Report
Quantitative CLTs in Deep Neural Networks
| العنوان: | Quantitative CLTs in Deep Neural Networks |
|---|---|
| المؤلفون: | Favaro, Stefano, Hanin, Boris, Marinucci, Domenico, Nourdin, Ivan, Peccati, Giovanni |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Computer Science - Artificial Intelligence, Mathematics - Probability, Statistics - Machine Learning |
| الوصف: | We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain quantitative bounds on normal approximations valid at large but finite $n$ and any fixed network depth. Our theorems show both for the finite-dimensional distributions and the entire process, that the distance between a random fully connected network (and its derivatives) to the corresponding infinite width Gaussian process scales like $n^{-\gamma}$ for $\gamma>0$, with the exponent depending on the metric used to measure discrepancy. Our bounds are strictly stronger in terms of their dependence on network width than any previously available in the literature; in the one-dimensional case, we also prove that they are optimal, i.e., we establish matching lower bounds. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.06092 |
| رقم الانضمام: | edsarx.2307.06092 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |