Hopfield circuit and continuous additive bidirectional associative memories Hopfield circuit arises from if each neuron has a strictly increasing signal function and if the synaptic connection matrix is symmetric C或=克+s,m,1 ● (3-21) continuous additive bidirectional associative memories =-Ax+2S,0,)m,+1 (3-22) i=1 y,=-Ay,+∑S,xm,+I (3-23) 2002.10.8
2002.10.8 Hopfield circuit and continuous additive bidirectional associative memories Hopfield circuit arises from if each neuron has a strictly increasing signal function and if the synaptic connection matrix is symmetric = − + + (3-21) • j j j i j i i i i i S x m I R x C x ( ) ' continuous additive bidirectional associative memories = • = + + p j j j i j i S y m I 1 i i xi - A x ( ) = • = + + p i i i i j j S x m I 1 j j j y - A y ( ) (3-22) (3-23)
3,4 ADDITIVE BIVALENT FEEDBACK 如 Discrete additive activation models correspond to neurons with threshold signal function The neurons can assume only two value:ON and OFF. ON represents the signal value +1.OFF represents 0 or-1. Bivalent models can represent asynchronous and stochastic behavior
Discrete additive activation models correspond to neurons with threshold signal function 3.4 ADDITIVE BIVALENT FEEDBACK The neurons can assume only two value: ON and OFF. ON represents the signal value +1. OFF represents 0 or –1. Bivalent models can represent asynchronous and stochastic behavior
Bivalent Additive BAM BAM-bidirectional associative memory Define a discrete additive BAM with threshold signal functions,arbitrary thresholds and inputs,an arbitrary but constant synaptic connection matrix M,and discrete time steps k. x=∑S,Oy)m,+1 (3-24) i=l y1-2S(a)m,+1, (3-25) i=1 2002.10.8
2002.10.8 Bivalent Additive BAM BAM-bidirectional associative memory Define a discrete additive BAM with threshold signal functions, arbitrary thresholds and inputs,an arbitrary but constant synaptic connection matrix M,and discrete time steps k. = + = + p j i j i k j j k i x S y m I 1 1 ( ) = + = + p i ij j k i i k j y S x m I 1 1 ( ) (3-24) (3-25)
Bivalent Additive BAM -Threshold binary signal functions ifxU S,(x)={S,(x-)fx=U, (3-26) 0 if x<U 讨 >V (3-27) -For arbitrary real-value thresholds .U=(U,…,Un) for neuronsFx =(v,...,Vp)for neurons Fy 2002.10.8
2002.10.8 Bivalent Additive BAM Threshold binary signal functions For arbitrary real-value thresholds for neurons for neurons (3-26) (3-27) = = − i k i i k i k i i i k i k i i if x U S x if x U if x U S x 0 ( ) 1 ( ) 1 = = − j k j j k j k j j j k j k j j if y V S y if y V if y V S y 0 ( ) 1 ( ) 1 ( ) U U Un , , = 1 FX ( ) V V Vp , , = 1 FY
A example for BAM model Example A 4-by-3 matrix M represents the forward synaptic projections from Fx to Fy A 3-by-4 matrix MT represents the backward synaptic projections from Fy to Fx -3 2 -3 1 0 -2 1 M"- 0 3 1 M= 0 3 2 2 2 -2 1 -1
A example for BAM model Example A 4-by-3 matrix M represents the forward synaptic projections from to . A 3-by-4 matrix MT represents the backward synaptic projections from to . FX FY FY FX − − − − = 2 1 1 0 3 2 1 2 0 3 0 2 M − − − − = 2 0 2 1 0 2 3 1 3 1 0 2 T M