Multistability of Switched Neural Networks With Gaussian Activation Functions Under State-Dependent Switching

This article presents theoretical results on the multistability of switched neural networks with Gaussian activation functions under state-dependent switching. It is shown herein that the number and location of the equilibrium points of the switched neural networks can be characterized by making use of the geometrical properties of Gaussian functions and local linearization based on the Brouwer fixed-point theorem. Four sets of sufficient conditions are derived to ascertain the existence of 7^p₁5^p₂3^p₃ equilibrium points, and 4^p₁3^p₂2^p₃ of them are locally stable, wherein p₁ , p₂ , and p₃ are nonnegative integers satisfying 0 ≤ p₁+p₂+p₃ ≤ n and n is the number of neurons. It implies that there exist up to 7ⁿ equilibria, and up to 4ⁿ of them are locally stable when p₁=n . It also implies that properly selecting p₁ , p₂ , and p₃ can engender a desirable number of stable equilibria. Two numerical examples are elaborated to substantiate the theoretical results.

Performance evaluation of multilayer perceptrons for discriminating and quantifying multiple kinds of odors with an electronic nose

This paper studies several types and arrangements of perceptron modules to discriminate and quantify multiple odors with an electronic nose. We evaluate the following types of multilayer perceptron. (A) A single multi-output (SMO) perceptron both for discrimination and for quantification. (B) An SMO perceptron for discrimination followed by multiple multi-output (MMO) perceptrons for quantification. (C) An SMO perceptron for discrimination followed by multiple single-output (MSO) perceptrons for quantification. (D) MSO perceptrons for discrimination followed by MSO perceptrons for quantification, called the MSO-MSO perceptron model, under the following conditions: (D1) using a simple one-against-all (OAA) decomposition method; (D2) adopting a simple OAA decomposition method and virtual balance step; and (D3) employing a local OAA decomposition method, virtual balance step and local generalization strategy all together. The experimental results for 12 kinds of volatile organic compounds at 85 concentration levels in the training set and 155 concentration levels in the test set show that the MSO-MSO perceptron model with the D3 learning procedure is the most effective of those tested for discrimination and quantification of many kinds of odors.

Sensitivity-based adaptive learning rules for binary feedforward neural networks

This paper proposes a set of adaptive learning rules for binary feedforward neural networks (BFNNs) by means of the sensitivity measure that is established to investigate the effect of a BFNN's weight variation on its output. The rules are based on three basic adaptive learning principles: the benefit principle, the minimal disturbance principle, and the burden-sharing principle. In order to follow the benefit principle and the minimal disturbance principle, a neuron selection rule and a weight adaptation rule are developed. Besides, a learning control rule is developed to follow the burden-sharing principle. The advantage of the rules is that they can effectively guide the BFNN's learning to conduct constructive adaptations and avoid destructive ones. With these rules, a sensitivity-based adaptive learning (SBALR) algorithm for BFNNs is presented. Experimental results on a number of benchmark data demonstrate that the SBALR algorithm has better learning performance than the Madaline rule II and backpropagation algorithms.