SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels
Open accessAbstract
We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence. Our source code is available on GitHub1.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Adam: A Method for Stochastic Optimization
Kingma, D. P., & Ba, J. (2014) · arXiv · doi:10.48550/arxiv.1412.6980 · Cited by 98,946 · see citing works
Gradient-based learning applied to document recognition
Lecun, Y., Bottou, L., Bengio, Y., & Haffner, P. (1998) · Proceedings of the IEEE · doi:10.1109/5.726791 · Cited by 58,805 · see citing works
Semi-supervised classification with graph convolutional networks
Kipf, T. N., & Welling, M. (2016) · arXiv · doi:10.48550/arxiv.1609.02907 · Cited by 24,853 · see citing works
Advances In Deep Learning On Graphs (Gsp'18 Workshop)Preprint
Defferrard, M., Bresson, X., & Vandergheynst, P. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1606.09375 · Cited by 6,912 · see citing works
Chung, F. (1996) · Regional conference series in mathematics · doi:10.1090/cbms/092 · Cited by 5,918 · see citing works
Neural Message Passing for Quantum ChemistryPreprint
Gilmer, J., Schoenholz, S. S., Riley, P. F., Vinyals, O., & Dahl, G. E. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1704.01212 · Cited by 5,414 · see citing works
Advances In Deep Learning On Graphs (Gsp'18 Workshop)
Defferrard, M. (2016) · Figshare · doi:10.5281/zenodo.1286817 · Cited by 4,977 · see citing works
Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2235192 · Cited by 4,421 · see citing works
Spectral Networks and Locally Connected Networks on Graphs
Bruna, J., Zaremba, W., Szlam, A., & LeCun, Y. (2013) · arXiv · doi:10.48550/arxiv.1312.6203 · Cited by 3,983 · see citing works
Geometric Deep Learning: Going beyond Euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2693418 · Cited by 3,661 · see citing works
Collective Classification in Network Data
Sen, P., Namata, G., Bilgic, M., Getoor, L., Gallagher, B., & Eliassi‐Rad, T. (2008) · AI Magazine · doi:10.1609/aimag.v29i3.2157 · Cited by 3,293 · see citing works
Piegl, L. A., & Tiller, W. (1997) · Monographs in visual communication · doi:10.1007/978-3-642-59223-2 · Cited by 2,869 · see citing works
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs
Monti, F., Boscaini, D., Masci, J., Rodola, E., Svoboda, J., & Bronstein, M. M. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.576 · Cited by 1,820 · see citing works
Unique Signatures of Histograms for Local Surface Description
Tombari, F., Salti, S., & Di Stefano, L. (2010) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-15558-1_26 · Cited by 1,480 · see citing works
Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs
Simonovsky, M., & Nikos Komodakis, A. (2017) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2017.11 · Cited by 1,346 · see citing works
Deep Convolutional Networks on Graph-Structured Data
Henaff, M., Bruna, J., & LeCun, Y. (2015) · arXiv · doi:10.48550/arxiv.1506.05163 · Cited by 1,255 · see citing works
GradientBased Learning Applied to Document Recognition
Haykin, S., & Kosko, B. (2009) · Institute of Electrical and Electronics Engineers eBooks · doi:10.1109/9780470544976.ch9 · Cited by 1,134 · see citing works
Weighted Graph Cuts without Eigenvectors A Multilevel Approach
Dhillon, I. S., Guan, Y., & Kulis, B. (2007) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2007.1115 · Cited by 1,037 · see citing works
Geodesic Convolutional Neural Networks on Riemannian Manifolds
Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P. (2015) · 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) · doi:10.1109/iccvw.2015.112 · Cited by 721 · see citing works
FAUST: Dataset and Evaluation for 3D Mesh Registration
Bogo, F., Romero, J., Loper, M., & Black, M. J. (2014) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2014.491 · Cited by 688 · see citing works
CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters
Levie, R., Monti, F., Bresson, X., & Bronstein, M. M. (2019) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2018.2879624 · Cited by 685 · see citing works
Learning shape correspondence with anisotropic convolutional neural networksPreprint
Boscaini, D., Masci, J., Rodolà, E., & Bronstein, M. (2016) · Neural Information Processing Systems · doi:10.48550/arxiv.1605.06437 · Cited by 540 · see citing works
SchNet: A continuous-filter convolutional neural network for modeling quantum interactions
Schütt, K. T., Kindermans, P.-J., Sauceda, H. E., Chmiela, S., Tkatchenko, A., & Müller, K. (2017) · Open Repository and Bibliography (University of Luxembourg) · doi:10.48550/arxiv.1706.08566 · Cited by 463 · see citing works
SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation
Yi, L., Su, H., Guo, X., & Guibas, L. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.697 · Cited by 461 · see citing works
Kim, V. G., Lipman, Y., & Funkhouser, T. A. (2011) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/1964921.1964974 · Cited by 311 · see citing works
SchNet: A continuous-filter convolutional neural network for modeling quantum interactionsPreprint
Schütt, K. T., Kindermans, P.-J., Sauceda, H. E., Chmiela, S., Tkatchenko, A., & Müller, K. (2017) · arXiv (Cornell University) · Cited by 302 · see citing works
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
Litany, O., Remez, T., Rodolà, E., Bronstein, A. M., & Bronstein, M. M. (2017) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.603 · Cited by 298 · see citing works
Kim, V. G., Lipman, Y., & Funkhouser, T. (2011) · ACM Transactions on Graphics · doi:10.1145/2010324.1964974 · Cited by 298 · see citing works
Intrinsic shape context descriptors for deformable shapes
Kokkinos, I., Bronstein, M. M., Litman, R., & Bronstein, A. M. (2012) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2012.6247671 · Cited by 162 · see citing works
Chen, T., Wang, Z., Li, L., Li, D., Li, Z., Chang, X., Bian, P., Liang, G., Wang, Q., & Xie, T. (2025) · Schloss Dagstuhl – Leibniz-Zentrum für Informatik · doi:10.4230/lipics.ecoop.2025.6
Flagged first, then by citations
2 of the 32 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
A Comprehensive Survey on Graph Neural Networks
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. S. (2021) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2020.2978386 · Cited by 11,000 · see citing works
Dynamic Graph CNN for Learning on Point Clouds
Wang, Y., Sun, Y., Liu, Z., Sarma, S. E., Bronstein, M. M., & Solomon, J. M. (2019) · ACM Transactions on Graphics · doi:10.1145/3326362 · Cited by 7,199 · see citing works
A Comprehensive Survey on Graph Neural Networks
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. (2020) · UTS ePRESS (University of Technology Sydney) · Cited by 3,174 · see citing works
Fast Graph Representation Learning with PyTorch GeometricPreprint
Fey, M., & Lenssen, J. E. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.02428 · Cited by 3,402 · see citing works
Self-citationGraph convolutional networks: a comprehensive review
Zhang, S., Tong, H., Xu, J., & Maciejewski, R. (2019) · Computational Social Networks · doi:10.1186/s40649-019-0069-y · Cited by 1,888 · see citing works
Deep Closest Point: Learning Representations for Point Cloud Registration
Wang, Y., & Solomon, J. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00362 · Cited by 1,151 · see citing works
CNN Variants for Computer Vision: History, Architecture, Application, Challenges and Future Scope
Bhatt, D., Patel, C., Talsania, H., Patel, J., Vaghela, R., Pandya, S., Modi, K., & Ghayvat, H. (2021) · Electronics · doi:10.3390/electronics10202470 · Cited by 890 · see citing works
Hierarchical Graph Representation Learning with Differentiable PoolingPreprint
Ying, R., You, J., Morris, C., Ren, X., Hamilton, W. L., & Leskovec, J. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1806.08804 · Cited by 798 · see citing works
Kriege, N. M., Johansson, F., & Morris, C. (2020) · Applied Network Science · doi:10.1007/s41109-019-0195-3 · Cited by 396 · see citing works
Learning Two-View Correspondences and Geometry Using Order-Aware Network
Zhang, J., Sun, D., Luo, Z., Yao, A., Zhou, L., Shen, T., Chen, Y., Liao, H., & Quan, L. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00594 · Cited by 387 · see citing works
Graph Convolutional Networks with EigenPooling
Ma, Y., Wang, S., Aggarwal, C. C., & Tang, J. (2019) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3292500.3330982 · Cited by 347 · see citing works
ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations
Ranjan, E., Sanyal, S., & Talukdar, P. P. (2020) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v34i04.5997 · Cited by 26 · see citing works
Spectral Clustering with Graph Neural Networks for Graph PoolingPreprint
Bianchi, F. M., Grattarola, D., & Alippi, C. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.00481 · Cited by 304 · see citing works
Distilling Knowledge From Graph Convolutional Networks
Yang, Y., Qiu, J., Song, M., Tao, D., & Wang, X. (2020) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr42600.2020.00710 · Cited by 269 · see citing works
Low-latency automotive vision with event cameras
Gehrig, D., & Scaramuzza, D. (2024) · Nature · doi:10.1038/s41586-024-07409-w · Cited by 255 · see citing works
DiffusionNet: Discretization Agnostic Learning on Surfaces
Sharp, N., Attaiki, S., Crane, K., & Ovsjanikov, M. (2022) · ACM Transactions on Graphics · doi:10.1145/3507905 · Cited by 264 · see citing works
Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds
Lei, H., Akhtar, N., & Mian, A. S. (2020) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.2983410 · Cited by 201 · see citing works
Graph-Based Object Classification for Neuromorphic Vision Sensing
Bi, Y., Chadha, A., Abbas, A., Bourtsoulatze, E., & Andreopoulos, Y. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00058 · Cited by 179 · see citing works
Understanding Attention and Generalization in Graph Neural NetworksPreprint
Knyazev, B. A., Taylor, G. W., & Amer, M. R. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.02850 · Cited by 174 · see citing works
Hierarchical Graph Convolutional Networks for Semi-supervised Node Classification
Hu, F., Zhu, Y., Wu, S., Wang, L., & Tan, T. (2019) · Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2019/630 · Cited by 171 · see citing works
Graph U-NetsPreprint
Gao, H., & Ji, S. (2019) · arXiv (Cornell University) · Cited by 206 · see citing works
AEGNN: Asynchronous Event-based Graph Neural Networks
Schaefer, S., Gehrig, D., & Scaramuzza, D. (2022) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr52688.2022.01205 · Cited by 169 · see citing works
Graph Neural Networks for Modelling Traffic Participant Interaction
Diehl, F., Brunner, T., Le, M. T., & Knoll, A. (2019) · IEEE Intelligent Vehicles Symposium · doi:10.1109/ivs.2019.8814066 · Cited by 163 · see citing works
Graph-Based Spatio-Temporal Feature Learning for Neuromorphic Vision Sensing
Bi, Y., Chadha, A., Abbas, A., Bourtsoulatze, E., & Andreopoulos, Y. (2020) · IEEE Transactions on Image Processing · doi:10.1109/tip.2020.3023597 · Cited by 160 · see citing works
Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks
Morris, C., Ritzert, M., Fey, M., Hamilton, W. L., Lenssen, J. E., Rattan, G., & Grohe, M. (2019) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v33i01.33014602 · Cited by 172 · see citing works
Self-citationSpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator
Gong, S., Chen, L., Bronstein, M. M., & Zafeiriou, S. P. (2019) · IEEE International Conference on Computer Vision Workshops · doi:10.1109/iccvw.2019.00509 · Cited by 149 · see citing works
Fast end-to-end learning on protein surfaces
Sverrisson, F., Feydy, J., Correia, B. E., & Bronstein, M. M. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.01502 · Cited by 150 · see citing works
TGNet: Geometric Graph CNN on 3-D Point Cloud Segmentation
Li, Y., Ma, L., Zhong, Z., Cao, D., & Li, J. (2019) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2019.2958517 · Cited by 141 · see citing works
Deep Graph Matching ConsensusPreprint
Fey, M., Lenssen, J. E., Morris, C., Masci, J., & Kriege, N. M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.09621 · Cited by 157 · see citing works
Self-citationSurvey on graph embeddings and their applications to machine learning problems on graphs
Makarov, I., Kiselev, D., Nikitinsky, N., & Šubelj, L. (2021) · PeerJ Computer Science · doi:10.7717/peerj-cs.357 · Cited by 127 · see citing works
A survey on deep geometry learning: From a representation perspective
Xiao, Y., Lai, Y., Zhang, F., Li, C., & Gao, L. (2020) · Computational Visual Media · doi:10.1007/s41095-020-0174-8 · Cited by 118 · see citing works
Wang, R., Yan, J., & Yang, X. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3078053 · Cited by 115 · see citing works
Understanding Pooling in Graph Neural Networks
Grattarola, D., Zambon, D., Bianchi, F. M., & Alippi, C. (2022) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2022.3190922 · Cited by 115 · see citing works
Robust Optimization as Data Augmentation for Large-scale Graphs
Kong, K., Li, G., Ding, M., Wu, Z., Zhu, C., Ghanem, B., Taylor, G., & Goldstein, T. (2022) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr52688.2022.00016 · Cited by 105 · see citing works
Leveraging Power Grid Topology in Machine Learning Assisted Optimal Power Flow
Falconer, T., & Mones, L. (2022) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2022.3187218 · Cited by 103 · see citing works
Liu, T., Li, Y., Jing, Q., Xie, Y., & Zhang, D. (2020) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2020.120684 · Cited by 98 · see citing works
Lagrangian Fluid Simulation with Continuous Convolutions
Ummenhofer, B., Prantl, L., Thuerey, N., & Koltun, V. (2020) · International Conference on Learning Representations · Cited by 97 · see citing works
Spatial Graph Convolutional Networks
Danel, T., Spurek, P., Tabor, J., Śmieja, M., Struski, Ł., Słowik, A., & Maziarka, Ł. (2020) · Communications in computer and information science · doi:10.1007/978-3-030-63823-8_76 · Cited by 97 · see citing works
Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities
Liu, C., Zhan, Y., Wu, J. X., Li, C., Du, B., Hu, W., Liu, T., & Tao, D. (2023) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2023/752 · Cited by 96 · see citing works
Three-Dimensional Structural Geological Modeling Using Graph Neural Networks
Hillier, M., Wellmann, F., Brodaric, B., de Kemp, E. A., & Schetselaar, E. (2021) · Mathematical Geosciences · doi:10.1007/s11004-021-09945-x · Cited by 92 · see citing works
Learning Dynamics via Graph Neural Networks for Human Pose Estimation and Tracking
Yang, Y., Ren, Z., Li, H., Zhou, C., Wang, X., & Hua, G. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.00798 · Cited by 91 · see citing works
MeshSDF: Differentiable Iso-Surface ExtractionPreprint
Remelli, E., Lukoianov, A., Richter, S., Guillard, B., Bagautdinov, T., Baqué, P., & Fua, P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.03997 · Cited by 90 · see citing works
Current and emerging deep-learning methods for the simulation of fluid dynamics
Lino, M., Fotiadis, S., Bharath, A. A., & Cantwell, C. D. (2023) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2023.0058 · Cited by 94 · see citing works
Deep Iterative Surface Normal Estimation
Lenssen, J. E., Osendorfer, C., & Masci, J. (2020) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr42600.2020.01126 · Cited by 86 · see citing works
Self-citationWang, C., Yang, J., Xie, L., & Yuan, J. (2019) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2019.00012 · Cited by 80 · see citing works
Quaternion Equivariant Capsule Networks for 3D Point Clouds
Zhao, Y., Birdal, T., Lenssen, J. E., Menegatti, E., Guibas, L. J., & Tombari, F. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58452-8_1 · Cited by 82 · see citing works
Self-citationMulti-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics
Lino, M., Fotiadis, S., Bharath, A. A., & Cantwell, C. D. (2022) · Physics of Fluids · doi:10.1063/5.0097679 · Cited by 80 · see citing works
A review of non-rigid transformations and learning-based 3D point cloud registration methods
Monji-Azad, S., Hesser, J., & Löw, N. (2023) · ISPRS Journal of Photogrammetry and Remote Sensing · doi:10.1016/j.isprsjprs.2022.12.023 · Cited by 81 · see citing works
A survey on Deep Learning Advances on Different 3D Data RepresentationsPreprint
Ahmed, E., Saint, A., Shabayek, A. E. R., Cherenkova, K., Das, R., Gusev, G., Aouada, D., & Ottersten, B. (2018) · arXiv (Cornell University) · doi:10.13140/rg.2.2.32083.02080 · Cited by 163 · see citing works
SPAGAN: Shortest Path Graph Attention Network
Yang, Y., Wang, X., Song, M., Yuan, J., & Tao, D. (2019) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2019/569 · Cited by 77 · see citing works
Superpixel Image Classification with Graph Attention Networks
Avelar, P., Tavares, A. R., da Silveira, T. L. T., Jung, C. R., & Lamb, L. C. (2020) · SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI) · doi:10.1109/sibgrapi51738.2020.00035 · Cited by 75 · see citing works
A Review on Deep Learning Approaches for 3D Data Representations in Retrieval and Classifications
Gezawa, A. S., Zhang, Y., Wang, Q., & Lei, Y. (2020) · IEEE Access · doi:10.1109/access.2020.2982196 · Cited by 71 · see citing works
A semi-supervised approach to architected materials design using graph neural networks
Guo, K., & Buehler, M. J. (2020) · Extreme Mechanics Letters · doi:10.1016/j.eml.2020.101029 · Cited by 71 · see citing works
Heterogeneous Deep Graph InfomaxPreprint
Ren, Y., Лю, Б., Huang, C., Dai, P., Bo, L., & Zhang, J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.08538 · Cited by 108 · see citing works
Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers
Rolínek, M., Swoboda, P., Zietlow, D., Paulus, A., Musil, V., & Martius, G. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-58604-1_25 · Cited by 18 · see citing works
Huang, J., Li, Z., Li, N., Liu, S., & Li, G. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00658 · Cited by 71 · see citing works
Smirnov, D., & Solomon, J. (2021) · ACM Transactions on Graphics · doi:10.1145/3450626.3459797 · Cited by 69 · see citing works
Mumuni, A., & Mumuni, F. (2021) · SN Computer Science · doi:10.1007/s42979-021-00735-0 · Cited by 71 · see citing works
Rethinking pooling in graph neural networksPreprint
Mesquita, D. P. P., Junior, A. H. D. S., & Samuel Kaski, A. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.11418 · Cited by 67 · see citing works
TactileGCN: A Graph Convolutional Network for Predicting Grasp Stability with Tactile Sensors
García-García, A., Zapata-Impata, B. S., Orts‐Escolano, S., Gil, P., & García‐Rodríguez, J. (2019) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2019.8851984 · Cited by 66 · see citing works
Event-Stream Representation for Human Gaits Identification Using Deep Neural Networks
Wang, Y., Zhang, X., Shen, Y., Du, B., Zhao, G., Lizhen, L. C. C., & Wen, H. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3054886 · Cited by 65 · see citing works
Graph Convolutional Networks: Algorithms, Applications and Open Challenges
Zhang, S., Tong, H., Xu, J., & Maciejewski, R. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-04648-4_7 · Cited by 66 · see citing works
Analyzing the Expressive Power of Graph Neural Networks in a Spectral Perspective
Balcılar, M., Renton, G., Héroux, P., Gaüzère, B., Adam, S., & Honeiné, P. (2021) · HAL · Cited by 62 · see citing works
B-Spline CNNs on Lie GroupsPreprint
Bekkers, E. J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.12057 · Cited by 62 · see citing works
Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs
Wandel, N., Weinmann, M., Neidlin, M., & Klein, R. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i8.20830 · Cited by 61 · see citing works
PFCNN: Convolutional Neural Networks on 3D Surfaces Using Parallel Frames
Yang, Y., Liu, S., Pan, H., Liu, Y., & Tong, X. (2020) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr42600.2020.01359 · Cited by 63 · see citing works
ExSpliNet: An interpretable and expressive spline-based neural network
Fakhoury, D., Fakhoury, E., & Speleers, H. (2022) · Neural Networks · doi:10.1016/j.neunet.2022.04.029 · Cited by 60 · see citing works
Hierarchical Representation Learning in Graph Neural Networks With Node Decimation Pooling
Bianchi, F. M., Grattarola, D., Livi, L., & Alippi, C. (2020) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2020.3044146 · Cited by 57 · see citing works
Laplacian2Mesh: Laplacian-Based Mesh Understanding
Dong, Q., Wang, Z., Li, M., Gao, J., Chen, S., Shu, Z., Xin, S., Tu, C., & Wang, W. (2023) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2023.3259044 · Cited by 57 · see citing works
Learning Hierarchical Review Graph Representations for Recommendation
Liu, Y., Yang, S., Zhang, Y., Miao, C., Nie, Z., & Zhang, J. (2021) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2021.3075052 · Cited by 56 · see citing works
Morales, X., Mill, J., Juhl, K. A., Acebes, C., Iriart, X., Legghe, B., Cochet, H., Backer, O. D., Paulsen, R. R., & Cámara, Ó. (2021) · Frontiers in Physiology · doi:10.3389/fphys.2021.694945 · Cited by 56 · see citing works
Yang, Y., Hossain, M. Z., Stone, E. A., & Rahman, S. (2023) · Pattern Recognition · doi:10.1016/j.patcog.2023.109966 · Cited by 54 · see citing works
A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
Pawar, S. A., San, O., Rasheed, A., & Vedula, P. (2020) · NORA - Norwegian Open Research Archives · Cited by 52 · see citing works
Graph-Free Knowledge Distillation for Graph Neural Networks
Deng, X., & Zhang, Z. M. (2021) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2021/320 · Cited by 52 · see citing works
FSPool: Learning Set Representations with Featurewise Sort PoolingPreprint
Zhang, Y., Hare, J. S., & Prügel‐Bennett, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.02795 · Cited by 54 · see citing works
Learning Two-View Correspondences and Geometry Using Order-Aware NetworkPreprint
Zhang, J., Sun, D., Luo, Z., Yao, A., Zhou, L., Shen, T., Chen, Y., Quan, L., & Liao, H. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1908.04964 · Cited by 51 · see citing works
A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
Pawar, S., San, O., Rasheed, A., & Vedula, P. (2020) · Theoretical and Computational Fluid Dynamics · doi:10.1007/s00162-019-00512-z · Cited by 49 · see citing works
Spiking Graph Convolutional Networks
Zhu, Z., Peng, J., Li, J., Chen, L., Yu, Q., & Luo, S. (2022) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2022/338 · Cited by 48 · see citing works
Wiersma, R., Nasikun, A., Eisemann, E., & Hildebrandt, K. (2022) · ACM Transactions on Graphics · doi:10.1145/3528223.3530166 · Cited by 48 · see citing works
Combinatorial Learning of Graph Edit Distance via Dynamic Embedding
Wang, R., Zhang, T., Yu, T., Yan, J., & Yang, X. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.00520 · Cited by 48 · see citing works
Deep orientation-aware functional maps: Tackling symmetry issues in Shape Matching
Donati, N., Corman, É., & Ovsjanikov, M. (2022) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr52688.2022.00082 · Cited by 47 · see citing works
Bahri, M., Bahl, G., & Zafeiriou, S. P. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.00937 · Cited by 47 · see citing works
Bouritsas, G., Bokhnyak, S., Ploumpis, S., Zafeiriou, S. P., & Bronstein, M. M. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00731 · Cited by 174 · see citing works
Vision-and-Language Pretrained Models: A Survey
Long, S., Cao, F., Han, S. C., & Yang, H. (2022) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2022/773 · Cited by 46 · see citing works
Fatigue driving recognition based on deep learning and graph neural network
Lin, Z., Qiu, T., Liu, P., Zhang, L., Zhang, S., & Mu, Z. (2021) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2021.102598 · Cited by 46 · see citing works
Graph Matching with Bi-level Noisy Correspondence
Lin, Y. B., Yang, M., Yu, J., Hu, P., Zhang, C., & Peng, X. (2023) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv51070.2023.02135 · Cited by 45 · see citing works
Pseudo-Siamese Graph Matching Network for Textureless Objects’ 6-D Pose Estimation
Wu, C., Chen, L., He, Z., & Jiang, J. (2021) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2021.3070501 · Cited by 45 · see citing works
MeshGAN: Non-linear 3D Morphable Models of FacesPreprint
Cheng, S., Bronstein, M. M., Zhou, Y., Kotsia, I., Pantić, M., & Zafeiriou, S. P. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1903.10384 · Cited by 45 · see citing works
Image classification using graph neural network and multiscale wavelet superpixels
Vasudevan, V., Bassenne, M., Islam, M. T., & Xing, L. (2023) · Pattern Recognition Letters · doi:10.1016/j.patrec.2023.01.003 · Cited by 44 · see citing works
Fabijańska, A., & Banasiak, R. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107608 · Cited by 44 · see citing works
A comprehensive review of graph convolutional networks: approaches and applications
Xu, X., Zhao, X., Wei, M., & Li, Z. (2023) · Electronic Research Archive · doi:10.3934/era.2023213 · Cited by 43 · see citing works
Bridging the Gap Between Spectral and Spatial Domains in Graph Neural NetworksPreprint
Balcılar, M., Renton, G., Héroux, P., Gaüzère, B., Adam, S., & Honeiné, P. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2003.11702 · Cited by 41 · see citing works
NURBS-Diff: A Differentiable Programming Module for NURBS
Prasad, A. D., Balu, A., Shah, H., Sarkar, S., Hegde, C., & Krishnamurthy, A. (2022) · Computer-Aided Design · doi:10.1016/j.cad.2022.103199 · Cited by 40 · see citing works
Higher-order Clustering and Pooling for Graph Neural Networks
Duval, A., & Malliaros, F. D. (2022) · ACM International Conference on Information and Knowledge Management (CIKM) · doi:10.1145/3511808.3557353 · Cited by 39 · see citing works
Revisiting Graph Neural Networks: Graph Filtering Perspective
Nt, H., Maehara, T., & Murata, T. (2021) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr48806.2021.9412278 · Cited by 40 · see citing works
LW-GCN: A Lightweight FPGA-based Graph Convolutional Network Accelerator
Tao, Z., Wu, C.-L., Liang, Y., Wang, K., & He, L. (2022) · ACM Transactions on Reconfigurable Technology and Systems · doi:10.1145/3550075 · Cited by 39 · see citing works
CurvaNet: Geometric Deep Learning based on Directional Curvature for 3D Shape Analysis
He, W., Jiang, Z., Zhang, C., & Sainju, A. M. (2020) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3394486.3403272 · Cited by 38 · see citing works
Yue, C., Khater, M. M. A., Attia, R. A. M., & Lu, D. (2020) · AIP Advances · doi:10.1063/1.5142796 · Cited by 37 · see citing works
A convolutional strategy on unstructured mesh for the adjoint vector modeling
Xu, M., Song, S., Sun, X., & Zhang, W. (2021) · Physics of Fluids · doi:10.1063/5.0044093 · Cited by 36 · see citing works
GMLS-Nets: A Framework for Learning from Unstructured Data
Sandia National Laboratories (SNL), A., Trask, N., Patel, R., Gross, B., & Atzberger, P. J. (2019) · doi:10.2172/1763256 · Cited by 35 · see citing works
- Authors
- Fey, M., Lenssen, J. E., Weichert, F., & Muller, H.
- Affiliations
- TU Dortmund University (DE)
- Venue
- 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition
- Publisher
- IEEE
- Published
- 2018-06
- Pages
- 869-877
- ISSN
- 1063-6919 (ISSN-L)
- OpenAlex
- W2768308213
- Cited by
- 459
- References
- 32
- Citations by year
- 2026: 18 · 2025: 47 · 2024: 58 · 2023: 64 · 2022: 68 · 2021: 76 · 2020: 68 · 2019: 54 · 2018: 6
- FWCI
- 20.82
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft (projects B2, SFB876)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Keywords
- geometric deep learning, B-splines, continuous kernels, convolutional neural networks, graph classification, mesh processing, shape correspondence, node classification, end-to-end learning
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
