Equivariant Deep Equilibrium Models for Imaging Inverse Problems

• URL: http://arxiv.org/abs/2511.18667v1
• Date: Mon, 24 Nov 2025 00:43:54 GMT
• Title: Equivariant Deep Equilibrium Models for Imaging Inverse Problems
• Authors: Alexander Mehta, Ruangrawee Kitichotkul, Vivek K Goyal, Julián Tachella,
• Abstract summary: Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data.<n>We show that backpropagation can be implemented modularly, simplifying training.<n>We find evidence that EI-trained DEQs approximate the proximal map of an invariant prior.
• Score: 50.91616288661183
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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