@inproceedings{
petersen2024newton,
title={Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms},
author={Felix Petersen and Christian Borgelt and Tobias Sutter and Hilde Kuehne and Oliver Deussen and Stefano Ermon},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=vjAORqq71s}
}
When training neural networks with custom objectives, such as ranking losses and shortest-path losses, a common problem is that they are, per se, non-differentiable. A popular approach is to continuously relax the objectives to provide gradients, enabling learning. However, such differentiable relaxations are often non-convex and can exhibit vanishing and exploding gradients, making them (already in isolation) hard to optimize. Here, the loss function poses the bottleneck when training a deep neural network. We present Newton Losses, a method for improving the performance of existing hard to optimize losses by exploiting their second-order information via their empirical Fisher and Hessian matrices. Instead of training the neural network with second-order techniques, we only utilize the loss function's second-order information to replace it by a Newton Loss, while training the network with gradient descent.  This makes our method computationally efficient. We apply Newton Losses to eight differentiable algorithms for sorting and shortest-paths, achieving significant improvements for less-optimized differentiable algorithms, and consistent improvements, even for well-optimized differentiable algorithms.
Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms
Felix Petersen Christian Borgelt Tobias Sutter Hilde Kuehne Oliver Deussen Stefano Ermon