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Geometric Deep Learning
Abstract
In the last decade, Deep Learning approaches (e.g. Convolutional Neural Networks and Recurrent Neural Networks) allowed to achieve unprecedented performance on a broad range of problems coming from a variety of different fields (e.g. Computer Vision and Speech Recognition). Despite the results obtained, research on DL techniques has mainly focused so far on data defined on Euclidean domains (i.e. grids). Nonetheless, in a multitude of different fields, such as: Biology, Physics, Network Science, Recommender Systems and Computer Graphics; one may have to deal with data defined on non-Euclidean domains (i.e. graphs and manifolds). The adoption of Deep Learning in these particular fields has been lagging behind until very recently, primarily since the non-Euclidean nature of data makes the definition of basic operations (such as convolution) rather elusive. Geometric Deep Learning deals in this sense with the extension of Deep Learning techniques to graph/manifold structured data.
Papers and Code
M. M. Bronstein, J. Bruna, Y. LeCun, A. Szlam, P. Vandergheynst, Geometric deep learning: going beyond Euclidean data, IEEE Signal Processing Magazine 2017 (Review paper)
H. Maron, M. Galun, N. Aigerman, M. Trope, N. Dym, E. Yumer, V. G. Kim, Y. Lipman, Convolutional Neural Networks on Surfaces via Seamless Toric Covers, 2017
K. T. Schütt, P. Kindermans, H. E. Sauceda, S. Chmiela, A. Tkatchenko, K. Müller, SchNet: A continuous-filter convolutional neural network for modeling quantum interactions, NIPS 2017
T. Lei, W. Jin, R. Barzilay, T. Jaakkola, Deriving Neural Architectures from Sequence and Graph Kernels, ICML 2017
R. Levie*, F. Monti*, X. Bresson, M. M. Bronstein, CayleyNets: Graph convolutional neural networks with complex rational spectral filters, 2017 (CayleyNet framework) [COMMUNITY DATASET]
O. Litany, T. Remez, E. Rodolà, A. M. Bronstein, M. M. Bronstein, Deep Functional Maps: Structured Prediction for Dense Shape Correspondence, 2017 (FMNet framework) [CODE]
F. Monti, X. Bresson, M. M. Bronstein, Geometric matrix completion with recurrent multi-graph neural networks, NIPS 2017 (CNNs on multiple graphs) [CODE]
J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, G. E. Dahl, Neural Message Passing for Quantum Chemistry, ICML 2017
Z. Huang, C. Wan, T. Probst, L. Van Gool, Deep Learning on Lie Groups for Skeleton-based Action Recognition, CVPR 2017 [CODE]
Y. Seo, M. Defferrard , P. Vandergheynst, X. Bresson,
Structured Sequence Modeling with Graph Convolutional Recurrent Networks
, 2016 (recurrent single graph CNN) [CODE]
L. Yi, H. Su, X. Guo, L. Guibas,
SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation
, CVPR 2017 (spectral transformer networks)
F. Monti*, D. Boscaini*, J. Masci, E. Rodolà, J. Svoboda, M. M. Bronstein, Geometric deep learning on graphs and manifolds using mixture model CNNs, CVPR 2017 (MoNet framework) [CODE] [VIDEO]
T. Kipf, M. Welling, Semi-supervised Classification with Graph Convolutional Networks, ICLR 2017 (simplification of ChebNet) [CODE]
M. Defferrard, X. Bresson, P. Vandergheynst, Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering, NIPS 2016 (ChebNet framework) [TF CODE] [PyTorch CODE]
M. Niepert, M. Ahmed, K. Kutzkov, Learning Convolutional Neural Networks for Graphs, ICML 2016
H. Dai, B. Dai, L. Song, Discriminative embeddings of latent variable models for structured data, ICML 2016
D. Boscaini, J. Masci, E. Rodolà, M. M. Bronstein, Learning shape correspondence with anisotropic convolutional neural networks, NIPS 2016 (Anisotropic CNN framework)
J. Masci, D. Boscaini, M. M. Bronstein, P. Vandergheynst, Geodesic convolutional neural networks on Riemannian manifolds, 3dRR 2015 (Geodesic CNN framework)
D. Duvenaud, D. Maclaurin, J. Aguilera-Iparraguirre, R. Gomez-Bombarelli, T. Hirzel, A. Aspuru-Guzik, R. P. Adams, Convolutional Networks on Graphs for Learning Molecular Fingerprints, NIPS 2015 (molecular fingerprints using graph CNNs)
J. Atwood, D. Towsley, Diffusion-Convolutional Neural Networks, 2015
M. Henaff, J. Bruna, Y. LeCun: Deep Convolutional Networks on Graph-Structured Data, 2015
J. Bruna, W. Zaremba, A. Szlam, Y. LeCun, Spectral Networks and Deep Locally Connected Networks on Graphs, ICLR 2014 (spectral CNN on graphs)
F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, G. Monfardini,
The graph neural network model,
Trans. Neural Networks 20(1):61-80, 2009 (first neural networks on graphs)
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