Summary of Unified Universality Theorem For Deep and Shallow Joint-group-equivariant Machines, by Sho Sonoda et al.
Unified Universality Theorem for Deep and Shallow Joint-Group-Equivariant Machines
by Sho Sonoda, Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda
First submitted to arxiv on: 22 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Representation Theory (math.RT); Machine Learning (stat.ML)
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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 proposed constructive universal approximation theorem for joint-group-equivariant feature maps, dubbed joint-equivariant machines, generalizes classical group-equivariance. The distribution of parameters is given in a closed-form expression called the ridgelet transform. This framework unifies the universal approximation theorems for both shallow and deep networks. Notably, fully-connected networks are not group-equivariant but are joint-group-equivariant. The theorem also provides common ground for understanding the approximation schemes of various learning machines. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way to understand how computers learn has been discovered. This breakthrough applies to many types of neural networks, from simple ones to complex deep networks. It shows that these networks can approximate any function with a high degree of accuracy. The research also reveals that some types of networks are more powerful than others. For example, networks that use joint-group-equivariant feature maps can learn and represent data in a more flexible way. This unified understanding of learning machines has many potential applications. |
