Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
This work introduces a general framework for adaptive activation functions in neural networks, potentially benefiting researchers and practitioners in deep learning by improving efficiency and performance, though it appears incremental as it builds on existing network architectures.
The authors tackled the problem of designing neural networks with adaptive activation functions by proposing Kronecker neural networks (KNNs), which use the Kronecker product to create wide networks with fewer parameters, and they demonstrated faster loss decay and global convergence under certain conditions, with empirical validation across various tasks.
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of constructing a very wide network while keeping the number of parameters low. Our theoretical analysis reveals that under suitable conditions, KNNs induce a faster decay of the loss than that by the feed-forward networks. This is also empirically verified through a set of computational examples. Furthermore, under certain technical assumptions, we establish global convergence of gradient descent for KNNs. As a specific case, we propose the Rowdy activation function that is designed to get rid of any saturation region by injecting sinusoidal fluctuations, which include trainable parameters. The proposed Rowdy activation function can be employed in any neural network architecture like feed-forward neural networks, Recurrent neural networks, Convolutional neural networks etc. The effectiveness of KNNs with Rowdy activation is demonstrated through various computational experiments including function approximation using feed-forward neural networks, solution inference of partial differential equations using the physics-informed neural networks, and standard deep learning benchmark problems using convolutional and fully-connected neural networks.