Summary of Stochastic Rounding Implicitly Regularizes Tall-and-thin Matrices, by Gregory Dexter et al.
Stochastic Rounding Implicitly Regularizes Tall-and-Thin Matrices
by Gregory Dexter, Christos Boutsikas, Linkai Ma, Ilse C.F. Ipsen, Petros Drineas
First submitted to arxiv on: 18 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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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 authors investigate stochastic nearness rounding of real matrices with many more rows than columns, motivated by its popularity in machine learning for training large-scale deep neural networks. The paper provides theoretical evidence and experimental evaluation showing that the smallest singular value of a stochastically rounded matrix is well bounded away from zero, regardless of the original matrix’s closeness to being rank-deficient or if it is indeed rank-deficient. This implicitly regularizes tall and skinny matrices to have full column rank. The proofs rely on results in random matrix theory and the idea that stochastic rounding errors do not concentrate in low-dimensional column spaces. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Stochastic nearness rounding helps make big neural networks work better by reducing problems with “tall and skinny” matrices, which are common in deep learning. The authors show that this method can automatically fix issues with these types of matrices, making it a useful tool for training large-scale models. |
Keywords
* Artificial intelligence * Deep learning * Machine learning
