Summary of Keep the Momentum: Conservation Laws Beyond Euclidean Gradient Flows, by Sibylle Marcotte et al.
Keep the Momentum: Conservation Laws beyond Euclidean Gradient Flows
by Sibylle Marcotte, Rémi Gribonval, Gabriel Peyré
First submitted to arxiv on: 21 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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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 A novel framework is proposed to characterize all conservation laws in the context of momentum-based dynamics for non-Euclidean geometries and neural networks. The study reveals that the conservation laws exhibit temporal dependence, unlike those in Euclidean gradient flow dynamics. Furthermore, the transition from gradient flows to momentum dynamics can result in a “conservation loss.” The research focuses on linear and ReLU neural networks, demonstrating that while there are fewer momentum conservation laws for linear networks in sufficiently over-parameterized regimes, no conservation law remains for ReLU networks. This phenomenon is also observed in non-Euclidean metrics, used in applications such as Nonnegative Matrix Factorization (NMF). |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this paper, scientists explore how to understand and work with something called “conservation laws” in a new way. They look at two different ways that data flows through computer programs, and they find some surprising differences between them. They also study what happens when you switch from one way of working to the other. This helps us learn more about how computers can be used for important tasks like image and sound recognition. |
Keywords
» Artificial intelligence » Relu
