Implicit Regularization of the Deep Inverse Prior Trained with Inertia
Journal:
arXiv
Published Date:
Jun 3, 2025
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.
