On the Power of Democratic Networks
Type of publication:  Journal paper 
Citation:  Mayo95.1 
Journal:  SIAM Journal of Discr. Math 
Volume:  9 
Number:  02 
Year:  1996 
Month:  5 
Abstract:  Linear Threshold Boolean units (LTU) are the basic processing components of artificial neural networks of Boolean activations. Quantization of their parameters is a central question in hardware implementation, when numerical technologies are used to store the configuration of the circuit. In the previous studies on the circuit complexity of feedforward neural networks, no differences had been made between a network with ``small'' integer weights and one composed of majority units (LTU with weights in {1,0, 1},',','), since any connection of weight w (w integer) can be simulated by w connections of value Sgn(w). This paper will focus on the circuit complexity of democratic networks, i.e. circuits of majority units with at most one connection between each pair of units. The main results presented are the following: any Boolean function can be computed by a depth3 nondegenerate democratic network and can be expressed as a linear threshold function of majorities; ATLEASTk and ATMOSTk are computable by a depth2, polynomial size democratic network; the smallest sizes of depth2 circuits computing PARITY are identical for a democratic network and for a usual network; the VC of the class of the majority functions is n 1, i.e. equal to that of the class of any linear threshold functions. 
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