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Traditional energy-based learning models associate a single energy metric toeach configuration of variables involved in the underlying optimizationprocess. Such models associate the lowest energy state to the optimalconfiguration of variables under consideration, and are thus inherentlydissipative. In this paper we propose an energy-efficient learning frameworkthat exploits structural and functional similarities between a machine learningnetwork and a general electrical network satisfying the Tellegen's theorem. Incontrast to the standard energy-based models, the proposed formulationassociates two energy components, namely, active and reactive energy to thenetwork. This ensures that the network's active-power is dissipated only duringthe process of learning, whereas the reactive-power is maintained to be zero atall times. As a result, in steady-state, the learned parameters are stored andself-sustained by electrical resonance determined by the network's nodalinductances and capacitances. Based on this approach, this paper introducesthree novel concepts: (a) A learning framework where the network's active-powerdissipation is used as a regularization for a learning objective function thatis subjected to zero total reactive-power constraint; (b) A dynamical systembased on complex-domain, continuous-time growth transforms which optimizes thelearning objective function and drives the network towards electrical resonanceunder steady-state operation; and (c) An annealing procedure that controls thetrade-off between active-power dissipation and the speed of convergence. As arepresentative example, we show how the proposed framework can be used fordesigning resonant support vector machines (SVMs), where we show that thesupport-vectors correspond to an LC network with self-sustained oscillations.

Resonant Machine Learning Based on Complex Growth Transform Dynamical Systems