用斯莱皮安函数实现局部高分辨率地理编码，提升细粒度任务表现
Localized, High-resolution Geographic Representations with Slepian Functions
- 基于球面斯莱皮安函数聚焦区域编码，提升局部细节表达能力
- 在五类任务中超越基线，支持高分辨率且计算高效
- 适合需要精细地理定位的模型，如疫情预测、生态分析
地理数据本质上具有局部性：疫情爆发集中于人口中心，生态模式沿海岸线显现，经济活动聚集于国界内。然而，现有机器学习模型对地理位置的编码在全局范围内均匀分配表示能力，难以满足细粒度应用的需求。本文提出一种基于球面斯莱皮安函数的地理编码器，可将表示能力集中于感兴趣区域，并在不增加大量计算成本的前提下实现高分辨率建模。对于需要全球上下文的场景，我们进一步设计了混合斯莱皮安-球谐编码器，有效平衡局部与全局性能，同时保持无极点问题和球面距离保真等优良特性。在涵盖分类、回归和图像增强预测的五项任务中，斯莱皮安编码均优于基线方法，并在多种神经网络架构下保持优势。
原文摘要 · Abstract (English)
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 that localized applications require. We propose a geographic location encoder built from spherical Slepian functions that concentrate representational capacity inside a region-of-interest and scale 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 range of neural network architectures.
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