Equivariant Deep Equilibrium Models for Imaging Inverse Problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914168544690176 |
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| author | Mehta, Alexander Kitichotkul, Ruangrawee Goyal, Vivek K Tachella, Julián |
| author_facet | Mehta, Alexander Kitichotkul, Ruangrawee Goyal, Vivek K Tachella, Julián |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Deep Equilibrium Models for Imaging Inverse Problems Mehta, Alexander Kitichotkul, Ruangrawee Goyal, Vivek K Tachella, Julián Image and Video Processing Machine Learning Signal Processing 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. |
| title | Equivariant Deep Equilibrium Models for Imaging Inverse Problems |
| topic | Image and Video Processing Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2511.18667 |