Feedforward sigmoidal networks--equicontinuity and fault-tolerance properties

Area of Science:

• Artificial Intelligence
• Machine Learning
• Neural Networks

Background:

• Sigmoidal feedforward artificial neural networks (FFANNs) are known universal approximators.
• Understanding the properties of these networks is crucial for their practical application.
• The relationship between network properties and performance, like fault tolerance, requires further investigation.

Purpose of the Study:

• To summarize universal approximation results for sigmoidal FFANNs.
• To analyze the equicontinuous properties of function sets represented by FFANNs.
• To investigate the relationship between equicontinuity and fault tolerance in FFANNs.

Main Methods:

• Reviewing universal approximation theorems for sigmoidal FFANNs.
• Analyzing the equicontinuity of identified function sets.
• Comparing the properties of arbitrary weight versus bounded weight FFANNs.

Main Results:

• Identified function sets represented by sigmoidal FFANNs with universal approximation properties.
• Demonstrated that generally used arbitrary weight FFANNs represent nonequicontinuous sets.
• Established a class of bounded weight sigmoidal FFANNs as equicontinuous sets.
• Analyzed fault-tolerance behavior and established error bounds for induced errors.

Conclusions:

• Equicontinuity is a key property related to the fault tolerance of sigmoidal FFANNs.
• Bounded weight FFANNs offer improved fault tolerance due to their equicontinuous nature.
• The findings provide a theoretical basis for designing more robust FFANNs.