Augmented field and augmented matrix Augmented field FxFy一h= M connects Fx to fy, n connects fy to Fx then the augmented field Fz intraconnects to itself by the square block matrix B B 2002.10.8
2002.10.8 Augmented field and augmented matrix Augmented field M connects to ,N connects to then the augmented field intraconnects to itself by the square block matrix B = Y X Z F F F FX FY FZ FX FY FY FX = 0 0 N M B
Augmented field and augmented matrix In the bam case when n=m then b=b hence a Bam symmetries an arbitrary rectangular matrix M In the general case, PM P is n-by-n matrix Qisp- by-p matriⅸx If and only if, n=M'P=p =0 the neurons in FZ are symmetrically intraconnected 2002.10.8
2002.10.8 Augmented field and augmented matrix In the BAM case,when then hence a BAM symmetries an arbitrary rectangular matrix M. In the general case, P is n-by-n matrix. Q is p-by-p matrix. M T N = T B = B = N Q P M C If and only if, the neurons in are symmetrically intraconnected M T N = T P = P T Q = Q T C = C FZ
3.3 ADDITIVE ACTIVATION MODELS Define additive activation model n+p coupled first-order differential equations defines the additive activation model y1=Ay1+S(xm+1(3-15 x=Ax1+∑S(y)mn+1(3-16) 2002.10.8
2002.10.8 3.3 ADDITIVE ACTIVATION MODELS Define additive activation model n+p coupled first-order differential equations defines the additive activation model = • = + + p j j j j i i S y n I 1 x -A x ( ) i i i = • = + + p j i i i j j S x m I 1 y -A y ( ) j j j （3－15） （3－16）
additive activation model define a The additive autoassociative model correspond to a system of n coupled first-order differential equations x=Ax1+∑S(x)mn+1(3-17) 2002.10.8
2002.10.8 additive activation model define The additive autoassociative model correspond to a system of n coupled first-order differential equations （3－17） = • = + + p j j j j i i S x m I 1 i i xi - A x ( )