Rational neural networks
This work addresses the challenge of optimizing neural network architectures for better efficiency and performance, though it appears incremental as it modifies an existing component (activation functions).
The authors tackled the problem of improving neural network performance by using rational activation functions instead of ReLU, proving that rational networks approximate smooth functions more efficiently with exponentially smaller depth.
We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks with exponentially smaller depth. The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU, as we demonstrate with numerical experiments.