Deep neural networks (DNNs) and deep learning approaches yield state-of-the-art performance in a range of machine learning tasks, including automatic speech recognition. The multi-layer transformations and activation functions in DNNs, or related network variations, allow complex and difficult data to be well modelled. However, the highly distributed representations associated with these models make it hard to interpret the parameters. The whole neural network is commonly treated a ``black box''. The behaviours of activation functions and the meanings of network parameters are rarely controlled in the standard DNN training. Though a sensible performance can be achieved, the lack of interpretations to network structures and parameters causes better regularisation and adaptation on DNN models challenging. In regularisation, parameters have to be regularised universally and indiscriminately. For instance, the widely used L2 regularisation encourages all parameters to be zeros. In adaptation, it requires to re-estimate a large number of independent parameters. Adaptation schemes in this framework cannot be effectively performed when there are limited adaptation data.

This thesis investigates structured deep neural networks. Special structures are explicitly designed, and they are imposed with desired interpretation to improve DNN regularisation and adaptation. For regularisation, parameters can be separately regularised based on their functions. For adaptation, parameters can be adapted in groups or partially adapted according to their roles in the network topology. Three forms of structured DNNs are proposed in this thesis. The contributions of these models are presented as follows.

The first contribution of this thesis is the multi-basis adaptive neural network. This form of structured DNN introduces a set of parallel sub-networks with restricted connections. The design of restricted connectivity allows different aspects of data to be explicitly learned. Sub-network outputs are then combined, and this combination module is used as the speaker-dependent structure that can be robustly estimated for adaptation.

The second contribution of this thesis is the stimulated deep neural network. This form of structured DNN relates and smooths activation functions in regions of the network. It aids the visualisation and interpretation of DNN models but also has the potential to reduce over-fitting. Novel adaptation schemes can be performed on it, taking advantages of the smooth property that the stimulated DNN offer.

The third contribution of this thesis is the deep activation mixture model. Also, this form of structured DNN encourages the outputs of activation functions to achieve a smooth surface. The output of one hidden layer is explicitly modelled as the sum of a mixture model and a residual model. The mixture model forms an activation contour, and the residual model depicts fluctuations around this contour. The smoothness yielded by a mixture model helps to regularise the overall model and allows novel adaptation schemes.