Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on geo-referenced satellite, image or text data. Despite the common aim of geographic INRs to distill Earth's data into compact, learning-friendly representations, we lack an understanding of how much information is contained in these Earth representations, and where that information is concentrated. The intrinsic dimension of a dataset measures the number of degrees of freedom required to capture its local variability, regardless of the ambient high-dimensional space in which it is embedded. This work provides the first study of the intrinsic dimensionality of geographic INRs. Analyzing INRs with ambient dimension between 256 and 512, we find that their intrinsic dimensions fall roughly between 2 and 10 and are sensitive to changing spatial resolution and input modalities during INR pre-training. Furthermore, we show that the intrinsic dimension of a geographic INR correlates with downstream task performance and can capture spatial artifacts, facilitating model evaluation and diagnostics. More broadly, our work offers an architecture-agnostic, label-free metric of information content that can enable unsupervised evaluation, model selection, and pre-training design across INRs.

翻译：在地球观测表征学习的背景下，地理隐式神经表征（INRs）通过基于地理参照的卫星、图像或文本数据训练的模型，将低维位置输入（经度、纬度）嵌入到高维嵌入中。尽管地理INRs的共同目标是将地球数据提炼为紧凑、易于学习的表征，但我们仍缺乏对这些地球表征包含多少信息以及信息集中位置的理解。数据集的内在维度衡量了捕捉其局部变异性所需的自由度数量，而无论其嵌入的环境高维空间如何。本研究首次对地理INRs的内在维度进行了探讨。通过分析环境维度在256至512之间的INRs，我们发现它们的内在维度大致介于2到10之间，并且对INR预训练过程中空间分辨率和输入模态的变化敏感。此外，我们证明了地理INR的内在维度与下游任务性能相关，并能捕捉空间伪影，从而促进模型评估与诊断。更广泛地说，我们的工作提供了一种与架构无关、无需标签的信息内容度量方法，能够支持跨INRs的无监督评估、模型选择和预训练设计。