Stochastic Shadow-Cutting Machine

Abstract

Recently, a new concept called shadow-cuts has recently been proposed for a fully-connected graph whose edge matrix is Hermitian with arbitrary complex numbers. Each neuron is associated with a phase and the sum of shadow cuts is defined as the sum of inter-cluster phased edges. However, the shadow-cut machine is 100% deterministic and therefore its modeling capacity is relatively limited. In this brief, we (i) extend it to stochastic domain which yields the so-called 'Stochastic Shadow-Cutting Machine' (SSCM), and (ii) show that choosing the energy function of the SSCM as the sum of shadow-cuts yields similar phenomena as in those from the statistical mechanics like Ising model, xy-model, pott model, Stochastic Hopfield Networks, etc., Thus, the proposed SSCM provides a general framework to examine various phenomena like the phase changes of the SSCM as the temperature increases. Because the SSCM in low temperatures behaves as an Associative Memory system (i.e., 'ferro-magnet'), it is possible to examine the critical temperatures when the SSCM cannot 'recover/remember' the patterns any more (i.e. 'anti-ferromagnet'), which we define as 'phase change' of the SSCM.