Czasopismo | ELEKTRONIKA - KONSTRUKCJE, TECHNOLOGIE, ZASTOSOWANIA | Rocznik 2013 - zeszyt 8

Bithreshold neurons learning

nr katalogowy: 78825

Artificial neural networks on the base of neural-like computational units have many applications and are intensively used for solving numerous important practical tasks [1]. It should be mentioned that many different models of neuron has been proposed. The one of more important features of these units is the activation function determining their outputs. Historically, the first proposed units had activation functions of threshold type according to developed models of brain cells. Using this type of activation Rosenblatt [2] designed the incremental consistent algorithm for the perceptron learning. The simple proof of it convergence was given by Novikoff [3]. Then Minsky and Papert [4] proved that Rosenblatt’s algorithm is inefficient in general case. Peled and Simeone were the first to produce a polynomial time algorithm for the threshold recognition problem [5]. They proposed linear programming approach based on polynomial-time Karmarker’s algorithm. It is well known that the threshold unit is incapable solving many rather easy recognition tasks [4] (e. g. the famous XOR - problem). The using of neurons with more complicated activation functions allowed surmounting this constrain. Historically, the one of the first designed advanced device were multi-threshold neural units [6]. But the efficient learning techniques for multi-threshold neuron based neural networks aren’t developed even in the case of one node. The present paper is devoted to the study of simplest case of multi-threshold units, namely bithreshold neurons. The paper consists of four sections. In the second section we focus our attention on complexity of learning of bithreshold neurons. Our main result is that the learning of bithreshold neurons is NP -complete. In the third section we describe the type of decision lists which represents bithreshold Boolean functions. This question is important in view of the known polynomial learning methods fo[...]

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