LEPA: Learning Geometric Equivariance in Satellite Remote Sensing Data with a Predictive Architecture

TL;DR

LEPA introduces a predictive architecture that learns geometric equivariance, enabling accurate spatial adjustments of satellite image embeddings without re-encoding, thus overcoming limitations of traditional interpolation methods.

Contribution

LEPA is a novel predictive model that explicitly learns geometric transformations in embedding space, improving spatial alignment in satellite remote sensing applications.

Findings

LEPA achieves an MRR over 0.8 on satellite imagery tasks.

Standard interpolation yields an MRR below 0.2, showing its limitations.

LEPA outperforms traditional methods in geometric adjustment accuracy.

Abstract

Geospatial foundation models provide precomputed embeddings that serve as compact feature vectors for large-scale satellite remote sensing data. While these embeddings can reduce data-transfer bottlenecks and computational costs, Earth observation (EO) applications can still face geometric mismatches between user-defined areas of interest and the fixed precomputed embedding grid. Standard latent-space interpolation is unreliable in this setting because the embedding manifold is highly non-convex, yielding representations that do not correspond to realistic inputs. We verify this using Prithvi-EO-2.0 to understand the shortcomings of interpolation applied to patch embeddings. As a substitute, we propose a Learned Equivariance-Predicting Architecture (LEPA). Instead of averaging vectors, LEPA conditions a predictor on geometric augmentations to directly predict the transformed embedding. We evaluate LEPA on NASA/USGS Harmonized Landsat-Sentinel (HLS) imagery and ImageNet-1k. Experiments show that standard interpolation achieves a mean reciprocal rank (MRR) below 0.2, whereas LEPA increases MRR to over 0.8, enabling accurate geometric adjustment without re-encoding.