Catching the Imposter: Self-Supervised Learning of Physical Coherence with Cross-Entity Feature Permutations

Machine learning approaches to spatiotemporal physical systems have primarily focused on next-frame prediction, with the goal of learning an accurate emulator for the system's evolution in time. However, these emulators are computationally expensive to train and are subject to performance pitfalls, such as compounding errors during autoregressive rollout. In this work, we take a different perspective and look at scientific tasks further downstream of predicting the next frame, such as estimation of a system's governing physical parameters. Accuracy on these tasks offers a uniquely quantifiable glimpse into the physical relevance of the representations of these models. We evaluate the effectiveness of general-purpose self-supervised methods in learning physics-grounded representations that are useful for downstream scientific tasks. Surprisingly, we find that not all methods designed for physical modeling outperform generic self-supervised learning methods on these tasks, and methods that learn in the latent space (e.g., joint embedding predictive architectures, or JEPAs) outperform those optimizing pixel-level prediction objectives. Code is available at https://github.com/helenqu/physical-representation-learning.

Self-supervised learning (SSL) is designed to learn generic, transferable representations rather than representations optimized for a single task. Most geospatial benchmarks evaluate representations solely through downstream tasks, providing limited insight into the information encoded within the representation itself. We ask a different question: do SSL representations of satellite imagery preserve statistical associations with environmental variables that co-vary with the imaging process? To answer this question, we probe SSL representations using co-located ERA5 reanalysis variables, a global dataset of physically consistent environmental variables, including temperature, precipitation, surface solar radiation, surface pressure, and volumetric soil water. These variables are physically related to the spectral reflectance and radar backscatter recorded by Sentinel-1 and Sentinel-2, making them meaningful evaluation targets despite not being used during SSL pretraining. We complement this probing analysis with intrinsic representation metrics to characterize representation geometry and investigate how these properties relate to downstream performance and the encoding of environmental signals. Using DINO, MAE, and MoCo models trained under identical conditions, we show that representation-level metrics distinguish models with similar downstream benchmark performance, providing complementary information beyond task-driven benchmarks. We further find that the linear accessibility of environmental signals is associated with performance on environmentally dependent tasks in the PANGAEA benchmark. Finally, we release ERA5 annotations co-located with the SSL4EO dataset to enable physically grounded representation evaluation for future geospatial foundation models.

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP), a spatially aware pretext regression task that predicts the relative position and scale between a pair of disentangled local views from the same image. By modeling part-to-part relationships in a continuous geometric space, SP encourages representations to capture fine-grained spatial dependencies beyond invariant categorical semantics, thereby learning the compositional structure of visual scenes. SP is implemented as a decoupled plug-in and can be seamlessly integrated into diverse SSL frameworks. Extensive experiments show consistent improvements across image recognition, fine-grained classification, semantic segmentation, and depth estimation, as well as substantial gains in out-of-distribution robustness for object recognition. To evaluate spatial reasoning, we introduce (1) a position and scale prediction task on image patch pairs and (2) a jigsaw understanding task requiring patch reordering and recognition after reconstruction. Strong performance on these tasks indicates improved spatial structure and geometric awareness. Overall, explicitly modeling spatial information provides an effective inductive bias for SSL, leading to more structured representations and better generalization. Code and models will be released.