Generalization and Guarantees in Deep Learning for Inverse Problems

Characterize the generalization behavior of deep learning-based methods for inverse problems across diverse datasets and ascertain the trade-off between empirical performance and robust theoretical guarantees such as stability, robustness, and convergence.

Background

The authors emphasize a paradigm shift toward data-driven approaches that often outperform handcrafted priors. However, this comes with interpretability challenges and the need for rigorous guarantees, especially in safety-critical domains.

They explicitly note that generalization across datasets and balancing empirical performance against theoretical assurances remain unresolved, motivating structured learning and new theory tailored to deep learning in inverse problems.