Deep Symmetry Networks

By Robert Gens, Pedro M. Domingos. 2014

280 citations recorded by the source corpus.

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In Model Architectures

Citations in the corpus

Spatial Transformer Networks (2015, methodology): “Cohen & Welling [6] analyse this behaviour in relation to symmetry groups, which is also exploited in the architecture proposed by Gens & Domingos [10], resulting in feature maps that are more invariant to symmetry groups.”
Deformable Convolutional Networks (2017, background): “Some works are devoted for speciﬁc transformations such as symmetry [13, 9], scale [29], and rotation [53].”
Why do deep convolutional networks generalize so poorly to small image transformations? (2018, methodology): “Alternatively, one could use specially designed features such as SIFT in which invariance is hard coded [7, 29, 30, 31] or neural network architectures that explicitly enforce invariance [36, 19, 5, 6, 11, 12, 47, 46, 8].”
Towards a Definition of Disentangled Representations (2018, background): “A long standing idea in ML is that such shortcomings can be reduced by introducing certain inductive biases into the model architecture that reﬂect the structure of the underlying data [12, 33, 21, 43].”
Equivariant Hamiltonian Flows (2019, neutral): “Learninggenerativemodelswithstructuredlatentrepresentationsisimportantforinterpretability, data efﬁciency, and generalisation [2, 7].”
Group Equivariant Convolutional Networks (2016, methodology): “A further challenge, already identiﬁed by Gens & Domingos (2014), is that a full enumeration of transformations in a group may not be feasible if the group is large.”
Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network (2018, background): “Recently, a number of papers have appeared that examine equivariance from the theoretical point of view, motivated by the understanding that the natural way to generalize convolutional networks to other types of data will likely lead through generalizing the notion of equivariance itself to other tr”
Spherical CNNs (2018, background): “It thus becomes natural to consider generalizations that exploit larger groups of symmetries, and indeed this has been the subject of several recent papers by Gens and Domingos (2014) Cohen and Welling (2017).”
Equivariance Through Parameter-Sharing (2017, methodology): “Invariance and equivariance through parameter-sharing is also discussed in several prior works (Cohen & Welling, 2016; Gens & Domingos, 2014).”
Deep Learning on Lie Groups for Skeleton-Based Action Recognition (2016, background): “[15] introduced deep symmetry networks (symnets), a generalization of convolutional networks that forms feature maps over arbitrary symmetry groups that are basically Lie groups.”
Deep Sets (2017, background): “…deep learning (LeCun et al., 2015) has witnessed applications to other structured settings, including graphs (Bruna et al., 2013; Duvenaud et al., 2015), groups (Gens & Domingos, 2014; Christopher, 2014; Cohen & Welling, 2016), sequences and hierarchies (Irsoy & Cardie, 2014; Socher et al., 2013).”
Exploiting Cyclic Symmetry in Convolutional Neural Networks (2016, background): “Gens & Domingos (2014) propose deep symmetry networks, a generalisation of CNNs that can form feature maps over arbitrary transformation groups.”
Learning SO(3) Equivariant Representations with Spherical CNNs (2017, background): “Gens and Domingos (2014) produce maps of finite-multiparameter groups, Zhou et al. (2017) and Marcos et al. (2016) use a rotational filter orbit to produce oriented feature maps and rotationally invariant features, and Lenc and Vedaldi (2015) propose a transformation layer which acts as a…”
Learning Steerable Filters for Rotation Equivariant CNNs (2017, background): “In [14] the regions in symmetry space to pool over are learned to become invariant only to nuisance deformations.”
Rotation Equivariant Vector Field Networks (2016, background): “2) Rotating the filters: Gens and Domingos [10] tackle the problem of the exploding dimensionality (discussed in Sec.”
A General Theory of Equivariant CNNs on Homogeneous Spaces (2018, neutral): “Other related work includes [24–31].”
Polar Transformer Networks (2017, background): “The same idea underlies the work in [7] which produces maps of multidimensional groups sampled at a finite set of anchor points.”