Analytic function approximation by path norm regularized deep networks
arXiv:2104.02095v44 citations
AI Analysis
This provides a theoretical foundation for function approximation in machine learning, though it appears incremental as it builds on existing regularization techniques.
The paper tackles the problem of approximating analytic functions using neural networks with absolute value activation and path norm regularization, achieving ε-approximation with logarithmic dependence on 1/ε in depth, width, and weights.
We show that neural networks with absolute value activation function and with the path norm, the depth, the width and the network weights having logarithmic dependence on $1/\varepsilon$ can $\varepsilon$-approximate functions that are analytic on certain regions of $\mathbb{C}^d$.