
Detecting Symmetries with Neural Networks
Identifying symmetries in data sets is generally difficult, but knowledg...
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The Heyde theorem on a group ℝ^n× D, where D is a discrete Abelian group
Heyde proved that a Gaussian distribution on the real line is characteri...
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Rotation Invariant Householder Parameterization for Bayesian PCA
We consider probabilistic PCA and related factor models from a Bayesian ...
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Equivariance Through ParameterSharing
We propose to study equivariance in deep neural networks through paramet...
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Invariantequivariant representation learning for multiclass data
Representations learnt through deep neural networks tend to be highly in...
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A Computationally Efficient Neural Network Invariant to the Action of Symmetry Subgroups
We introduce a method to design a computationally efficient Ginvariant ...
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Visual Representations: Defining Properties and Deep Approximations
Visual representations are defined in terms of minimal sufficient statis...
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Probabilistic symmetry and invariant neural networks
In an effort to improve the performance of deep neural networks in datascarce, noni.i.d., or unsupervised settings, much recent research has been devoted to encoding invariance under symmetry transformations into neural network architectures. We treat the neural network input and output as random variables, and consider group invariance from the perspective of probabilistic symmetry. Drawing on tools from probability and statistics, we establish a link between functional and probabilistic symmetry, and obtain generative functional representations of joint and conditional probability distributions that are invariant or equivariant under the action of a compact group. Those representations completely characterize the structure of neural networks that can be used to model such distributions and yield a general program for constructing invariant stochastic or deterministic neural networks. We develop the details of the general program for exchangeable sequences and arrays, recovering a number of recent examples as special cases.
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