Summary of The Geometry Of the Set Of Equivalent Linear Neural Networks, by Jonathan Richard Shewchuk and Sagnik Bhattacharya
The Geometry of the Set of Equivalent Linear Neural Networks
by Jonathan Richard Shewchuk, Sagnik Bhattacharya
First submitted to arxiv on: 23 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Geometry (cs.CG)
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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 characterizes the geometry and topology of the set of weight vectors that compute the same linear transformation in a neural network. It defines the fiber of W as the set of weight vectors that produce the same output under matrix multiplication, and shows that this fiber is an algebraic variety. The authors then stratify the fiber into manifolds of varying dimensions, called strata, and derive their dimensions and relationships. They also show how to determine the tangent and normal spaces at each point on a given stratum. This research provides a deeper understanding of the geometry of neural networks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies the patterns in the weights of a special kind of computer program called a neural network. It looks at the set of all possible weight combinations that produce the same result, and breaks it down into smaller parts or “strata”. The researchers figure out how many dimensions these strata have and how they fit together. They also show how to find the direction and normal direction of each point on one of these strata. This helps us better understand how neural networks work. |
Keywords
» Artificial intelligence » Neural network
