Tanis, Oscar (2022) Statistical Mechanics of a Nonlinear Learning System. Master's Thesis / Essay, Physics.
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Abstract
Statistical mechanics can give valuable fundamental insight into the qualities of Artificial Intelligence (AI) architectures. Modern developments in AI architectures call for further insight into the qualities of fundamentally nonlinear classifiers. The off-line generalizing behavior of a multiplicative nonlinear extension of the perceptron was explored using mathematical methods derived from statistical mechanics. While a general treatment is hindered by challenges related to nonlinearity, exact results were obtained for a simplified low-dimensional binary version of the system in the limits of high and low temperature. At high temperature, the generalization error was found to conform to a quotient of exponential functions of the number of training examples presented, while in the low temperature limit the generalization error conforms to a sum of exponential decaying functions. These results may facilitate fundamental comparison with neural networks’ performance on identical tasks, which may motivate whether nonlinear architectures can be competitive in learning nonlinear behavior.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Jansen, T.L.C. and Banerjee, T. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 01 Apr 2022 08:42 |
| Last Modified: | 01 Apr 2022 08:42 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/26806 |
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