Summary of Hamiltonian Mechanics Of Feature Learning: Bottleneck Structure in Leaky Resnets, by Arthur Jacot et al.
Hamiltonian Mechanics of Feature Learning: Bottleneck Structure in Leaky ResNets
by Arthur Jacot, Alexandre Kaiser
First submitted to arxiv on: 27 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
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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 paper studies Leaky ResNets, which are a type of neural network that interpolates between ResNets and fully connected nets based on an effective depth hyperparameter. The authors also explore representation geodesics, which are continuous paths in representation space from input to output that minimize the parameter norm of the network. They provide a Lagrangian and Hamiltonian reformulation, highlighting the importance of kinetic energy and potential energy in favoring small layer derivatives and low-dimensional representations, respectively. This balance between the two energies offers an intuitive understanding of feature learning in ResNets, which is used to explain the emergence of a bottleneck structure observed in previous work. The authors also train with an adaptive layer step-size to adapt to the separation of timescales. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores how neural networks like Leaky ResNets learn features from data. It shows that these networks can be thought of as moving along a path in “representation space” that tries to find the simplest way to represent the data. The authors give a new way to understand this process by using ideas from physics, where they talk about “kinetic energy” and “potential energy”. This helps explain why some neural networks have a “bottleneck” or a special layer that is important for learning features. The paper also shows how to train these networks in a way that takes into account this bottleneck. |
Keywords
* Artificial intelligence * Hyperparameter * Neural network
