In this paper we address the instability issue of generative adversarial network (GAN) by proposing a new similarity metric in unitary space of Schur decomposition for 2D representations of audio and speech signals. We show that encoding departure from normality computed in this vector space into the generator optimization formulation helps to craft more comprehensive spectrograms. We demonstrate the effectiveness of binding this metric for enhancing stability in training with less mode collapse compared to baseline GANs. Experimental results on subsets of UrbanSound8k and Mozilla common voice datasets have shown considerable improvements on the quality of the generated samples measured by the Fr\échet inception distance. Moreover, reconstructed signals from these samples, have achieved higher signal to noise ratio compared to regular LS-GANs.
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