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Motivated by objects such as electric fields or fluid streams, we study theproblem of learning stochastic fields, i.e. stochastic processes whose samplesare fields like those occurring in physics and engineering. Considering generaltransformations such as rotations and reflections, we show that spatialinvariance of stochastic fields requires an inference model to be equivariant.Leveraging recent advances from the equivariance literature, we studyequivariance in two classes of models. Firstly, we fully characteriseequivariant Gaussian processes. Secondly, we introduce Steerable ConditionalNeural Processes (SteerCNPs), a new, fully equivariant member of the NeuralProcess family. In experiments with Gaussian process vector fields, images, andreal-world weather data, we observe that SteerCNPs significantly improve theperformance of previous models and equivariance leads to improvements intransfer learning tasks.

Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes