By Akira Hirose
This monograph instructs graduate- and undergraduate-level scholars in electric engineering, informatics, keep watch over engineering, mechanics, robotics, bioengineering at the innovations of complex-valued neural networks. Emphasizing uncomplicated techniques and methods of puzzling over neural networks, the writer specializes in neural networks that take care of advanced numbers; the sensible merits of complex-valued neural networks, and their origins; the advance of central purposes? The e-book makes use of certain examples to reply to those questions and extra.
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Extra info for Complex-Valued Neural Networks
2 Neural dynamics “Behavior” of a neural network has the following two aspects. 1. Processing tasks. A neural network reacts to signals, presented by the environment, by processing the presented input information in a manner meaningful to the network or network users. 2. Learning or Self-organization. The network changes itself to process information meaningfully. , network topology. We call the details of the behavior the neurodynamics. 2 and the following sections present several examples of neurodynamics.
We will ﬁnd in the following section that the Hebbian rule is applicable in correlation learning when teacher signals are given to the network in a bunch or time-sequentially. 6, it is also useful in function approximation in supervised learning. In the following sections, we present variously functional neural networks using the Hebbian rule. 3 Associative memory 49 is processed in the network, so that the readers can grasp some hints to apply the dynamics in various application ﬁelds. 3. 1 Function: Memory and recall of pattern information Associative memories typify the spirit of neural networks.
3 Energy function We can interpret the recall operation as a process to minimize a certain energy function. 21) decreases along with the progress of the recall y −→ sµ , and becomes a relative minimum at the end. The energy is also called Lyapunov function. It is a quadratic form of y, and W is the metric matrix of the energy. We can understand the decrease of the energy intuitively as follows. 15). 17), all the products are approximately zero except for that with the memorized vector nearest to the signal (s2 in the previous case).
Complex-Valued Neural Networks by Akira Hirose