ENN: A Neural Network with DCT Adaptive Activation Functions
This addresses the expressiveness limitation in neural networks for researchers and practitioners, though it appears incremental as it builds on existing activation function methods with a new parametrization.
The paper tackles the problem of fixed activation functions in neural networks by introducing ENN, which models activation functions using the Discrete Cosine Transform and adapts them during training, resulting in performance that outperforms state-of-the-art benchmarks with above a 40% gap in accuracy in some scenarios.
The expressiveness of neural networks highly depends on the nature of the activation function, although these are usually assumed predefined and fixed during the training stage. Under a signal processing perspective, in this paper we present Expressive Neural Network (ENN), a novel model in which the non-linear activation functions are modeled using the Discrete Cosine Transform (DCT) and adapted using backpropagation during training. This parametrization keeps the number of trainable parameters low, is appropriate for gradient-based schemes, and adapts to different learning tasks. This is the first non-linear model for activation functions that relies on a signal processing perspective, providing high flexibility and expressiveness to the network. We contribute with insights in the explainability of the network at convergence by recovering the concept of bump, this is, the response of each activation function in the output space. Finally, through exhaustive experiments we show that the model can adapt to classification and regression tasks. The performance of ENN outperforms state of the art benchmarks, providing above a 40% gap in accuracy in some scenarios.