This paper analyzes the effects of magnetic saturation, including cross-saturation and secondary saliencies, on the saliency-based sensorless control of interior permanent magnet synchronous machines. These effects are mitigated by adaptively decoupling saturation-induced saliencies via a structured neural network. This paper includes the identification of the dominant saturation-induced components of the carrier-signal current interfering with the rotor-position-dependent component being tracked, characterization of these components, and implementation of a nonlinear adaptive saturation-induced-component structured neural network model to perform their decoupling.