Summary of Topological Obstruction to the Training Of Shallow Relu Neural Networks, by Marco Nurisso et al.
Topological obstruction to the training of shallow ReLU neural networks
by Marco Nurisso, Pierrick Leroy, Francesco Vaccarino
First submitted to arxiv on: 18 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Algebraic Geometry (math.AG); Algebraic Topology (math.AT)
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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 The study examines the relationship between the geometry of the loss landscape and optimization trajectories in shallow ReLU neural networks trained using gradient flow. The research reveals the presence of topological obstruction in the loss landscape, which is attributed to the homogeneous nature of the ReLU activation function. This obstruction constrains the training trajectories to lie on a product of quadric hypersurfaces whose shape depends on the initialization of the network’s parameters. The paper discusses how this obstruction can limit the set of reachable parameters during training and proves that these quadrics can have multiple connected components, making the global optimum unreachable in certain cases. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This study explores how simple neural networks behave when trained using gradient flow. It finds that the shape of the loss landscape is influenced by the activation function used. This means that the path that the network takes during training is restricted to specific areas, making it harder for the network to reach its optimal performance. The research shows that this limitation can make it impossible to find the best solution. |
Keywords
» Artificial intelligence » Optimization » Relu
