Title: Localized, High-resolution Geographic Representations with Slepian Functions

Abstract:

Geographic information is inherently local in nature. Phenomena such as disease outbreaks tend to cluster within dense population hubs, ecological trends often follow coastal lines, and economic activities are typically confined within national boundaries. Conversely, conventional machine learning models that incorporate geographic location assign representational capacity evenly across the entire planet. This uniform distribution makes it difficult for these models to achieve the fine-grained resolution necessary for localized applications. To address this limitation, we introduce a geographic location encoder utilizing spherical Slepian functions. This approach concentrates representational power within a specific region of interest and achieves high-resolution scaling without imposing heavy computational burdens. For scenarios that necessitate a broader global context, we offer a hybrid encoder combining Slepian functions with Spherical Harmonics. This hybrid model effectively manages the trade-off between local and global performance while preserving key features, such as pole-safety and the preservation of spherical-surface distances. Our evaluation across five distinct tasks—including classification, regression, and image-augmented prediction—demonstrates that Slepian encodings surpass baseline methods and maintain their performance edge across a diverse array of neural network architectures.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC