Summary of On the Stability Of a Non-hyperbolic Nonlinear Map with Non-bounded Set Of Non-isolated Fixed Points with Applications to Machine Learning, by Roberta Hansen et al.
On the Stability of a non-hyperbolic nonlinear map with non-bounded set of non-isolated fixed points with applications to Machine Learning
by Roberta Hansen, Matias Vera, Lautaro Estienne, Luciana Ferrer, Pablo Piantanida
First submitted to arxiv on: 5 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Dynamical Systems (math.DS)
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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 SUCPA algorithm, developed to correct supervised machine learning classifier scores, is analyzed for convergence as a dynamical system. The non-linear map derived from the algorithm is found to be non-hyperbolic with non-isolated fixed points, requiring an ad-hoc geometrical approach for convergence analysis. For binary classification problems, global asymptotic stability is proven, while numerical experiments on real-world applications, including sentiment polarity and cat-dog image classification, support the theoretical results. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper studies a way to correct mistakes made by machine learning algorithms called SUCPA. The authors look at how this algorithm works over time and prove that it’s stable for certain types of problems. They also show examples of using this algorithm to classify things like whether a sentence is positive or negative, and whether an image shows a cat or dog. You can find the code they used online. |
Keywords
* Artificial intelligence * Classification * Image classification * Machine learning * Supervised
