An experimental study on nonlinear function computation for neural/fuzzy hardware design

Area of Science:

• Computational intelligence
• Artificial intelligence
• Machine learning

Background:

• Nonlinear functions are crucial for artificial neural networks (ANNs) and fuzzy inference systems (FISs).
• Efficient computation of these functions impacts system performance, including approximation capability and mapping smoothness.
• Understanding this influence is key for optimizing neurofuzzy systems (NFSs).

Purpose of the Study:

• To experimentally evaluate the influence of basic nodal nonlinear function computation on NFS performance.
• To compare the performance of sigmoid-logistic and Gaussian kernel functions within ANNs and extend findings to FISs.
• To analyze the impact on system architecture size, approximation capability, and mapping smoothness.

Main Methods:

• Utilized an accuracy-controllable approximation algorithm for hardware implementation of kernel functions.
• Selected backpropagation neural networks (BPNNs) and radial basis function (RBF) networks for ANN analysis.
• Employed functional equivalence theorems to extend ANN results to fuzzy inference systems (FISs).
• Observed adaptive neurofuzzy inference system (ANFIS) behavior for learning systems.

Main Results:

• Demonstrated that the computation of nonlinear kernel functions significantly affects NFS performance metrics.
• Identified differences in approximation capability and mapping smoothness between sigmoid-logistic and Gaussian functions.
• Validated findings through extensive simulations on benchmark approximation problems.

Conclusions:

• The method of computing nonlinear functions is a critical factor in NFS performance.
• Results provide insights for selecting and implementing kernel functions in ANNs, FISs, and ANFIS.
• Optimized function computation can lead to improved system efficiency and accuracy.