# Constrained Deep Learning using Conditional Gradient and Applications in Computer Vision

arXiv: https://arxiv.org/abs/1803.06453 · HTML: https://mlsanity.com/paper/1803.06453/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2018.

## Built on by (most cited first, 7 of 7)

- [Model-Based Domain Generalization](https://mlsanity.com/paper/2102.11436/) (2021)
- [Adversarial Robustness with Semi-Infinite Constrained Learning](https://mlsanity.com/paper/2110.15767/) (2021)
- [Compression-aware Training of Neural Networks using Frank-Wolfe](https://mlsanity.com/paper/2205.11921/) (2022)
- [Don't Be Greedy, Just Relax! Pruning LLMs via Frank-Wolfe](https://mlsanity.com/paper/2510.13713/) (2025)
- [Scalable Projection-Free Optimization](https://mlsanity.com/paper/2105.03527/) (2021)
- [Neuro-physical dynamic load modeling using differentiable parametric optimization](https://mlsanity.com/paper/2203.10582/) (2022)
- [Soft-Constrained Optimization of Latent Space in Variational Autoencoders](https://mlsanity.com/paper/2607.23751/) (2026)

## Abstract (arXiv)

A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better accuracy to compression. But support for general constraints within widely used libraries remains scarce and their broader deployment within many applications that can benefit from them remains under-explored. Part of the reason is that Stochastic gradient descent (SGD), the workhorse for training deep neural networks, does not natively deal with constraints with global scope very well. In this paper, we revisit a classical first order scheme from numerical optimization, Conditional Gradients (CG), that has, thus far had limited applicability in training deep models. We show via rigorous analysis how various constraints can be naturally handled by modifications of this algorithm. We provide convergence guarantees and show a suite of immediate benefits that are possible -- from training ResNets with fewer layers but better accuracy simply by substituting in our version of CG to faster training of GANs with 50% fewer epochs in image inpainting applications to provably better generalization guarantees using efficiently implementable forms of recently proposed regularizers.