Summary of On the Ability Of Deep Networks to Learn Symmetries From Data: a Neural Kernel Theory, by Andrea Perin and Stephane Deny
On the Ability of Deep Networks to Learn Symmetries from Data: A Neural Kernel Theory
by Andrea Perin, Stephane Deny
First submitted to arxiv on: 16 Dec 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 A machine learning educator writing for a technical audience can generate a medium-difficulty summary as follows: This paper investigates how deep networks can learn symmetries present in datasets, specifically focusing on supervised classification where some classes include all transformations of a cyclic group. The authors derive a neural kernel theory to analyze symmetry learning in the infinite-width limit and find that generalization is successful when class separation prevails over class-orbit density in the kernel space defined by the architecture. This occurs when classes are sufficiently distinct and class orbits are sufficiently dense. The framework also applies to equivariant architectures like CNNs, recovering their success when the architecture matches the inherent symmetry of the data. Empirically, the theory reproduces the generalization failure of finite-width networks trained on partially observed versions of rotated-MNIST. Conventional networks lack a mechanism to learn symmetries that have not been explicitly embedded in their architecture a priori. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about how machine learning models can understand patterns in data. It looks at deep neural networks and how they can learn from the symmetries present in datasets. The authors want to know if these models can generalize symmetry invariance even when some classes are only partially observed during training. They use a special type of architecture called an equivariant architecture, which is good at learning symmetries. The results show that conventional networks struggle to learn symmetries unless they are explicitly designed to do so. |
Keywords
» Artificial intelligence » Classification » Generalization » Machine learning » Supervised
