Localized, High-resolution Geographic Representations with Slepian Functions

Geographic data is fundamentally local. Disease outbreaks cluster in population centers, ecological patterns emerge along coastlines, and economic activity concentrates within country borders. Machine learning models that encode geographic location, however, distribute representational capacity uniformly across the globe, struggling at the fine-grained resolutions localized applications require. We propose a geographic location encoder built from spherical Slepian functions that concentrates representational capacity inside a region-of-interest and scales to high resolutions without extensive computational demands. For settings requiring global context, we present a hybrid Slepian-Spherical Harmonic encoder that efficiently bridges the tradeoff between local-global performance, while retaining desirable properties such as pole-safety and spherical-surface-distance preservation. Across five tasks spanning classification, regression, and image-augmented prediction, Slepian encodings outperform baselines and retain performance advantages across a wide variety of neural network architectures.

Many machine learning tasks take a known location on Earth and predict something about that spot, like the house price there, which species live there, or the local temperature. To do this, a model first has to turn a raw latitude and longitude into numbers it can learn from, which is the job of a "location encoder." The catch is that today's encoders spread their detail evenly across the whole planet, so sharpening one place means adding detail everywhere at once. That quickly gets slow and memory-hungry, and it grows unstable near the poles, even though most tasks we care about are local: outbreaks cluster in cities, and ecosystems hug coastlines. We instead use a tool from signal processing called Slepian functions, which pack almost all of their detail inside a region you choose. Think of a fixed budget of detail to spend on a map: rather than spreading it evenly, we pour most of it into the area that matters and keep just a rough sketch of the rest for context. Because the method is defined directly on the globe, it also avoids the distortions of flat maps and the breakdown at the poles. We pair this sharp local view with a coarse global one, and we show the same idea works across time as well as space. Tested on five tasks, from housing prices to species mapping to climate, our encoder beats standard methods while using far less memory and compute, because it spends its detail where the data actually lives.