were rarely successful for continuous recognition tasks because of their limited ability to model temporal dependencies. One approach to this limitation was to use neural networks as a pre-processing, feature transformation or dimensionality reduction, step prior to HMM based recognition. However, more recently, LSTM and related recurrent neural networks (RNNs), Time Delay Neural Networks(TDNN's), and transformers. have demonstrated improved performance in this area. Deep feedforward and recurrent neural networks Deep Neural Networks and Denoising Autoencoders are also under investigation. A deep feedforward neural network (DNN) is an artificial neural network with multiple hidden layers of units between the input and output layers. Similar to shallow neural networks, DNNs can model complex non-linear relationships. DNN architectures generate compositional models, where extra layers enable composition of features from lower layers, giving a huge learning capacity and thus the potential of modeling complex patterns of speech data. A success of DNNs in large vocabulary speech recognition occurred in 2010 by industrial researchers, in collaboration with academic researchers, where large output layers of the DNN based on context dependent HMM states constructed by decision trees were adopted. See comprehensive reviews of this development and of the state of the art as of October 2014 in the recent Springer book from Microsoft Research. See also the related background of automatic speech recognition and the impact of various machine learning paradigms, notably including deep learning, in recent overview articles. One fundamental principle of deep learning is to do away with hand-crafted feature engineering and to use raw features. This principle was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear filter-bank features, showing its superiority over the Mel-Cepstral features which contain a few stages of fixed transformation from spectrograms. The true "raw" features of speech, waveforms, have more recently been shown to produce excellent larger-scale speech recognition results. End-to-end automatic speech recognition Since 2014, there has been much research interest in "end-to-end" ASR. Traditional phonetic-based (i.e., all HMM-based model) approaches required separate components and training for the pronunciation, acoustic, and language model. End-to-end models jointly learn all the components of the speech recognizer. This is valuable since it simplifies the training process and deployment process. For example, a n-gram language model is required for all HMM-based systems, and a typical n-gram language model often takes several gigabytes in memory making them impractical to deploy on mobile devices. Consequently, modern commercial