Improving Neural Networks by Adopting Amplifying and Attenuating Neurons

In the present study, an amplifying neuron and attenuating neuron, which can be easily implemented into neural networks without any significant additional computational effort, are proposed. The activated output value is squared for the amplifying neuron, while the value becomes its reciprocal for the attenuating one. Theoretically, the order of neural networks increases when the amplifying neuron is placed in the hidden layer. The performance assessments of neural networks were conducted to verify that the amplifying and attenuating neurons enhance the performance of neural networks. From the numerical experiments, it was revealed that the neural networks that contain the amplifying and attenuating neurons yield more accurate results, compared to those without them.Comment: 8 pages, the figure 6-(b) and (c) were exchange

An Approach to Stable Gradient Descent Adaptation of Higher-Order Neural Units

Stability evaluation of a weight-update system of higher-order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring stability of the weight-update system (at every single adaptation step) naturally results in adaptation stability of the whole neural architecture that adapts to target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.Comment: 2016, 13 page