AlphaEarth distinguishes cities but compresses urban variation

AlphaEarth 能区分城市，但压缩了城市的多样性

Abstract: Cities differ in built form, land cover and development history, complicating comparison across places and time. Satellite foundation models map Earth’s surface onto common numerical representations. Yet the tasks and targets used to shape them typically do not focus on cities: globally consistent labels for urban function do not exist, and many datasets - especially land cover and land use classifications - collapse the built environment into few classes.

摘要： 城市在建筑形态、土地覆盖和发展史上各不相同，这使得跨地区和跨时间的比较变得复杂。卫星基础模型将地球表面映射为通用的数值表示。然而，用于构建这些模型的任务和目标通常并不关注城市：全球范围内不存在统一的城市功能标签，且许多数据集（尤其是土地覆盖和土地利用分类）将建筑环境简化为少数几种类别。

Here we audit the representation, focusing on AlphaEarth but with broader applicability to other Earth embeddings, by probing the geometry and geography of embeddings for 1,000 urban areas in 162 countries. We find that cities occupy a shifted but overlapping region on the hypersphere, 62.7° from the global mean direction, and continent and climate predict 24.3% of variation among the mean directions of urban centres in excluded countries.

在此，我们通过探测 162 个国家中 1,000 个城市区域的嵌入（embeddings）几何和地理特征，对这种表示进行了审计，重点关注 AlphaEarth，但其结论也适用于其他地球嵌入模型。我们发现，城市在超球面上占据了一个偏移但重叠的区域，距离全局平均方向 62.7°；此外，大洲和气候因素可以解释被排除国家中城市中心平均方向 24.3% 的变异性。

Inside cities, degrees of urbanisation carry 8.9% of the variation, and what they leave holds shared directions whose local orientation varies, not one universal axis of urbanisation. Retained variation is itself unequal: dispersion within urban centres is 14.1% greater per standard deviation of national development, even after adjusting for population, land area and continent.

在城市内部，城市化程度承载了 8.9% 的变异性，而剩余部分则表现为共享方向，其局部取向各异，并非存在单一的通用城市化轴线。保留下来的变异性本身也是不均衡的：即使在调整了人口、土地面积和大洲因素后，国家发展水平每增加一个标准差，城市中心内部的离散度就会增加 14.1%。

Further controls suggest cities in developing countries present less contrast in vegetation and texture, and dispersion follows that contrast: full adjustment for it leaves at most 6.4% of the gradient. Annually, a city’s representation moves nearly eight times more than redrawing its own pixels explains, and contracts where the 2022 loss of Sentinel-1B removed a pass direction. AlphaEarth’s representations therefore support comparison across regions, while the differences between its annual layers are not yet validated for comparison over time.

进一步的控制变量分析表明，发展中国家的城市在植被和纹理上的对比度较低，而离散度随这种对比度变化：在完全调整该因素后，梯度仅剩下最多 6.4%。从年度来看，城市表示的移动幅度几乎是其自身像素重绘所能解释的八倍，且在 2022 年 Sentinel-1B 卫星失效导致缺失一个观测方向的区域，其表示会出现收缩。因此，AlphaEarth 的表示支持跨区域比较，但其年度层级之间的差异尚未经过验证，尚不能用于跨时间比较。