Preservation of Dynamics of Discrete Time Hopfield Neural Network: Perturbation/Quantization Analysis

EasyChair Preprint 15657

Abstract

In this research paper,  ε-perturbation  of diagonal elements of symmetric synaptic weight matrix, W   ( with ε>0 )  of  Hopfield  Associative  Memory (HAM)  ( resulting  in updated  synaptic  weight  matrix  W  bar=W+ε I )  is  assumed  to  ensure  that  the  sufficient  condition  of  convergence  theorem  is  satisfied. It is proved that under such perturbation, stable  states of HAM  based  on  synaptic  weight  matrix   W   are a  subset of  those  of  HAM  based  on W  bar .  This result is generalized to prove  that  if  W bar =W+R ,  ( where W, R   have  the  same  eigenvectors ),  the  stable  states of HAM  based  on  W   are  preserved  as  some of  those  of   W  bar .   Based on known  literature, such   perturbations  ensure  that  minimum  cut  in  the  graph  associated  with  W   is  same  as  that  associated  with W.  Also,  preservation  of  interesting  dynamics ( e.g. stable  states )  under  quantization  of  synaptic  weights  is   explored.

Keyphrases: Hopfield neural network, Quantization Analysis, convergence theorem, perturbation analysis, stable states

@booklet{EasyChair:15657,
  author    = {Rama Murthy Garimella},
  title     = {Preservation of Dynamics of Discrete Time Hopfield  Neural  Network: Perturbation/Quantization  Analysis},
  howpublished = {EasyChair Preprint 15657},
  year      = {EasyChair, 2025}}