TY - GEN

T1 - Stochastic Shadow-Cutting Machine

AU - Uykan, Zekeriya

AU - Jantti, Riku

N1 - Publisher Copyright:
© 2023 IEEE.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - 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.

AB - 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.

KW - associative memory systems

KW - Graphs with complex-valued edges

KW - inter-cluster phased edges

KW - Ising model

KW - statistical mechanics

KW - Stochastic Shadow-Cutting Machine

UR - http://www.scopus.com/inward/record.url?scp=85183472800&partnerID=8YFLogxK

U2 - 10.1109/TELFOR59449.2023.10372707

DO - 10.1109/TELFOR59449.2023.10372707

M3 - Conference article in proceedings

AN - SCOPUS:85183472800

T3 - 2023 31st Telecommunications Forum, TELFOR 2023 - Proceedings

BT - 2023 31st Telecommunications Forum, TELFOR 2023 - Proceedings

PB - IEEE

T2 - Telecommunications Forum

Y2 - 21 November 2023 through 22 November 2023

ER -