All the trajectories of an extended averaged Hebbian learning equation on the quantum state space are the e-geodesics
Yoshio Uwano · Mathematical Modelling and Geometry · 2016
In this paper, two families of trajectories on the quantum state space (QSS) originating from a synaptic-neuron model and from quantum information geometry meet together.The extended averaged Hebbian learning equation (EAHLE) on the QSS developed by the author and Yuya [1] from a Hebbian synaptic-neuron model is studied from a quantum-informationgeometric point of view.It is shown that all the trajectories of the EAHLE are the egeodesics, the autoparallel curves with respect to the exponential-type parallel transport, on the QSS.As a secondary outcome, an explicit representation of solution of the averaged Hebbian learning equation, the origin of the EAHLE, is derived from that of the e-geodesics on the QSS.