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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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GrooveSquid.com Paper Summaries

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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