تقرير
Analytical Solution of a Three-layer Network with a Matrix Exponential Activation Function
| العنوان: | Analytical Solution of a Three-layer Network with a Matrix Exponential Activation Function |
|---|---|
| المؤلفون: | Gai, Kuo, Zhang, Shihua |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning |
| الوصف: | In practice, deeper networks tend to be more powerful than shallow ones, but this has not been understood theoretically. In this paper, we find the analytical solution of a three-layer network with a matrix exponential activation function, i.e., $$ f(X)=W_3\exp(W_2\exp(W_1X)), X\in \mathbb{C}^{d\times d} $$ have analytical solutions for the equations $$ Y_1=f(X_1),Y_2=f(X_2) $$ for $X_1,X_2,Y_1,Y_2$ with only invertible assumptions. Our proof shows the power of depth and the use of a non-linear activation function, since one layer network can only solve one equation,i.e.,$Y=WX$. Comment: 8 pages,1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.02540 |
| رقم الأكسشن: | edsarx.2407.02540 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |