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

arXiv: https://arxiv.org/abs/2603.07246 · HTML: https://mlsanity.com/paper/2603.07246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [RemoteCLIP: A Vision Language Foundation Model for Remote Sensing](https://mlsanity.com/paper/2306.11029/) (2023)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [CROMA: Remote Sensing Representations with Contrastive Radar-Optical Masked Autoencoders](https://mlsanity.com/paper/2311.00566/) (2023)
- [Prithvi-EO-2.0: A Versatile Multi-Temporal Foundation Model for Earth Observation Applications](https://mlsanity.com/paper/2412.02732/) (2024)
- [AlphaEarth Foundations: An embedding field model for accurate and efficient global mapping from sparse label data](https://mlsanity.com/paper/2507.22291/) (2025)
- [TerraMind: Large-Scale Generative Multimodality for Earth Observation](https://mlsanity.com/paper/2504.11171/) (2025)
- [EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modeling](https://mlsanity.com/paper/2502.09509/) (2025)
- [AnySat: One Earth Observation Model for Many Resolutions, Scales, and Modalities](https://mlsanity.com/paper/2412.14123/) (2024)
- [Learning and Leveraging World Models in Visual Representation Learning](https://mlsanity.com/paper/2403.00504/) (2024)
- [PANGAEA: A Global and Inclusive Benchmark for Geospatial Foundation Models](https://mlsanity.com/paper/2412.04204/) (2024)
- [Predicting Gradient is Better: Exploring Self-Supervised Learning for SAR ATR with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2311.15153/) (2023)
- [Self-supervised learning of Split Invariant Equivariant representations](https://mlsanity.com/paper/2302.10283/) (2023)
- [Galileo: Learning Global & Local Features of Many Remote Sensing Modalities](https://mlsanity.com/paper/2502.09356/) (2025)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Structuring Representation Geometry with Rotationally Equivariant Contrastive Learning](https://mlsanity.com/paper/2306.13924/) (2023)
- [Global and Dense Embeddings of Earth: Major TOM Floating in the Latent Space](https://mlsanity.com/paper/2412.05600/) (2024)
- [Steerable Transformers for Volumetric Data](https://mlsanity.com/paper/2405.15932/) (2024)
- [Latent Space Cartography: Generalised Metric-Inspired Measures and Measure-Based Transformations for Generative Models](https://mlsanity.com/paper/1902.02113/) (2019)
- [Steerable Equivariant Representation Learning](https://mlsanity.com/paper/2302.11349/) (2023)
- [REJEPA: A Novel Joint-Embedding Predictive Architecture for Efficient Remote Sensing Image Retrieval](https://mlsanity.com/paper/2504.03169/) (2025)

## Abstract (arXiv)

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.