Geometric Calculi and Automatic Learning An Outline

Signal representation and processing are the backbone of mathematically-aided engineering. Among the myriad of ideas and results in that realm, many sorts of algorithms and techniques capable of learning from experience have taken the stage in the last decades, with a crescendo of great successes in a variety of fronts in recent years. This paper provides a sketchy outline of those developments that seem more relevant or promising in view of their bearing on the geometric calculus (multivector) representations of signals and the concomitant automatic learning algorithms. The corresponding artificial neurons, and their organization in networks, may be seen as a way to transcend the biologically inspired neuron networks much as the wheel or aviation transcended legs or bird flight. Recent developments suggest that there are exciting research opportunities ahead.