in terms of the bias-variance tradeo\u000b\n(Geman et al., 1992). Ideally, inductive biases both improve the search for solutions without\nsubstantially diminishing performance, as well as help \fnd solutions which generalize in a\ndesirable way; however, mismatched inductive biases can also lead to suboptimal performance\nby introducing constraints that are too strong.\nInductive biases can express assumptions about either the data-generating process or the space\nof solutions. For example, when \ftting a 1D function to data, linear least squares follows\nthe constraint that the approximating function be a linear model, and approximation errors\nshould be minimal under a quadratic penalty. This re\rects an assumption that the datagenerating process can be explained simply, as a line process corrupted by additive Gaussian\nnoise. Similarly, L2 regularization prioritizes solutions whose parameters have small values,\nand can induce unique solutions and global structure to otherwise ill-posed problems. This can"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3786-6db4-11ee-9f33-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-15", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "noise. Similarly, L2 regularization prioritizes solutions whose parameters have small values,\nand can induce unique solutions and global structure to otherwise ill-posed problems. This can\nbe interpreted as an assumption about the learning process: that searching for good solutions\nis easier when there is less ambiguity among solutions. Note, these assumptions need not be\nexplicit|they re\rect interpretations of how a model or algorithm interfaces with the world.\n(Box 1) use a relational inductive bias . While not a precise, formal de\fnition, we use this term to\nrefer generally to inductive biases (Box 2) which impose constraints on relationships and interactions\namong entities in a learning process.\nCreative new machine learning architectures have rapidly proliferated in recent years, with\n(perhaps not surprisingly given the thesis of this paper) practitioners often following a design pattern\nof composing elementary building blocks to form more complex, deep2computational hierarchies and\ngraphs3. Building blocks such as \\fully connected\" layers are stacked into \\multilayer perceptrons\"\n(MLPs), \\convolutional layers\" are stacked into \\convolutional neural networks\" (CNNs), and a\nstandard recipe for an image processing network is, generally, some variety of CNN composed with\na MLP. This composition of layers provides a particular type of relational inductive bias|that"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3787-6db4-11ee-ab60-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-16", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "standard recipe for an image processing network is, generally, some variety of CNN composed with\na MLP. This composition of layers provides a particular type of relational inductive bias|that\nof hierarchical processing|in which computations are performed in stages, typically resulting in\nincreasingly long range interactions among information in the input signal. As we explore below, the\nbuilding blocks themselves also carry various relational inductive biases (Table 1). Though beyond\nthe scope of this paper, various non-relational inductive biases are used in deep learning as well: for\nexample, activation non-linearities, weight decay, dropout (Srivastava et al., 2014), batch and layer\nnormalization (Io\u000be and Szegedy, 2015; Ba et al., 2016), data augmentation, training curricula, and\noptimization algorithms all impose constraints on the trajectory and outcome of learning.\n2This pattern of composition in depth is ubiquitous in deep learning, and is where the \\deep\" comes from.\n3Recent methods (Liu et al., 2018) even automate architecture construction via learned graph editing procedures.\n5\nComponent Entities Relations Rel. inductive bias Invariance\nFully connected Units All-to-all Weak Convolutional Grid elements Local Locality Spatial translation\nRecurrent Timesteps Sequential Sequentiality Time translation\nGraph network Nodes Edges Arbitrary Node, edge permutations"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3788-6db4-11ee-93cf-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-17", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Recurrent Timesteps Sequential Sequentiality Time translation\nGraph network Nodes Edges Arbitrary Node, edge permutations\nTable 1: Various relational inductive biases in standard deep learning components. See also Section 2.\nTo explore the relational inductive biases expressed within various deep learning methods, we\nmust identify several key ingredients, analogous to those in Box 1: what are the entities , what are\ntherelations , and what are the rules for composing entities and relations, and computing their\nimplications? In deep learning, the entities and relations are typically expressed as distributed\nrepresentations, and the rules as neural network function approximators; however, the precise forms\nof the entities, relations, and rules vary between architectures. To understand these di\u000berences\nbetween architectures, we can further ask how each supports relational reasoning by probing:\n\u000eThe arguments to the rule functions (e.g., which entities and relations are provided as input).\n\u000eHow the rule function is reused , orshared , across the computational graph (e.g., across di\u000berent\nentities and relations, across di\u000berent time or processing steps, etc.).\n\u000eHow the architecture de\fnes interactions versus isolation among representations (e.g., by\napplying rules to draw conclusions about related entities, versus processing them separately).\n2.1 Relational inductive biases in standard deep learning building blocks\n2.1.1 Fully connected layers"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3789-6db4-11ee-b218-00155d3fea2c
encoding: FLOAT32
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{"uid": "1806.01261-18", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "applying rules to draw conclusions about related entities, versus processing them separately).\n2.1 Relational inductive biases in standard deep learning building blocks\n2.1.1 Fully connected layers\nPerhaps the most common building block is a fully connected layer (Rosenblatt, 1961). Typically\nimplemented as a non-linear vector-valued function of vector inputs, each element, or \\unit\", of\nthe output vector is the dot product between a weight vector, followed by an added bias term, and\n\fnally a non-linearity such as a recti\fed linear unit (ReLU). As such, the entities are the units in\nthe network, the relations are all-to-all (all units in layer iare connected to all units in layer j),\nand the rules are speci\fed by the weights and biases. The argument to the rule is the full input\nsignal, there is no reuse, and there is no isolation of information (Figure 1a). The implicit relational\ninductive bias in a fully connected layer is thus very weak: all input units can interact to determine\nany output unit's value, independently across outputs (Table 1).\n2.1.2 Convolutional layers\nAnother common building block is a convolutional layer (Fukushima, 1980; LeCun et al., 1989). It is"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b378a-6db4-11ee-baed-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-19", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "2.1.2 Convolutional layers\nAnother common building block is a convolutional layer (Fukushima, 1980; LeCun et al., 1989). It is\nimplemented by convolving an input vector or tensor with a kernel of the same rank, adding a bias\nterm, and applying a point-wise non-linearity. The entities here are still individual units (or grid\nelements, e.g. pixels), but the relations are sparser. The di\u000berences between a fully connected layer\nand a convolutional layer impose some important relational inductive biases: locality and translation\ninvariance (Figure 1b). Locality re\rects that the arguments to the relational rule are those entities in\nclose proximity with one another in the input signal's coordinate space, isolated from distal entities.\nTranslation invariance re\rects reuse of the same rule across localities in the input. These biases\nare very e\u000bective for processing natural image data because there is high covariance within local\n6\n(a) Fully connected\nSharing in space (b) Convolutional\nSharing in time (c) Recurrent\nFigure 1: Reuse and sharing in common deep learning building blocks. (a) Fully connected layer,\nin which all weights are independent, and there is no sharing. (b) Convolutional layer, in which"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b378b-6db4-11ee-aa48-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-20", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "in which all weights are independent, and there is no sharing. (b) Convolutional layer, in which\na local kernel function is reused multiple times across the input. Shared weights are indicated by\narrows with the same color. (c) Recurrent layer, in which the same function is reused across di\u000berent\nprocessing steps.\nneighborhoods, which diminishes with distance, and because the statistics are mostly stationary\nacross an image (Table 1).\n2.1.3 Recurrent layers\nA third common building block is a recurrent layer (Elman, 1990), which is implemented over a\nsequence of steps. Here, we can view the inputs and hidden states at each processing step as the\nentities, and the Markov dependence of one step's hidden state on the previous hidden state and\nthe current input, as the relations. The rule for combining the entities takes a step's inputs and\nhidden state as arguments to update the hidden state. The rule is reused over each step (Figure 1c),\nwhich re\rects the relational inductive bias of temporal invariance (similar to a CNN's translational\ninvariance in space). For example, the outcome of some physical sequence of events should not\ndepend on the time of day. RNNs also carry a bias for locality in the sequence via their Markovian\nstructure (Table 1)."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b378c-6db4-11ee-8337-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-21", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "depend on the time of day. RNNs also carry a bias for locality in the sequence via their Markovian\nstructure (Table 1).\n2.2 Computations over sets and graphs\nWhile the standard deep learning toolkit contains methods with various forms of relational inductive\nbiases, there is no \\default\" deep learning component which operates on arbitrary relational structure.\nWe need models with explicit representations of entities and relations, and learning algorithms which\n\fnd rules for computing their interactions, as well as ways of grounding them in data. Importantly,\nentities in the world (such as objects and agents) do not have a natural order; rather, orderings\ncan be de\fned by the properties of their relations. For example, the relations between the sizes of\na set of objects can potentially be used to order them, as can their masses, ages, toxicities, and\nprices. Invariance to ordering|except in the face of relations|is a property that should ideally be\nre\rected by a deep learning component for relational reasoning.\nSets are a natural representation for systems which are described by entities whose order is\nunde\fned or irrelevant; in particular, their relational inductive bias does not come from the presence\nof something, but rather from the absence . For illustration, consider the task of predicting the center\n7\nH H\nO\nThe brown \ndog jumped. The"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b378d-6db4-11ee-9ce4-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-22", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "of something, but rather from the absence . For illustration, consider the task of predicting the center\n7\nH H\nO\nThe brown \ndog jumped. The \nbrown dog jumped (a) (b) \n(c) (d) \n(e) (f) \nMolecule Mass-Spring System \nn-body System Rigid Body System \nSentence and Parse Tree Image and Fully-Connected Scene Graph Figure 2: Di\u000berent graph representations. (a) A molecule, in which each atom is represented as a\nnode and edges correspond to bonds (e.g. Duvenaud et al., 2015). (b) A mass-spring system, in\nwhich the rope is de\fned by a sequence of masses which are represented as nodes in the graph (e.g.\nBattaglia et al., 2016; Chang et al., 2017). (c) A n-body system, in which the bodies are nodes and\nthe underlying graph is fully connected (e.g. Battaglia et al., 2016; Chang et al., 2017). (d) A rigid\nbody system, in which the balls and walls are nodes, and the underlying graph de\fnes interactions\nbetween the balls and between the balls and the walls (e.g. Battaglia et al., 2016; Chang et al., 2017)."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b378e-6db4-11ee-b259-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-23", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "between the balls and between the balls and the walls (e.g. Battaglia et al., 2016; Chang et al., 2017).\n(e) A sentence, in which the words correspond to leaves in a tree, and the other nodes and edges\ncould be provided by a parser (e.g. Socher et al., 2013). Alternately, a fully connected graph could\nbe used (e.g. Vaswani et al., 2017). (f) An image, which can be decomposed into image patches\ncorresponding to nodes in a fully connected graph (e.g. Santoro et al., 2017; Wang et al., 2018c).\nof mass of a solar system comprised of nplanets, whose attributes (e.g., mass, position, velocity,\netc.) are denoted by fx1;x2;:::;xng. For such a computation, the order in which we consider the\nplanets does not matter because the state can be described solely in terms of aggregated, averaged\nquantities. However, if we were to use a MLP for this task, having learned the prediction for a\nparticular input ( x1;x2;:::;xn) would not necessarily transfer to making a prediction for the same"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b378f-6db4-11ee-8cd1-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-24", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "particular input ( x1;x2;:::;xn) would not necessarily transfer to making a prediction for the same\ninputs under a di\u000berent ordering ( xn;x1;:::;x2). Since there are n! such possible permutations, in\nthe worst case, the MLP could consider each ordering as fundamentally di\u000berent, and thus require\nan exponential number of input/output training examples to learn an approximating function.\nA natural way to handle such combinatorial explosion is to only allow the prediction to depend\non symmetric functions of the inputs' attributes. This might mean computing shared per-object\n8\nfeaturesff(x1);:::;f (xn)gwhich are then aggregated in a symmetric way (for example, by taking\ntheir mean). Such an approach is the essence of the Deep Sets and related models (Zaheer et al.,\n2017; Edwards and Storkey, 2016; Pevn\u0012 y and Somol, 2017), which we explore further in Section 4.2.3.\nOf course, permutation invariance is not the only important form of underlying structure in\nmany problems. For example, each object in a set may be a\u000bected by pairwise interactions with\nthe other objects in the set (Hartford et al., 2018). In our planets scenario, consider now the"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3790-6db4-11ee-b7ac-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-25", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "the other objects in the set (Hartford et al., 2018). In our planets scenario, consider now the\ntask of predicting each individual planet's position after a time interval, \u0001 t. In this case, using\naggregated, averaged information is not enough because the movement of each planet depends on\nthe forces the other planets are exerting on it. Instead, we could compute the state of each object\nasx0\ni=f(xi;P\njg(xi;xj)), wheregcould compute the force induced by the j-th planet on the\ni-th planet, and fcould compute the future state of the i-th planet which results from the forces\nand dynamics. The fact that we use the same geverywhere is again a consequence of the global\npermutation invariance of the system; however, it also supports a di\u000berent relational structure\nbecausegnow takes two arguments rather than one.4\nThe above solar system examples illustrate two relational structures: one in which there are\nno relations, and one which consists of all pairwise relations. Many real-world systems (such as\nin Figure 2) have a relational structure somewhere in between these two extremes, however, with\nsome pairs of entities possessing a relation and others lacking one. In our solar system example, if\nthe system instead consists of the planets and their moons, one may be tempted to approximate"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3791-6db4-11ee-9ea1-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-26", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "some pairs of entities possessing a relation and others lacking one. In our solar system example, if\nthe system instead consists of the planets and their moons, one may be tempted to approximate\nit by neglecting the interactions between moons of di\u000berent planets. In practice, this means\ncomputing interactions only between some pairs of objects, i.e. x0\ni=f(xi;P\nj2\u000e(i)g(xi;xj)), where\n\u000e(i)\u0012f1;:::;ngis a neighborhood around node i. This corresponds to a graph, in that the i-th\nobject only interacts with a subset of the other objects, described by its neighborhood. Note, the\nupdated states still do not depend in the order in which we describe the neighborhood.5\nGraphs, generally, are a representation which supports arbitrary (pairwise) relational structure, and computations over graphs a\u000bord a strong relational inductive bias beyond that which\nconvolutional and recurrent layers can provide.\n3 Graph networks\nNeural networks that operate on graphs, and structure their computations accordingly, have been\ndeveloped and explored extensively for more than a decade under the umbrella of \\graph neural\nnetworks\" (Gori et al., 2005; Scarselli et al., 2005, 2009a; Li et al., 2016), but have grown rapidly"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3792-6db4-11ee-b532-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-27", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "networks\" (Gori et al., 2005; Scarselli et al., 2005, 2009a; Li et al., 2016), but have grown rapidly\nin scope and popularity in recent years. We survey the literature on these methods in the next\nsub-section (3.1). Then in the remaining sub-sections, we present our graph networks framework,\nwhich generalizes and extends several lines of work in this area.\n3.1 Background\nModels in the graph neural network family (Gori et al., 2005; Scarselli et al., 2005, 2009a; Li et al.,\n2016) have been explored in a diverse range of problem domains, across supervised, semi-supervised,\nunsupervised, and reinforcement learning settings. They have been e\u000bective at tasks thought to\nhave rich relational structure, such as visual scene understanding tasks (Raposo et al., 2017; Santoro\n4We could extend this same analysis to increasingly entangled structures that depend on relations among triplets\n(i.e.,g(xi;xj;xk)), quartets, and so on. We note that if we restrict these functions to only operate on subsets of xi\nwhich are spatially close, then we end back up with something resembling CNNs. In the most entangled sense, where"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3793-6db4-11ee-9414-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-28", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "which are spatially close, then we end back up with something resembling CNNs. In the most entangled sense, where\nthere is a single relation function g(x1; : : : ;xn), we end back up with a construction similar to a fully connected layer.\n5The invariance which this model enforces is the invariance under isomorphism of the graph.\n9\net al., 2017) and few-shot learning (Garcia and Bruna, 2018). They have also been used to learn\nthe dynamics of physical systems (Battaglia et al., 2016; Chang et al., 2017; Watters et al., 2017;\nvan Steenkiste et al., 2018; Sanchez-Gonzalez et al., 2018) and multi-agent systems (Sukhbaatar\net al., 2016; Hoshen, 2017; Kipf et al., 2018), to reason about knowledge graphs (Bordes et al., 2013;\nO~ noro-Rubio et al., 2017; Hamaguchi et al., 2017), to predict the chemical properties of molecules\n(Duvenaud et al., 2015; Gilmer et al., 2017), to predict tra\u000ec on roads (Li et al., 2017; Cui et al.,\n2018), to classify and segment images and videos (Wang et al., 2018c; Hu et al., 2017) and 3D"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3794-6db4-11ee-bae2-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-29", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "2018), to classify and segment images and videos (Wang et al., 2018c; Hu et al., 2017) and 3D\nmeshes and point clouds (Wang et al., 2018d), to classify regions in images (Chen et al., 2018a), to\nperform semi-supervised text classi\fcation (Kipf and Welling, 2017), and in machine translation\n(Vaswani et al., 2017; Shaw et al., 2018; Gulcehre et al., 2018). They have been used within both\nmodel-free (Wang et al., 2018b) and model-based (Hamrick et al., 2017; Pascanu et al., 2017;\nSanchez-Gonzalez et al., 2018) continuous control, for model-free reinforcement learning (Hamrick\net al., 2018; Zambaldi et al., 2018), and for more classical approaches to planning (Toyer et al.,\n2017).\nMany traditional computer science problems, which involve reasoning about discrete entities and\nstructure, have also been explored with graph neural networks, such as combinatorial optimization\n(Bello et al., 2016; Nowak et al., 2017; Dai et al., 2017), boolean satis\fability (Selsam et al., 2018),\nprogram representation and veri\fcation (Allamanis et al., 2018; Li et al., 2016), modeling cellular"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3795-6db4-11ee-bcc0-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-30", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "program representation and veri\fcation (Allamanis et al., 2018; Li et al., 2016), modeling cellular\nautomata and Turing machines (Johnson, 2017), and performing inference in graphical models\n(Yoon et al., 2018). Recent work has also focused on building generative models of graphs (Li et al.,\n2018; De Cao and Kipf, 2018; You et al., 2018; Bojchevski et al., 2018), and unsupervised learning of\ngraph embeddings (Perozzi et al., 2014; Tang et al., 2015; Grover and Leskovec, 2016; Garc\u0013 \u0010a-Dur\u0013 an\nand Niepert, 2017).\nThe works cited above are by no means an exhaustive list, but provide a representative crosssection of the breadth of domains for which graph neural networks have proven useful. We point\ninterested readers to a number of existing reviews which examine the body of work on graph neural\nnetworks in more depth. In particular, Scarselli et al. (2009a) provides an authoritative overview of\nearly graph neural network approaches. Bronstein et al. (2017) provides an excellent survey of deep\nlearning on non-Euclidean data, and explores graph neural nets, graph convolution networks, and\nrelated spectral approaches. Recently, Gilmer et al. (2017) introduced the message-passing neural"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3796-6db4-11ee-a434-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-31", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "related spectral approaches. Recently, Gilmer et al. (2017) introduced the message-passing neural\nnetwork (MPNN), which uni\fed various graph neural network and graph convolutional network\napproaches (Monti et al., 2017; Bruna et al., 2014; Hena\u000b et al., 2015; De\u000berrard et al., 2016;\nNiepert et al., 2016; Kipf and Welling, 2017; Bronstein et al., 2017) by analogy to message-passing\nin graphical models. In a similar vein, Wang et al. (2018c) introduced the non-local neural network\n(NLNN), which uni\fed various \\self-attention\"-style methods (Vaswani et al., 2017; Hoshen, 2017;\nVeli\u0014 ckovi\u0013 c et al., 2018) by analogy to methods from computer vision and graphical models for\ncapturing long range dependencies in signals.\n3.2 Graph network (GN) block\nWe now present our graph networks (GN) framework, which de\fnes a class of functions for\nrelational reasoning over graph-structured representations. Our GN framework generalizes and\nextends various graph neural network, MPNN, and NLNN approaches (Scarselli et al., 2009a; Gilmer\net al., 2017; Wang et al., 2018c), and supports constructing complex architectures from simple"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3797-6db4-11ee-a951-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-32", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "et al., 2017; Wang et al., 2018c), and supports constructing complex architectures from simple\nbuilding blocks. Note, we avoided using the term \\neural\" in the \\graph network\" label to re\rect\nthat they can be implemented with functions other than neural networks, though here our focus is\non neural network implementations.\nThe main unit of computation in the GN framework is the GN block , a \\graph-to-graph\" module\n10\nBox 3: Our de\fnition of \\graph\"\nAttributesviek"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3798-6db4-11ee-97b5-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-33", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "<latexit"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3799-6db4-11ee-ac1a-00155d3fea2c
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{"uid": "1806.01261-42", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Here we use \\graph\" to mean a directed, attributed multi-graph with a global attribute. In our\nterminology, a node is denoted as vi, an edge as ek, and the global attributes as u. We also use\nskandrkto indicate the indices of the sender and receiver nodes (see below), respectively, for\nedgek. To be more precise, we de\fne these terms as:\nDirected : one-way edges, from a \\sender\" node to a \\receiver\" node.\nAttribute : properties that can be encoded as a vector, set, or even another graph.\nAttributed : edges and vertices have attributes associated with them.\nGlobal attribute : a graph-level attribute.\nMulti-graph : there can be more than one edge between vertices, including self-edges.\nFigure 2 shows a variety of di\u000berent types of graphs corresponding to real data that we may be\ninterested in modeling, including physical systems, molecules, images, and text.\nwhich takes a graph as input, performs computations over the structure, and returns a graph as\noutput. As described in Box 3, entities are represented by the graph's nodes , relations by the edges ,\nand system-level properties by global attributes. The GN framework's block organization emphasizes\ncustomizability and synthesizing new architectures which express desired relational inductive biases."}


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{"uid": "1806.01261-43", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "and system-level properties by global attributes. The GN framework's block organization emphasizes\ncustomizability and synthesizing new architectures which express desired relational inductive biases.\nThe key design principles are: Flexible representations (see Section 4.1); Con\fgurable within-block\nstructure (see Section 4.2); and Composable multi-block architectures (see Section 4.3).\nWe introduce a motivating example to help make the GN formalism more concrete. Consider\npredicting the movements a set of rubber balls in an arbitrary gravitational \feld, which, instead of\nbouncing against one another, each have one or more springs which connect them to some (or all) of\nthe others. We will refer to this running example throughout the de\fnitions below, to motivate the\ngraph representation and the computations operating over it. Figure 2 depicts some other common\nscenarios that can be represented by graphs and reasoned over using graph networks.\n3.2.1 De\fnition of \\graph\"\nWithin our GN framework, a graph is de\fned as a 3-tuple G=(u;V;E )(see Box 3 for details of\ngraph representations). The uis a global attribute; for example, umight represent the gravitational"}


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{"uid": "1806.01261-44", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "graph representations). The uis a global attribute; for example, umight represent the gravitational\n\feld. TheV=fvigi=1:Nvis the set of nodes (of cardinality Nv), where each viis a node's attribute.\nFor example, Vmight represent each ball, with attributes for position, velocity, and mass. The\nE=f(ek;rk;sk)gk=1:Neis the set of edges (of cardinality Ne), where each ekis the edge's attribute,\nrkis the index of the receiver node, and skis the index of the sender node. For example, Emight\nrepresent the presence of springs between di\u000berent balls, and their corresponding spring constants.\n11\nAlgorithm 1 Steps of computation in a full GN block.\nfunction GraphNetwork (E,V,u)\nfork2f1:::Negdo\ne0\nk \u001ee(ek;vrk;vsk;u) .1. Compute updated edge attributes\nend for\nfori2f1:::Nngdo\nletE0\ni=f(e0\nk;rk;sk)grk=i;k=1:Ne\n\u0016 e0\ni \u001ae!v(E0\ni) .2. Aggregate edge attributes per node\nv0"}


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{"uid": "1806.01261-45", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "\u0016 e0\ni \u001ae!v(E0\ni) .2. Aggregate edge attributes per node\nv0\ni \u001ev(\u0016 e0\ni;vi;u) .3. Compute updated node attributes\nend for\nletV0=fv0gi=1:Nv\nletE0=f(e0\nk;rk;sk)gk=1:Ne\n\u0016 e0 \u001ae!u(E0) .4. Aggregate edge attributes globally\n\u0016 v0 \u001av!u(V0) .5. Aggregate node attributes globally\nu0 \u001eu(\u0016 e0;\u0016 v0;u) .6. Compute updated global attribute\nreturn (E0;V0;u0)\nend function\n3.2.2 Internal structure of a GN block\nA GN block contains three \\update\" functions, \u001e, and three \\aggregation\" functions, \u001a,\ne0\nk=\u001ee(ek;vrk;vsk;u)\nv0\ni=\u001ev\u0000\n\u0016 e0\ni;vi;u\u0001\nu0=\u001eu\u0000\n\u0016 e0;\u0016 v0;u\u0001\u0016 e0\ni=\u001ae!v\u0000\nE0\ni\u0001\n\u0016 e0=\u001ae!u\u0000\nE0\u0001"}


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{"uid": "1806.01261-46", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "i=\u001ae!v\u0000\nE0\ni\u0001\n\u0016 e0=\u001ae!u\u0000\nE0\u0001\n\u0016 v0=\u001av!u\u0000\nV0\u0001(1)\nwhereE0\ni=f(e0\nk;rk;sk)grk=i;k=1:Ne,V0=fv0\nigi=1:Nv, andE0=S\niE0\ni=f(e0\nk;rk;sk)gk=1:Ne.\nThe\u001eeis mapped across all edges to compute per-edge updates, the \u001evis mapped across all\nnodes to compute per-node updates, and the \u001euis applied once as the global update. The \u001a\nfunctions each take a set as input, and reduce it to a single element which represents the aggregated\ninformation. Crucially, the \u001afunctions must be invariant to permutations of their inputs, and should\ntake variable numbers of arguments (e.g., elementwise summation, mean, maximum, etc.).\n3.2.3 Computational steps within a GN block\nWhen a graph, G, is provided as input to a GN block, the computations proceed from the edge, to\nthe node, to the global level. Figure 3 shows a depiction of which graph elements are involved in"}


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{"uid": "1806.01261-47", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "the node, to the global level. Figure 3 shows a depiction of which graph elements are involved in\neach of these computations, and Figure 4a shows a full GN block, with its update and aggregation\nfunctions. Algorithm 1 shows the following steps of computation:\n1.\u001eeis applied per edge, with arguments ( ek;vrk;vsk;u), and returns e0\nk. In our springs example,\nthis might correspond to the forces or potential energies between two connected balls. The\nset of resulting per-edge outputs for each node, i, is,E0\ni=f(e0\nk;rk;sk)grk=i;k=1:Ne. And\nE0=S\niE0\ni=f(e0\nk;rk;sk)gk=1:Neis the set of all per-edge outputs.\n2.\u001ae!vis applied to E0\ni, and aggregates the edge updates for edges that project to vertex i, into\n\u0016 e0\ni, which will be used in the next step's node update. In our running example, this might\ncorrespond to summing all the forces or potential energies acting on the ithball.\n12\nvi"}


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{"uid": "1806.01261-172", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Figure 3: Updates in a GN block. Blue indicates the element that is being updated, and black\nindicates other elements which are involved in the update (note that the pre-update value of the\nblue element is also used in the update). See Equation 1 for details on the notation.\n3.\u001evis applied to each node i, to compute an updated node attribute, v0\ni. In our running\nexample,\u001evmay compute something analogous to the updated position, velocity, and kinetic\nenergy of each ball. The set of resulting per-node outputs is, V0=fv0\nigi=1:Nv.\n4.\u001ae!uis applied to E0, and aggregates all edge updates, into \u0016 e0, which will then be used in the\nnext step's global update. In our running example, \u001ae!umay compute the summed forces\n(which should be zero, in this case, due to Newton's third law) and the springs' potential\nenergies.\n5.\u001av!uis applied to V0, and aggregates all node updates, into \u0016 v0, which will then be used in\nthe next step's global update. In our running example, \u001av!umight compute the total kinetic\nenergy of the system."}


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topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-173", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "the next step's global update. In our running example, \u001av!umight compute the total kinetic\nenergy of the system.\n6.\u001euis applied once per graph, and computes an update for the global attribute, u0. In our\nrunning example, \u001eumight compute something analogous to the net forces and total energy\nof the physical system.\nNote, though we assume this sequence of steps here, the order is not strictly enforced: it is possible\nto reverse the update functions to proceed from global, to per-node, to per-edge updates, for example.\nKearnes et al. (2016) computes edge updates from nodes in a similar manner.\n3.2.4 Relational inductive biases in graph networks\nOur GN framework imposes several strong relational inductive biases when used as components in\na learning process. First, graphs can express arbitrary relationships among entities, which means\nthe GN's input determines how representations interact and are isolated, rather than those choices\nbeing determined by the \fxed architecture. For example, the assumption that two entities have a\nrelationship|and thus should interact|is expressed by an edge between the entities' corresponding\nnodes. Similarly, the absence of an edge expresses the assumption that the nodes have no relationship\nand should not in\ruence each other directly."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-174", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "nodes. Similarly, the absence of an edge expresses the assumption that the nodes have no relationship\nand should not in\ruence each other directly.\nSecond, graphs represent entities and their relations as sets, which are invariant to permutations.\nThis means GNs are invariant to the order of these elements6, which is often desirable. For example,\nthe objects in a scene do not have a natural ordering (see Sec. 2.2).\nThird, a GN's per-edge and per-node functions are reused across all edges and nodes, respectively.\nThis means GNs automatically support a form of combinatorial generalization (see Section 5.1):\nbecause graphs are composed of edges, nodes, and global features, a single GN can operate on\ngraphs of di\u000berent sizes (numbers of edges and nodes) and shapes (edge connectivity).\n6Note, an ordering can be imposed by encoding the indices in the node or edge attributes, or via the edges\nthemselves (e.g. by encoding a chain or partial ordering).\n13\n4 Design principles for graph network architectures\nThe GN framework can be used to implement a wide variety of architectures, in accordance with\nthe design principles listed above in Section 3.2, which also correspond to the sub-sections (4.1,"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-175", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "the design principles listed above in Section 3.2, which also correspond to the sub-sections (4.1,\n4.2, and 4.3) below. In general, the framework is agnostic to speci\fc attribute representations and\nfunctional forms. Here, however, we focus mainly on deep learning architectures, which allow GNs\nto act as learnable graph-to-graph function approximators.\n4.1 Flexible representations\nGraph networks support highly \rexible graph representations in two ways: \frst, in terms of the\nrepresentation of the attributes; and second, in terms of the structure of the graph itself.\n4.1.1 Attributes\nThe global, node, and edge attributes of a GN block can use arbitrary representational formats. In\ndeep learning implementations, real-valued vectors and tensors are most common. However, other\ndata structures such as sequences, sets, or even graphs could also be used.\nThe requirements of the problem will often determine what representations should be used for\nthe attributes. For example, when the input data is an image, the attributes might be represented\nas tensors of image patches; however, when the input data is a text document, the attributes might\nbe sequences of words corresponding to sentences.\nFor each GN block within a broader architecture, the edge and node outputs typically correspond"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-176", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "be sequences of words corresponding to sentences.\nFor each GN block within a broader architecture, the edge and node outputs typically correspond\nto lists of vectors or tensors, one per edge or node, and the global outputs correspond to a single\nvector or tensor. This allows a GN's output to be passed to other deep learning building blocks\nsuch as MLPs, CNNs, and RNNs.\nThe output of a GN block can also be tailored to the demands of the task. In particular,\n\u000eAnedge-focused GN uses the edges as output, for example to make decisions about interactions\namong entities (Kipf et al., 2018; Hamrick et al., 2018).\n\u000eAnode-focused GN uses the nodes as output, for example to reason about physical systems\n(Battaglia et al., 2016; Chang et al., 2017; Wang et al., 2018b; Sanchez-Gonzalez et al., 2018).\n\u000eAgraph-focused GN uses the globals as output, for example to predict the potential energy of\na physical system (Battaglia et al., 2016), the properties of a molecule (Gilmer et al., 2017),\nor answers to questions about a visual scene (Santoro et al., 2017).\nThe nodes, edges, and global outputs can also be mixed-and-matched depending on the task. For"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-177", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "or answers to questions about a visual scene (Santoro et al., 2017).\nThe nodes, edges, and global outputs can also be mixed-and-matched depending on the task. For\nexample, Hamrick et al. (2018) used both the output edge and global attributes to compute a policy\nover actions.\n4.1.2 Graph structure\nWhen de\fning how the input data will be represented as a graph, there are generally two scenarios:\n\frst, the input explicitly speci\fes the relational structure; and second, the relational structure must\nbe inferred or assumed. These are not hard distinctions, but extremes along a continuum.\nExamples of data with more explicitly speci\fed entities and relations include knowledge graphs,\nsocial networks, parse trees, optimization problems, chemical graphs, road networks, and physical\nsystems with known interactions. Figures 2a-d illustrate how such data can be expressed as graphs.\nExamples of data where the relational structure is not made explicit, and must be inferred or\nassumed, include visual scenes, text corpora, programming language source code, and multi-agent\n14\nsystems. In these types of settings, the data may be formatted as a set of entities without relations,\nor even just a vector or tensor (e.g., an image). If the entities are not speci\fed explicitly, they might"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1b3829-6db4-11ee-8a38-00155d3fea2c
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{"uid": "1806.01261-178", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "or even just a vector or tensor (e.g., an image). If the entities are not speci\fed explicitly, they might\nbe assumed, for instance, by treating each word in a sentence (Vaswani et al., 2017) or each local\nfeature vector in a CNN's output feature map, as a node (Watters et al., 2017; Santoro et al., 2017;\nWang et al., 2018c) (Figures 2e-f). Or, it might be possible to use a separate learned mechanism to\ninfer entities from an unstructured signal (Luong et al., 2015; Mnih et al., 2014; Eslami et al., 2016;\nvan Steenkiste et al., 2018). If relations are not available, the simplest approach is to instantiate all\npossible directed edges between entities (Figure 2f). This can be prohibitive for large numbers of\nentities, however, because the number of possible edges grows quadratically with the number of\nnodes. Thus developing more sophisticated ways of inferring sparse structure from unstructured\ndata (Kipf et al., 2018) is an important future direction.\n4.2 Con\fgurable within-block structure\nThe structure and functions within a GN block can be con\fgured in di\u000berent ways, which o\u000bers"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-179", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "4.2 Con\fgurable within-block structure\nThe structure and functions within a GN block can be con\fgured in di\u000berent ways, which o\u000bers\n\rexibility in what information is made available as inputs to its functions, as well as how output edge,\nnode, and global updates are produced. In particular, each \u001ein Equation 1 must be implemented\nwith some function, f, wheref's argument signature determines what information it requires as\ninput; in Figure 4, the incoming arrows to each \u001edepict whether u,V, andEare taken as inputs.\nHamrick et al. (2018) and Sanchez-Gonzalez et al. (2018) used the full GN block shown in Figure 4a.\nTheir\u001eimplementations used neural networks (denoted NNe,NNv, and NNubelow, to indicate that\nthey are di\u000berent functions with di\u000berent parameters). Their \u001aimplementations used elementwise\nsummation, but averages and max/min could also be used,\n\u001ee(ek;vrk;vsk;u):=fe(ek;vrk;vsk;u) = NNe([ek;vrk;vsk;u]) (2)\n\u001ev\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi;u\u0001"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-180", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "v\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi;u\u0001\n= NNv\u0000\n[\u0016 e0\ni;vi;u]\u0001\n\u001eu\u0000\n\u0016 e0;\u0016 v0;u\u0001:=fu\u0000\n\u0016 e0;\u0016 v0;u\u0001\n= NNu\u0000\n[\u0016 e0;\u0016 v0;u]\u0001\n\u001ae!v\u0000\nE0\ni\u0001:= =X\nfk:rk=ige0\nk\n\u001av!u\u0000\nV0\u0001:= =X\niv0\ni\n\u001ae!u\u0000\nE0\u0001:= =X\nke0\nk\nwhere [ x;y;z] indicates vector/tensor concatenation. For vector attributes, a MLP is often used for\n\u001e, while for tensors such as image feature maps, CNNs may be more suitable.\nThe\u001efunctions can also use RNNs, which requires an additional hidden state as input and\noutput. Figure 4b shows a very simple version of a GN block with RNNs as \u001efunctions: there is no\nmessage-passing in this formulation, and this type of block might be used for recurrent smoothing of"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-181", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "message-passing in this formulation, and this type of block might be used for recurrent smoothing of\nsome dynamic graph states. Of course, RNNs as \u001efunctions could also be used in a full GN block\n(Figure 4a).\nA variety of other architectures can be expressed in the GN framework, often as di\u000berent\nfunction choices and within-block con\fgurations. The remaining sub-sections explore how a GN's\nwithin-block structure can be con\fgured in di\u000berent ways, with examples of published work which\nuses such con\fgurations. See the Appendix for details.\n15\n(a) Full GN block\nu0,u0hid"}


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