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

Understand

Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e.

• stochastic processes whose samples are fields like those occurring in physics and engineering.
• Considering general transformations such as rotations and reflections, we show that spatial invariance of stochastic fields requires an inference model to be equivariant.
• Leveraging recent advances from the equivariance literature, we study equivariance in two classes of models.