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 \textit{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 \textbf{($\sim$ 22M vs $\sim$ 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.