Semiring Artificial Neural Networks and Weighted Automata And an Application to Digital Image Encoding

摘要

In their seminal paper McCulloch and Pitts have shown the strong relationship between finite automata and so-called McCulloch-Pitts networks. Our goal is to extend this result to weighted automata. In other words, we want to integrate artificial neural networks and weighted automata. For this task, we introduce semiring artificial neural networks, that is, artificial neural networks which implement the addition and the multiplication of semirings. We present a construction of a semiring artificial neural network from a given weighted automaton, and back again. After that, we show how we can approach the problem of encoding an image into a weighted automaton by using a semiring artificial neural network in this process.