# Controlling Neural Networks via Energy Dissipation

arXiv: https://arxiv.org/abs/1904.03081 · HTML: https://mlsanity.com/paper/1904.03081/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2019.

## Built on by (most cited first, 12 of 12)

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- [PAC-Bayesian Learning of Optimization Algorithms](https://mlsanity.com/paper/2210.11113/) (2022)
- [Hierarchical Optimization-Derived Learning](https://mlsanity.com/paper/2302.05587/) (2023)
- [From Learning to Optimize to Learning Optimization Algorithms](https://mlsanity.com/paper/2405.18222/) (2024)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [A Generalization Result for Convergence in Learning-to-Optimize](https://mlsanity.com/paper/2410.07704/) (2024)

## Abstract (arXiv)

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.