O. Abdel-hamid, A. Mohamed, H. Jiang, and G. Penn, Applying convolutional neural networks concepts to hybrid nn-hmm model for speech recognition, Acoustics, Speech and Signal Processing, pp.4277-4280, 2012.

P. Arena, L. Fortuna, G. Muscato, and M. G. Xibilia, Multilayer perceptrons to approximate quaternion valued functions, Neural Networks, vol.10, issue.2, pp.335-342, 1997.

P. Arena, L. Fortuna, L. Occhipinti, and M. G. Xibilia, Neural networks for quaternion-valued function approximation, IEEE International Symposium on, vol.6, pp.307-310, 1994.

A. Nicholas and J. Aspragathos, A comparative study of three methods for robot kinematics. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, vol.28, pp.135-145, 1998.

A. Gaudet, Deep quaternion networks, 2017.

F. Chollet, , 2015.

I. Danihelka, G. Wayne, B. Uria, N. Kalchbrenner, and A. Graves, Associative long short-term memory, 2016.

B. Steven, P. Davis, and . Mermelstein, Comparison of parametric representations for monosyllabic word recognition in continuously spoken sentences, Readings in speech recognition, pp.65-74, 1990.

S. Furui, Speaker-independent isolated word recognition based on emphasized spectral dynamics, IEEE International Conference on ICASSP'86, vol.11, pp.1991-1994, 1986.

S. John, L. F. Garofolo, . Lamel, M. William, J. G. Fisher et al., Darpa timit acoustic-phonetic continous speech corpus cd-rom. nist speech disc 1-1.1. NASA STI/Recon technical report n, vol.93, 1993.

A. Graves, S. Fernández, F. Gomez, and J. Schmidhuber, Connectionist temporal classification: labelling unsegmented sequence data with recurrent neural networks, Proceedings of the 23rd international conference on Machine learning, pp.369-376, 2006.

A. Graves, M. Abdel-rahman, and G. Hinton, Speech recognition with deep recurrent neural networks, Acoustics, speech and signal processing (icassp), 2013 ieee international conference on, pp.6645-6649, 2013.

K. Greff, K. Rupesh, J. Srivastava, . Koutník, R. Bas et al., Lstm: A search space odyssey, IEEE transactions on neural networks and learning systems, vol.28, pp.2222-2232, 2017.

K. He, X. Zhang, S. Ren, and J. Sun, Delving deep into rectifiers: Surpassing human-level performance on imagenet classification, Proceedings of the IEEE international conference on computer vision, pp.1026-1034, 2015.

G. Hinton, L. Deng, D. Yu, G. E. Dahl, A. Mohamed et al., Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups, Signal Processing Magazine, vol.29, issue.6, pp.82-97, 2012.

A. Hirose and S. Yoshida, Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence, IEEE Transactions on Neural Networks and learning systems, vol.23, issue.4, pp.541-551, 2012.

T. Isokawa, T. Kusakabe, N. Matsui, and F. Peper, Quaternion neural network and its application, International Conference on Knowledge-Based and Intelligent Information and Engineering Systems, pp.318-324, 2003.

D. Kingma and J. Ba, Adam: A method for stochastic optimization, 2014.

Y. Lecun, P. Haffner, L. Bottou, and Y. Bengio, Object recognition with gradient-based learning, Shape, contour and grouping in computer vision, pp.319-345

. Springer, , 1999.

N. Matsui, T. Isokawa, H. Kusamichi, F. Peper, and H. Nishimura, Quaternion neural network with geometrical operators, Journal of Intelligent & Fuzzy Systems, vol.15, pp.149-164, 2004.

T. Minemoto, T. Isokawa, H. Nishimura, and N. Matsui, Feed forward neural network with random quaternionic neurons, Signal Processing, vol.136, pp.59-68, 2017.
DOI : 10.1016/j.sigpro.2016.11.008

M. Mohri, F. Pereira, and M. Riley, Weighted finite-state transducers in speech recognition, Computer Speech and Language, vol.16, issue.1, pp.69-88, 2002.
DOI : 10.1006/csla.2001.0184

URL : https://repository.upenn.edu/cgi/viewcontent.cgi?article=1010&context=cis_papers

T. Nitta, A quaternary version of the back-propagation algorithm, Neural Networks, vol.5, pp.2753-2756, 1995.

T. Parcollet, M. Morchid, P. Bousquet, R. Dufour, G. Linarès et al., Quaternion neural networks for spoken language understanding, Spoken Language Technology Workshop (SLT), pp.362-368, 2016.
DOI : 10.1109/slt.2016.7846290

URL : https://hal.archives-ouvertes.fr/hal-02107532

T. Parcollet, M. Morchid, and G. Linares, Deep quaternion neural networks for spoken language understanding, Automatic Speech Recognition and Understanding Workshop, pp.504-511, 2017.
DOI : 10.1109/asru.2017.8268978

URL : https://hal.archives-ouvertes.fr/hal-02107630

T. Parcollet, M. Ravanelli, M. Morchid, G. Linarès, C. Trabelsi et al., Quaternion recurrent neural networks, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02107628

T. Parcollet, Y. Zhang, M. Morchid, C. Trabelsi, G. Linarès et al., Quaternion convolutional neural networks for end-to-end automatic speech recognition, 2018.
DOI : 10.21437/interspeech.2018-1898

URL : https://hal.archives-ouvertes.fr/hal-02107611

V. Peddinti, D. Povey, and S. Khudanpur, A time delay neural network architecture for efficient modeling of long temporal contexts, Sixteenth Annual Conference of the International Speech Communication Association, 2015.

C. Soo-, C. Pei, and . Cheng, Color image processing by using binary quaternionmoment-preserving thresholding technique, IEEE Transactions on Image Processing, vol.8, issue.5, pp.614-628, 1999.

D. Povey, A. Ghoshal, G. Boulianne, L. Burget, O. Glembek et al., The kaldi speech recognition toolkit, IEEE 2011 Workshop on Automatic Speech Recognition and Understanding, p.11, 2011.

M. Ravanelli, P. Brakel, M. Omologo, and Y. Bengio, Improving speech recognition by revising gated recurrent units, Proc. Interspeech, 2017.
DOI : 10.21437/interspeech.2017-775

URL : http://arxiv.org/pdf/1710.00641

M. Ravanelli, P. Brakel, M. Omologo, and Y. Bengio, Light gated recurrent units for speech recognition, IEEE Transactions on Emerging Topics in Computational Intelligence, vol.2, issue.2, pp.92-102, 2018.
DOI : 10.1109/tetci.2017.2762739

URL : http://arxiv.org/pdf/1803.10225

S. Sabour, N. Frosst, and G. E. Hinton, Dynamic routing between capsules, 2017.

H. Sak, A. Senior, and F. Beaufays, Long short-term memory recurrent neural network architectures for large scale acoustic modeling, Fifteenth annual conference of the international speech communication association, 2014.

S. Sangwine, Fourier transforms of colour images using quaternion or hypercomplex, numbers. Electronics letters, vol.32, pp.1979-1980, 1996.
DOI : 10.1049/el:19961331

N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, Dropout: A simple way to prevent neural networks from overfitting, The Journal of Machine Learning Research, vol.15, issue.1, pp.1929-1958, 2014.

P. Titouan, M. Morchid, and G. Linares, Quaternion denoising encoderdecoder for theme identification of telephone conversations, Proc. Interspeech, pp.3325-3328, 2017.

M. Tygert, J. Bruna, S. Chintala, Y. Lecun, S. Piantino et al., A mathematical motivation for complex-valued convolutional networks, Neural computation, vol.28, issue.5, pp.815-825, 2016.
DOI : 10.1162/neco_a_00824

URL : http://arxiv.org/pdf/1503.03438

A. Waibel, T. Hanazawa, G. Hinton, K. Shikano, and K. J. Lang, Phoneme recognition using time-delay neural networks, Readings in speech recognition, pp.393-404, 1990.

S. Wisdom, T. Powers, J. Hershey, J. L. Roux, and L. Atlas, Full-capacity unitary recurrent neural networks, Advances in Neural Information Processing Systems, pp.4880-4888, 2016.

D. Xu, H. Zhang, and . Zhang, Learning alogrithms in quaternion neural networks using ghr calculus, Neural Network World, vol.27, issue.3, p.271, 2017.

Y. Zhang, M. Pezeshki, P. Brakel, S. Zhang, C. Laurent-yoshua et al., Towards end-to-end speech recognition with deep convolutional neural networks, 2017.