Spectral Convolutional Conditional Neural Processes

TL;DR

This paper introduces spectral ConvCNPs, a novel approach that performs global convolution in the frequency domain to better capture long-range dependencies in neural processes, improving modeling of functions over continuous domains.

Contribution

The paper proposes spectral ConvCNPs, combining Fourier-based global convolution with neural processes to enhance their ability to model complex, long-range dependencies efficiently.

Findings

Spectral ConvCNPs outperform previous models on synthetic datasets.

They effectively capture long-range dependencies with reduced computational costs.

Validated on real-world datasets, showing improved predictive performance.

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.