Designing equivariance as an inductive bias into deep-nets has been a prominent approach to build effective models, e.g., a convolutional neural network incorporates translation equivariance. However, incorporating these inductive biases requires knowledge about the equivariance properties of the data, which may not be available, e.g., when encountering a new domain. To address this, we study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. We propose to use the partition distance to empirically quantify the accuracy of the recovered equivariance. Also, we theoretically analyze the method for Gaussian data and provide a bound on the mean squared gap between the studied discovery scheme and the oracle scheme. Empirically, we show that the approach recovers known equivariances, such as permutations and shifts, on sum of numbers and spatially-invariant data.

Original languageEnglish (US)
Pages (from-to)1527-1545
Number of pages19
JournalProceedings of Machine Learning Research
StatePublished - 2022
Event25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain
Duration: Mar 28 2022Mar 30 2022

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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