PhaseDNN - A Parallel Phase Shift Deep Neural Network for Adaptive Wideband Learning

TL;DR

PhaseDNN introduces a parallel neural network approach using phase shifts to efficiently learn high-dimensional functions across a wide frequency spectrum, accelerating convergence and improving uniformity in wideband learning.

Contribution

The paper presents a novel parallel neural network architecture, PhaseDNN, that employs phase shifts to enable efficient wideband frequency learning in high-dimensional functions.

Findings

Demonstrates uniform learning from low to high frequencies.

Achieves faster convergence in high-frequency ranges.

Validates effectiveness through numerical experiments.

Abstract

In this paper, we propose a phase shift deep neural network (PhaseDNN) which provides a wideband convergence in approximating a high dimensional function during its training of the network. The PhaseDNN utilizes the fact that many DNN achieves convergence in the low frequency range first, thus, a series of moderately-sized of DNNs are constructed and trained in parallel for ranges of higher frequencies. With the help of phase shifts in the frequency domain, implemented through a simple phase factor multiplication on the training data, each DNN in the series will be trained to approximate the target function's higher frequency content over a specific range. Due to the phase shift, each DNN achieves the speed of convergence as in the low frequency range. As a result, the proposed PhaseDNN system is able to convert wideband frequency learning to low frequency learning, thus allowing a uniform learning to wideband high dimensional functions with frequency adaptive training. Numerical results have demonstrated the capability of PhaseDNN in learning information of a target function from low to high frequency uniformly.