Spectral Convolutional Conditional Neural Processes
Peiman Mohseni, Nick Duffield
Conditional Neural Processes (CNPs) are a class of probabilistic models that leverage neural networks to parameterize conditional stochastic processes. Through simple maximum-likelihood training and the ability to produce well‐calibrated uncertainty estimates, CNPs have emerged as powerful tools for modeling data that naturally resides on a continuum—such as temporal signals, spatial fields, or functional trajectories. However, early variants of the CNP family rely on fixed finite-dimensional representations of observations, which can lead to information loss and a mismatch with the inherently infinite-dimensional nature of stochastic processes, ultimately degrading predictive performance. Convolutional CNPs (ConvCNPs) address this issue by mapping observations into an infinite-dimensional embedding and applying a convolutional neural network. Yet, their reliance on local discrete kernels introduces a trade-off: large kernels are needed to capture long-range dependencies, but they come at significant computational and memory costs.To overcome this limitation, we exploit the compact and global representation provided by the frequency domain, inspired by Fourier Neural Operators (FNOs) in approximating solution operators of parametric partial differential equations (PDEs). We introduce Spectral Convolutional Conditional Neural Processes (SConvCNPs), which directly parameterize global convolutional filters in the frequency domain. We validate SConvCNPs' effectiveness through several experiments on both synthetic and real-world datasets.