New Neural Process Methods Using Fourier Transform and Volterra Series for Irregular Data
A new preprint introduces set Fourier convolutions (SFConvs) and a Volterra-series framework to improve translation-equivariant neural processes for modeling functions from sparse, irregular data. Existing approaches either lack interpretability or scale poorly — quadratically with observations — when handling non-uniform inputs. The work offers a theoretically grounded alternative that scales linearly and achieves near-global receptive fields, potentially benefiting scientific and engineering applications involving irregular measurements.
Researchers have posted a preprint on arXiv proposing two new conditional neural process (CNP) architectures — SFConvCNPs and SFVConvCNPs — designed to overcome key limitations of current translation-equivariant neural processes. The paper leverages the Volterra series expansion to characterize continuous translation-equivariant operators as sums of higher-order convolutions, providing analytical transparency and enabling efficient first-order approximations. Building on this, the authors introduce set Fourier convolutions (SFConvs), a frequency-domain parameterization that works directly on irregularly sampled data points without requiring a dense uniform grid. Unlike attention-based methods that scale quadratically with the number of observations, SFConvs achieve approximately linear scaling while maintaining global receptive fields. Experiments on both synthetic and real-world datasets are reported to show competitive or superior performance against state-of-the-art baselines. The work was submitted in late May 2026 and revised in June 2026, and has not yet undergone formal peer review.
What's missing
As a preprint, the paper has not been peer-reviewed. The authors do not discuss computational memory overhead of the frequency-domain parameterization in detail, nor do they address potential limitations in very high-dimensional input spaces. Scalability claims (linear complexity) may depend on approximation quality trade-offs not fully characterized in the abstract.
What different sources said
- arXiv stat.MLCenter
Revisiting Neural Processes via Fourier Transform and Volterra Series
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