Understanding Musical Sound with Forward Models and Physical Models

This research report describes an approach to parameter estimation for physical models of sound-generating systems using distal teachers and forward models, [Jordan and Rumelhart, 1992, Jordan, 1990]. The general problem is to nd an inverse model of a sound-generating system that transforms sounds to action parameters; these parameters constitute a model-based description of the sound. We rst show that a two-layer feed-forward model is capable of performing inverse mappings for a simple physical model of a string. We refer to this learning strategy as direct inverse modeling; it requires an explicit teacher and it is only suitable for convex regions of the parameter space. A model of two strings was implemented that had non-convex regions in its parameter space. We show how the direct modeling strategy failed at the task of learning the inverse model in this case and that forward models can be used, in conjunction with distal teachers, to bias the learning of an inverse model so that non-convex regions are mapped to single points in the parameter space. Our results show that forward models are appropriate for learning to map sounds to parametric representations.