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Incorporating geometric inductive biases into models can aid interpretability and generalization, but encoding to a specific geometric structure can be challenging due to the imposed topological constraints.
The princeton shape benchmark
Philip Shilane, Patrick Min, Michael Kazhdan, and Thomas Funkhouser · 2004
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Representation learning: A review and new perspectives
Yoshua Bengio, Aaron Courville, and Pascal Vincent · 2013
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Lie groups, Lie algebras, and representations
Brian C Hall and Brian C Hall · 2013
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Auto-Encoding Variational Bayes
Diederik P. Kingma and Max Welling · 2014
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Danilo Rezende and Shakir Mohamed · 2015
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Group equivariant convolutional networks
Taco Cohen and Max Welling · 2016
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Irina Higgins, Loic Matthey, Arka Pal, Christopher Burgess, Xavier Glorot, Matthew Botvinick, Shakir Mohamed, and Alexander Lerchner · 2017
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Topological Constraints on Homeomorphic Auto-Encoding
Pim de Haan and Luca Falorsi · 2018
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Explorations in Homeomorphic Variational Auto-Encoding
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Hyperbolic neural networks
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On the generalization of equivariance and convolution in neural networks to the action of compact groups
Risi Kondor and Shubhendu Trivedi · 2018
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Spherical latent spaces for stable variational autoencoders
Jiacheng Xu and Greg Durrett · 2018
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Symmetry-based disentangled representation learning requires interaction with environments
Hugo Caselles-Dupré, Michael Garcia Ortiz, and David Filliat · 2019
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Affine equivariant autoencoder
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Cheap orthogonal constraints in neural networks: A simple parametrization of the orthogonal and unitary group
Mario Lezcano-Casado and David Martınez-Rubio · 2019
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Yu Meng, Jiaxin Huang, Guangyuan Wang, Chao Zhang, Honglei Zhuang, Lance Kaplan, and Jiawei Han · 2019
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Geometric deep learning: Grids, groups, graphs, geodesics, and gauges
Michael M Bronstein, Joan Bruna, Taco Cohen, and Petar Veličković · 2021
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Neighborhood geometric structure-preserving variational autoencoder for smooth and bounded data sources
Xingyu Chen, Chunyu Wang, Xuguang Lan, Nanning Zheng, and Wenjun Zeng · 2021
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Smooth normalizing flows
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Neighborhood reconstructing autoencoders
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Riemannian continuous normalizing flows
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Topological autoencoders
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Diffusion Variational Autoencoders
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Symmetry-based representations for artificial and biological general intelligence
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Equivariant representation learning via class-pose decomposition
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Learning symmetric embeddings for equivariant world models
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Quantifying and learning linear symmetry-based disentanglement
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Kendall shape-vae: Learning shapes in a generative framework
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Unsupervised learning of group invariant and equivariant representations
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Towards building a group-based unsupervised representation disentanglement framework
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Rigid body flows for sampling molecular crystal structures
Jonas Köhler, Michele Invernizzi, Pim de Haan, and Frank Noé · 2023
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Delving into discrete normalizing flows on so (3) manifold for probabilistic rotation modeling
Yulin Liu, Haoran Liu, Yingda Yin, Yang Wang, Baoquan Chen, and He Wang · 2023
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