NLDSI-BWE: Non Linear Dynamical Systems-Inspired Multi Resolution Discriminators for Speech Bandwidth Extension

In this paper, we design two nonlinear dynamical systems-inspired discriminators -- the Multi-Scale Recurrence Discriminator (MSRD) and the Multi-Resolution Lyapunov Discriminator (MRLD) -- to explicitly model the inherent deterministic chaos of speech. MSRD is designed based on Recurrence representations to capture self-similarity dynamics. MRLD is designed based on Lyapunov exponents to capture nonlinear fluctuations and sensitivity to initial conditions. Through extensive design optimization and the use of depthwise-separable convolutions in the discriminators, our framework surpasses prior AP-BWE model with a 44x reduction in the discriminator parameter count (22M vs 0. 48M). To the best of our knowledge, for the first time, this paper demonstrates how BWE can be supervised by the subtle non-linear chaotic physics of voiced sound production to achieve a significant reduction in the discriminator size.