On the stability and generalization of neural networks with VC dimension and fuzzy feature encoders

Abstract

Abstract Structuring a suitable depth and width based on the complexity of data is a difficult task in network training. Overparameterized deep networks with stochastic gradient descent optimization exhibit excellent accuracy on both training and validation set but are highly computationally expensive. The success of deep learning demands an efficient method to configure deep architectures based on the complexity of data. Here we developed a new strategy called FEVCFNN to structure a network based on sample complexity with fuzzy logic and VC Dimension for binary classification problems. Here preprocessing is done with a new technique called fuzzy feature encoders that transforms the data by increasing the dimension of input features based on the sample complexity evaluated through VC Dimension. VC Dimension is calculated on a class of least ϵ identifiable function space defined over the weight space identified by the processing state of the network. Using fuzzy set theory, VC Dimension evaluates a feasible bound for parameter size and structures a network based on sample complexity. Comparative study shows FEVCFNN gives high-performance results in minimum parameter size and less number of hidden nodes.