Number Of Random Patterns Research Articles

Weight space structure and analysis using a finite replica number in the Isingperceptron

The weight space of the Ising perceptron, in which a set of random patterns isstored, is examined using the generating function of the partition functionϕ(n) = (1/N)log[Zn] as the dimension ofthe weight vector N tends to infinity, where Z is the partition function and represents the configurational average. We utilizeϕ(n) for two purposes, depending on the value of the ratioα = M/N, whereM is the number ofrandom patterns. For α<αs = 0.833..., we employ ϕ(n), in conjunction with Parisi’s one-step replica symmetry breaking scheme in the limit of , to evaluate the complexity that characterizes the number of disjoint clusters of weightsthat are compatible with a given set of random patterns, which indicates that, intypical cases, the weight space is equally dominated by a single large cluster ofexponentially many weights and exponentially many small clusters of a single weight. Forα>αs, on theother hand, ϕ(n) is used to assess the rate function of a small probability that a given set of random patterns is atypicallyseparable by the Ising perceptrons. We show that the analyticity of the rate function changes atα = αGD = 1.245..., which implies that the dominant configuration of the atypically separable patternsexhibits a phase transition at this critical ratio. Extensive numerical experiments areconducted to support the theoretical predictions.

Feedback-testing by using multiple input signature registers

In this article, the use of Multiple Input Signature Registers (MISRs) as random pattern generators is investigated. This additional function helps to reduce hardware overhead and testing time, when BIST (Built-In Self-Test) structures are integrated on the chip, because the MISR can at the same time generate test patterns and collect test responses. A formula is presented, which determines the number of clock cycles needed to generate a given number of random patterns. Finally we suggest a method for how the number of test patterns can be reduced when the MISR acts as test pattern generator and compressor in a feedback loop.

Pattern recognition in Hopfield type networks with a finite range of connections

We study pattern recognition in linear Hopfield type networks of N neurons where each neuron is connected to the z subsequent neurons such that the state of the i th neuron at time t+1 is determined by the states of neurons i+1, ..., i+z at time t. We find that for small values of z/N the retrieval behavior differs considerably from the behavior of diluted Hopfield networks. The maximum number of random patterns that can be retrieved increases in a non linear way with z and the asymptotic mean overlap between input and output patterns decreases sharply as z is decreased and reaches zero at a finite value of z

Aliasing Errors in Signature in Analysis Registers

The authors discuss aliasing errors in signature analysis registers for self-testing networks and review analytical results. The results show that when p, the probability that an error will occur at a network output, is close to 1/2, there is a bound of the aliasing error. The analysis uses a graph to represent the probability of transition, the Markov process, and z-transforms to analyze the behavior of the signature analysis register. For very small p(p?0) and very large p(p?1), the aliasing error solution for primitive polynomials is a series of terms (1-?)n in magnitude (where n is the number of random patterns being applied to the network or the length of the network output sequence). As compared with nonprimitive polynomials, whose solution is n(1-?)n or n2(1-?)n, in general primitive polynomials are much better with respect to aliasing. Simulation results are shown for aliasing errors for these polynomials, which give insight as to how aliasing occurs.