SatCLIP Earth-representation intrinsic dimension is far below ambient size and increases with spatial resolution
measured in 1 paper- The global intrinsic dimension (ID) of frozen SatCLIP location-encoder embeddings (256-d ambient) is far below the ambient dimension under distance-based estimators (MLE 1.96 for SatCLIP-L10, 2.03 for SatCLIP-L40, on 100k land points; Table 1), but is estimator- and sampling-dependent: the angle-based FisherS gives 5.00 (L10) and 8.08 (L40), and TwoNN under Fibonacci sampling gives 44.14 (L10) and 12.80 (L40) versus about 2 under other sampling schemes (Table 3). [rao-etal-2025-measuring-intrinsic-dimension-of-earth-representations] - In SatCLIP variants the authors pre-train with different spherical-harmonic band limits (L = 10, 20, 40), the paper reports that global FisherS ID rises with the spatial-resolution parameter L (Fig. 5), and rises with the number of pre-training input modalities (Fig. 6). [rao-etal-2025-measuring-intrinsic-dimension-of-earth-representations] - Across encoders, FisherS ID of frozen embeddings correlates positively with downstream task performance (Fig. 3a), while TwoNN ID of the activations of a task head trained on top correlates negatively (Fig. 3b); purely observational, no causal intervention on the encoder geometry. [rao-etal-2025-measuring-intrinsic-dimension-of-earth-representations]