On Temporal Summation in Chaotic Neural Network with Incremental Learning

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Chaotic Neural Networks And Incremental Learning

The incremental learning was developed by using the chaotic neurons. The chaotic neurons and the chaotic neural networks were proposed by Aihara (Aihara, Tanabe &Toyoda, 1990).

We presented the incremental learning that provides an associative memory (Asakawa, Deguchi & Ishii, 2001; Deguchi & Ishii, 2004; Deguchi, Fukuta & Ishii, 2013; Deguchi, Matsuo, Kimura & Ishii, 2009-07; Deguchi, Takahashi & Ishii, 2014). The network type is an interconnected network, in which each neuron receives one external input, and is defined as follows (Aihara, Tanabe & Toyoda, 1990):

, (1), (2), (3), (4) where is the output of the -th neuron at time , is the output sigmoid function described below in (5), , , are the time decay constants, is the input to the -th neuron at time , is the weight for external inputs, is the size—the number of the neurons in the network, is the connection weight from the -th neuron to the -th neuron, and is the parameter that specifies the relation between the neuron output and the refractoriness.