Summary of Newton Losses: Using Curvature Information For Learning with Differentiable Algorithms, by Felix Petersen et al.
Newton Losses: Using Curvature Information for Learning with Differentiable Algorithms
by Felix Petersen, Christian Borgelt, Tobias Sutter, Hilde Kuehne, Oliver Deussen, Stefano Ermon
First submitted to arxiv on: 24 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper addresses a common issue in training neural networks with custom objectives, such as ranking losses and shortest-path losses. These objectives are often non-differentiable, making it challenging to optimize the network using gradient-based methods. To overcome this hurdle, researchers have resorted to continuously relaxing these objectives to provide gradients, enabling learning. However, these differentiable relaxations can be non-convex and exhibit vanishing or exploding gradients, further complicating optimization. In response, the authors propose Newton Losses, a method that leverages the second-order information of the loss function via its empirical Fisher and Hessian matrices. Instead of training the network with second-order techniques, the authors only utilize the loss function’s second-order information to replace it with a Newton Loss, while still training the network using gradient descent. This approach is computationally efficient and achieves significant improvements for less-optimized differentiable algorithms. The authors demonstrate the effectiveness of Newton Losses on eight differentiable algorithms for sorting and shortest-paths. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper solves a problem with training neural networks that have special goals, like ranking things or finding the shortest path. These goals are hard to work with because they aren’t easily changed (non-differentiable). To get around this issue, people usually relax these goals so they can be changed and the network can learn. However, these relaxed goals can also cause problems, making it harder to optimize the network. The authors of this paper came up with a new way to solve this problem called Newton Losses. Instead of changing the entire goal, they only use the important parts of it to make the optimization process easier and more efficient. They tested their method on several different algorithms for sorting and finding the shortest path and saw big improvements. |
Keywords
» Artificial intelligence » Gradient descent » Loss function » Optimization
