Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms
This addresses the bottleneck of vanishing and exploding gradients in custom objectives like ranking and shortest-path losses for machine learning practitioners, though it is incremental as it builds on existing differentiable relaxations.
The paper tackles the problem of non-differentiable objectives in neural network training by introducing Newton Losses, which use second-order information to replace hard-to-optimize losses, resulting in significant improvements for eight differentiable algorithms in sorting and shortest-paths.
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.