Equivariant Learning of Stochastic Fields: Gaussian Processes and Steerable Conditional Neural Processes
This work is significant for researchers and practitioners working with physical and engineering fields, as it provides a new method for learning stochastic fields with improved performance and transfer learning capabilities.
This paper addresses the challenge of learning stochastic fields, which are stochastic processes whose samples are fields commonly found in physics and engineering. The authors demonstrate that spatial invariance in stochastic fields necessitates an equivariant inference model. They introduce Steerable Conditional Neural Processes (SteerCNPs), a novel fully equivariant model, which significantly outperforms previous models in experiments with Gaussian process vector fields, images, and real-world weather data.
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. Firstly, we fully characterise equivariant Gaussian processes. Secondly, we introduce Steerable Conditional Neural Processes (SteerCNPs), a new, fully equivariant member of the Neural Process family. In experiments with Gaussian process vector fields, images, and real-world weather data, we observe that SteerCNPs significantly improve the performance of previous models and equivariance leads to improvements in transfer learning tasks.