Equivariant Splitting: Self-supervised learning from incomplete data

2025-10-01

AI Summary

This work addresses inverse problem reconstruction—such as image inpainting, accelerated MRI, and compressed sensing—under a challenging setting: only a single incomplete forward model (e.g., low-rank or highly underdetermined) is available, and no ground-truth labels exist. We propose a novel self-supervised learning framework centered on an equivariant reconstruction network, whose output is theoretically guaranteed to be equivariant to transformations of the observed measurement. Leveraging this property, we design a self-supervised split loss that provides an unbiased estimator—in expectation—of the ideal supervised loss. Crucially, our method requires neither clean labels nor auxiliary data assumptions; it relies solely on one degraded observation and structural priors encoded in the forward model. Extensive experiments demonstrate that our approach significantly outperforms existing self-supervised and weakly supervised methods, achieving state-of-the-art reconstruction quality—especially in highly underdetermined regimes.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for training is expensive or even impossible. In this paper, we propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model. We introduce a new definition of equivariance in the context of reconstruction networks, and show that the combination of self-supervised splitting losses and equivariant reconstruction networks results in unbiased estimates of the supervised loss. Through a series of experiments on image inpainting, accelerated magnetic resonance imaging, and compressive sensing, we demonstrate that the proposed loss achieves state-of-the-art performance in settings with highly rank-deficient forward models.

Problem

• Self-supervised learning for inverse problems without ground-truth data
• Handling single incomplete observation models in reconstruction networks
• Achieving unbiased supervised loss via equivariance and splitting losses

Innovation

• Self-supervised learning from incomplete data
• Equivariant reconstruction networks for unbiased estimates
• Combining splitting losses with equivariant networks