تقرير
Continuous limits of residual neural networks in case of large input data
| العنوان: | Continuous limits of residual neural networks in case of large input data |
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| المؤلفون: | Herty, M., Thuenen, A., Trimborn, T., Visconti, G. |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, Mathematics - Optimization and Control, 35Q83, 49J15, 49J20, 92B20 |
| الوصف: | Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean--field limit and show well--posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2112.14150 |
| رقم الأكسشن: | edsarx.2112.14150 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |