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Equivariant Deep Equilibrium Models for Imaging Inverse Problems

Year: 2026

Type: conference-paper

Abstract: Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed point of a learned operator. However, training DEQs with complex EI losses requires implicit differentiation through fixed-point computations, whose implementation can be challenging. We show that backpropagation can be implemented modularly, simplifying training. Experiments demonstrate that DEQs trained with implicit differentiation outperform those trained with Jacobian-free backpropagation and other baseline methods. Additionally, we find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.

Source: IEEE International Conference on Acoustics Speech and Signal Processing

DOI: 10.1109/icassp55912.2026.11463665

Authors: Alexander Mehta, Ruangrawee Kitichotkul, Vivek K Goyal, Julián Tachella

Institutions: University of California, Berkeley, Boston University, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de Physique de l'ENS de Lyon

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4417060337

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