Stochastic Shadow-Cutting Machine

Zekeriya Uykan*, Riku Jantti

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

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.

Original languageEnglish
Title of host publication2023 31st Telecommunications Forum, TELFOR 2023 - Proceedings
PublisherIEEE
Number of pages4
ISBN (Electronic)979-8-3503-0313-1
DOIs
Publication statusPublished - 1 Jan 2024
MoE publication typeA4 Conference publication
EventTelecommunications Forum - Belgrade, Serbia
Duration: 21 Nov 202322 Nov 2023

Publication series

Name2023 31st Telecommunications Forum, TELFOR 2023 - Proceedings

Conference

ConferenceTelecommunications Forum
Abbreviated titleTELFOR
Country/TerritorySerbia
CityBelgrade
Period21/11/202322/11/2023

Keywords

  • associative memory systems
  • Graphs with complex-valued edges
  • inter-cluster phased edges
  • Ising model
  • statistical mechanics
  • Stochastic Shadow-Cutting Machine

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