New Neural Process Methods Using Fourier Transform and Volterra Series for Irregular Data
Researchers introduced two new neural process variants that use Fourier transforms and Volterra series to model unknown functions from irregularly sampled data more efficiently. The methods address limitations in existing translation-equivariant neural processes by improving interpretability and computational scalability. This work advances probabilistic machine learning approaches for scientific and engineering applications where data collection is sparse or non-uniform.
A new arXiv paper proposes improved neural process models designed to learn unknown functions from finite, irregularly sampled measurements—a common challenge in science and engineering. The authors identify two key limitations in existing translation-equivariant neural processes: lack of interpretability in how components combine, and computational inefficiency when handling irregular data. They address these through two main contributions: using Volterra expansion to analytically characterize translation-equivariant operators, and introducing set Fourier convolutions (SFConvs) that operate in the frequency domain, achieve global receptive fields, and scale linearly with observation count. The resulting models—SFConvCNPs and SFVConvCNPs—are evaluated on synthetic and real-world datasets, demonstrating improvements over existing baselines.
What's missing
The paper does not discuss computational wall-clock time comparisons or memory requirements in practice, only theoretical scaling properties. Additionally, the specific real-world datasets used and their domains are not detailed in the abstract, limiting assessment of generalization claims.
What different sources said
- arXiv stat.MLCenter
Revisiting Neural Processes via Fourier Transform and Volterra Series
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