# A Variational Inequality Model for Learning Neural Networks

arXiv: https://arxiv.org/abs/2210.15064 · HTML: https://mlsanity.com/paper/2210.15064/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [A lifted Bregman strategy for training unfolded proximal neural network Gaussian denoisers](https://mlsanity.com/paper/2408.08742/) (2024)

## Abstract (arXiv)

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent training procedure consists of minimizing highly non-convex objectives based on data sets of huge dimension. In this context, current methodologies are not guaranteed to produce global solutions. We present an alternative approach which foregoes the optimization framework and adopts a variational inequality formalism. The associated algorithm guarantees convergence of the iterates to a true solution of the variational inequality and it possesses an efficient block-iterative structure. A numerical application is presented.