We propose to formulate the training of neural networks with side optimization goals, such as obtaining structured weight matrices, as lexicographic optimization problem. The lexicographic order can be maintained during training by optimizing the side-optimization goal exclusively in the null space of batch activations. We call the resulting training method Safe Regularization, because the side optimization goal can be safely integrated into the training with limited influence on the main optimization goal. Moreover, this results in a higher robustness regarding the choice of regularization hyperparameters. We validate our training method with multiple real-world regression data sets with the side-optimization goal of obtaining sparse weight matrices.     «

We propose to formulate the training of neural networks with side optimization goals, such as obtaining structured weight matrices, as lexicographic optimization problem. The lexicographic order can be maintained during training by optimizing the side-optimization goal exclusively in the null space of batch activations. We call the resulting training method Safe Regularization, because the side optimization goal can be safely integrated into the training with limited influence on the main optimi...     »