On interpretations of a feed-forward neural network

Summary form only given, as follows. Interpretations of a feedforward neural network are described. For the interpretations, a network is decomposed into a successive combination of unit transformations. A unit transformation stands for a transformation from one layer output to the next higher layer output. This transformation is further divided into an affine part and a sigmoid nonlinear part. The affine part is interpreted using the singular-value decomposition technique, and the sigmoid nonlinear part is interpreted based on a classification of its input space into direction-invariant subspaces. Also described is an application of the interpretations, which is applied to an exclusive OR feedforward neural network.<>