Report
On the Stability of a non-hyperbolic nonlinear map with non-bounded set of non-isolated fixed points with applications to Machine Learning
| العنوان: | On the Stability of a non-hyperbolic nonlinear map with non-bounded set of non-isolated fixed points with applications to Machine Learning |
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| المؤلفون: | Hansen, Roberta, Vera, Matias, Estienne, Lautaro, Ferrer, Luciana, Piantanida, Pablo |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Mathematics - Dynamical Systems |
| الوصف: | This paper deals with the convergence analysis of the SUCPA (Semi Unsupervised Calibration through Prior Adaptation) algorithm, defined from a first-order non-linear difference equations, first developed to correct the scores output by a supervised machine learning classifier. The convergence analysis is addressed as a dynamical system problem, by studying the local and global stability of the nonlinear map derived from the algorithm. This map, which is defined by a composition of exponential and rational functions, turns out to be non-hyperbolic with a non-bounded set of non-isolated fixed points. Hence, a non-standard method for solving the convergence analysis is used consisting of an ad-hoc geometrical approach. For a binary classification problem (two-dimensional map), we rigorously prove that the map is globally asymptotically stable. Numerical experiments on real-world application are performed to support the theoretical results by means of two different classification problems: Sentiment Polarity performed with a Large Language Model and Cat-Dog Image classification. For a greater number of classes, the numerical evidence shows the same behavior of the algorithm, and this is illustrated with a Natural Language Inference example. The experiment codes are publicly accessible online at the following repository: https://github.com/LautaroEst/sucpa-convergence |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.03051 |
| رقم الانضمام: | edsarx.2401.03051 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |