By David S. Touretzky, Jeffrey L. Elman, Terrence J. Sejnowski
Connectionist types
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Extra resources for Connectionist Models. Proceedings of the 1990 Summer School
Sample text
In addition, another algorithm is given for transforming a low order energy function into a (possibly) higher one by elimination o f some or all o f the hidden vari ables. (Formal proofs are given in (Pinkas 9 0 ) ) . This algorithms allow us to trade the computational power • A n y k-order term (ofllissi^t)* POSITIVE coefficient a, can be replaced b y a term o f order (ifc - 1 ) of the form : a itf"? x{- (Y*l± 2aX{T) + 2aXkT -f (2k — 3 ) a T , generating an equiva 2 function with one additional hidden lent energy variable .
Formal proofs are given in (Pinkas 9 0 ) ) . This algorithms allow us to trade the computational power • A n y k-order term (ofllissi^t)* POSITIVE coefficient a, can be replaced b y a term o f order (ifc - 1 ) of the form : a itf"? x{- (Y*l± 2aX{T) + 2aXkT -f (2k — 3 ) a T , generating an equiva 2 function with one additional hidden lent energy variable . 2 W h e n term is negative: - 3 X Y Z U « - 6 X T - 6 Y T - 6ZT - 6UT + 2 1 T . 3 W h e n term is positive: XYZU a XYZ - 2XT - 2YT - 2ZT + 2UT + 5 T « XY - 2XV - 2YV + 2ZV + 3 T ' -2XT - 2YT - 2ZT + 2UT + 5 T E X A M P L E 6 .
J. Hopfield "Neurons with graded response have col lective computational properties like those of two-state neurons". Proceedings of the National Academy of Sci ences U S A , 1984,Vol 81, p p . 3088-3092. J. Hopfield, D . W . Tank "Neural Computation o f De cisions in Optimization Problems" Biological Cyber netics, Vol 52, pp. 144-152. G . Pinkas, "Energy Minimization and the Satisfiability of Propositional Calculus " Technical Report: WUCS90-03, Department of Computer Science, Washington University 1990 D .