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Deep neural networks (DNNs) are widely utilized for acoustic modeling in speech recognition systems. Through training, DNNs used for phoneme recognition nonlinearly transform the time-frequency representation of a speech signal into a sequence of invariant phonemic categories. However, little is known about how this nonlinear mapping is performed and what its implications are for the classification of individual phones and phonemic categories. In this paper, we analyze a sigmoid DNN trained for a phoneme recognition task and characterized several aspects of the nonlinear transformations that occur in hidden layers. We show that the function learned by deeper hidden layers becomes increasingly nonlinear, and that network selectively warps the feature space so as to increase the discriminability of acoustically similar phones, aiding in their classification. We also demonstrate that the nonlinear transformation of the feature space in deeper layers is more dedicated to the phone instances that are more difficult to discriminate, while the more separable phones are dealt with in the superficial layers of the network. This study describes how successive nonlinear transformations are applied to the feature space non-uniformly when a deep neural network model learns categorical boundaries, which may partly explain their superior performance in pattern classification applications.