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Largest theoretical contribution to Neural Networks comes from VC Dimensionwhich characterizes the sample complexity of classification model in aprobabilistic view and are widely used to study the generalization error. Sofar in the literature the VC Dimension has only been used to approximate thegeneralization error bounds on different Neural Network architectures. VCDimension has not yet been implicitly or explicitly stated to fix the networksize which is important as the wrong configuration could lead to highcomputation effort in training and leads to over fitting. So there is a need tobound these units so that task can be computed with only sufficient number ofparameters. For binary classification tasks shallow networks are used as theyhave universal approximation property and it is enough to size the hidden layerwidth for such networks. The paper brings out a theoretical justification onrequired attribute size and its corresponding hidden layer dimension for agiven sample set that gives an optimal binary classification results withminimum training complexity in a single layered feed forward network framework.The paper also establishes proof on the existence of bounds on the width of thehidden layer and its range subjected to certain conditions. Findings in thispaper are experimentally analyzed on three different dataset using Mathlab 2018(b) software.

Limiting Network Size within Finite Bounds for Optimization