Spectral Convolutional Conditional Neural Processes

Abstract

Neural Processes (NPs) are meta-learning models that learn to map sets of observations to approximations of the corresponding posterior predictive distributions. By accommodating variable-sized, unstructured collections of observations and enabling probabilistic predictions at arbitrary query points, NPs provide a flexible framework for modeling functions over continuous domains. Since their introduction, numerous variants have emerged; however, early formulations shared a fundamental limitation: they compressed the observed data into finite-dimensional global representations via aggregation operations such as mean pooling. This strategy induces an intrinsic mismatch with the infinite-dimensional nature of the stochastic processes that NPs intend to model. 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 spectral ConvCNPs (SConvCNPs), which perform 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 SConvCNPs on both synthetic and real-world datasets, demonstrating how ideas from operator learning can advance the capabilities of NPs.