Controlling Neural Networks via Energy Dissipation

TL;DR

This paper introduces energy dissipating neural networks that iteratively optimize a cost function, providing provable guarantees for image reconstruction tasks like super-resolution and CT, ensuring adherence to data models during inference.

Contribution

The work proposes a novel neural network framework that guarantees convergence to the true data model by integrating energy-based descent with adaptive step sizes.

Findings

Guarantees convergence to the global minimum of the energy

Effective in super-resolution and CT reconstruction tasks

Extensions to convex feasibility problems demonstrated

Abstract

The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures even exhibit superior performance for the solution of (ill-posed) image reconstruction problems such as deblurring, super-resolution, or medical image reconstruction. The drawback of purely learning-based methods, however, is that they cannot provide provable guarantees for the trained network to follow a given data formation process during inference. In this work we propose energy dissipating networks that iteratively compute a descent direction with respect to a given cost function or energy at the currently estimated reconstruction. Therefore, an adaptive step size rule such as a line-search, along with a suitable number of iterations can guarantee the reconstruction to follow a given data formation model encoded in the energy to arbitrary precision, and hence control the model's behavior even during test time. We prove that under standard assumptions, descent using the direction predicted by the network converges (linearly) to the global minimum of the energy. We illustrate the effectiveness of the proposed approach in experiments on single image super resolution and computed tomography (CT) reconstruction, and further illustrate extensions to convex feasibility problems.