Spectral Convolutional Conditional Neural Processes

Peiman Mohseni, Nick Duffield

Keywords: neural process, stochastic process, meta learning, fourier neural operator

Abstract:

Neural processes (NPs) are probabilistic meta-learning models that map sets of observations to the corresponding posterior predictive distributions, enabling inference at arbitrary domain points. Their ability to handle variable-sized collections of unstructured observations, combined with simple maximum-likelihood training and uncertainty-aware predictions, makes them well-suited for modeling data over continuous domains.
Since their introduction, several variants have been proposed. Early approaches typically represented observed data using finite-dimensional summary embeddings obtained through aggregation schemes such as mean pooling. However, this strategy fundamentally mismatches the infinite-dimensional nature of the generative processes that NPs aim to capture.
Convolutional conditional neural processes (ConvCNPs) address this limitation by constructing infinite-dimensional functional embeddings processed through convolutional neural networks (CNNs) to enforce translation equivariance. Yet CNNs with local spatial kernels struggle to capture long-range dependencies without resorting to large kernels, which impose significant computational costs. To overcome this limitation, we propose the Spectral ConvCNP (SConvCNP), which performs global convolution in the frequency domain. Inspired by Fourier neural operators (FNOs) for learning solution operators of partial differential equations (PDEs), our approach directly parameterizes convolution kernels in the frequency domain, leveraging the relatively compact yet global Fourier representation of many natural signals. We validate the effectiveness of SConvCNP on both synthetic and real-world datasets, demonstrating how ideas from operator learning can advance the capabilities of NPs.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 26003