| Abstract: |
| Deep learning has made significant progress in data science and natural science. Some studies have linked deep neural networks to dynamical systems, but the network structure is restricted to a residual network. It is known that residual networks can be regarded as a numerical discretization of dynamical systems. In this talk, we consider the traditional network structure and prove that vanilla feedforward networks can also be used for the numerical discretization of dynamical systems, where the width of the network is equal to the input and output dimensions. The proof is based on the properties of the leaky-ReLU function and the numerical technique of the splitting method for solving differential equations. The results could provide a new perspective for understanding the approximation properties of feedforward neural networks. In particular, the minimum width of neural networks for universal approximation can be derived and the relationship between mapping conpositions and regular languages can be constructed. |
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