K-WTA NETWORK WITH EQUALLY-LEVELED COMPETITORS
Ruxandra L. Costea, V. Bucata, Corneliu A. Marinov · 2004
We study an analog KWTA circuit supplied with a list of nondistinct inputs. We show that a proper scaling of inputs and a big gain for amplifiers guarantee a correct selection of winners along with the network stability. 1. GENERALITIES Motivated by large applications in signal and data processing, the selection of the K largest items of a list of N> K elements has attracted the analog circuit and neural network theorists and designers [7] – [12]. One way of its approach is through the O(N 2) Hopfield (continuous time) network studied in [1] – [6]. It is a net which is fed by N current sources d = ( d1, d2, … , dN) and evolves according to: du( t) = s[ −lu( t) + Tv( t) + b]. (1) dt Here the vector b embeds the sources, bi = di – pN + 2pK, where p is the 1 1 interconnection conductance. In (1), l = + ( N −1) p and s = where ρ and C ρ C are the ground resistance and capacitance of each neuron. The state components ui(t) are the voltages at each neuron input, while vi(t) = tanh(λ ui (t)) ∈ (–1,1) corresponds to its output. Here "the gain " λ controls the slope of characteristics and plays a chief role in our reasoning. The interconnection matrix is: 1