Implicit Regularization of the Deep Inverse Prior Trained with Inertia

• URL: http://arxiv.org/abs/2506.02986v1
• Date: Tue, 03 Jun 2025 15:24:54 GMT
• Title: Implicit Regularization of the Deep Inverse Prior Trained with Inertia
• Authors: Nathan Buskulic, Jalal Fadil, Yvain Quéau,
• Abstract summary: We provide convergence and recovery guarantees for self-supervised neural networks applied to inverse problems.<n>We show that training a network with our inertial algorithm enjoys similar recovery guarantees though with a less sharp linear convergence rate.
• Score: 2.089191490381739
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to inverse problems, such as Deep Image/Inverse Prior, and trained with inertia featuring both viscous and geometric Hessian-driven dampings. We study both the continuous-time case, i.e., the trajectory of a dynamical system, and the discrete case leading to an inertial algorithm with an adaptive step-size. We show in the continuous-time case that the network can be trained with an optimal accelerated exponential convergence rate compared to the rate obtained with gradient flow. We also show that training a network with our inertial algorithm enjoys similar recovery guarantees though with a less sharp linear convergence rate.

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