By Clark Jeffries (auth.), Clark Jeffries (eds.)
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Additional resources for Code Recognition and Set Selection with Neural Networks
Thus x corresponds to an answer set. 6 Set Selection Neural Networks with Perturbations Let us consider terms of the type [Lgj(Xj)-1]2 where the sum is over all j in a given subset Sk in a set selection problem. Each such term is nonnegative and is zero at any feasible constant trajectory. 5) would generally create new, unwanted constant trajectories. 10) where the first and third sums are over all subsets Sk containing element i , the second sum is over all j E Sk with j * i, and the fourth sum is over all j E Sk.
1 Dense Memory with High Order Neural Networks In this chapter we develop the memory model, a dynamical system neural network model which simulates memory retrieval. The time evolution of a trajectory of such a system is mathematical recognition, meaning convergence to one of several attractors referred to as mathematical memories. The attractors are pre specified constant trajectories or limit cycles. Thus mathematical recognition amounts to convergence from an input vector in n-dimensional space to one of the memories represented as an n-vector with components ±1.
N With this algebraic machinery in place we are in a position to simplify an analysis of the conventional formulation of the high order neural network model. It can be proved that if 12 is derived from.!! 14), then Aa(g) = Bb(g). As an example, let us rewrite the two-dimensional neural network model dxl/dt dx2/dt = -Xl + gl (l-g2) - (l-g l )g2 =-x2 - gl(l-gz) + (l-gl)g2 in the A format dxl/dt = -Xl + gl - g2 dx2/dt =-x2 - gl + g2 an = 0, al = 1, a2 = -1, and a12 = 0 while boo = 0, blO = 1, b OI = -1, and b ll = O.