Titouan Parcollet

Machine Learning (ML) techniques have allowed a great performance improvement of different challenging tasks (Spoken Language Understanding, Image Processing, Motion Management, Robotic ...). Among these methods, Neural Networks (NN), recently received a great interest from researchers due to their representation capability of complex internal structures in a low dimensional subspace. However, NNs employ document representations based on a basic level (because of their 1-Dimensionality). Therefore, these basic representations reveal little in way of document statistical structure by only considering each feature as a single entity, ignoring relations between them. My thesis propose to remedy this weakness by extending the hyper-complex numbers, also called quaternions, to neural networks called QNNs for Quaternion Neural Networks. Indeed, in a real-valued neural network, multidimensional features require to be reduced to a one dimensional vector before the learning process, while an appropriate solution is to process a multidimensional input as a single homogeneous entity. All these drawbacks can be alleviated thanks to the fourth dimensionality of quaternions and the hamilton product.

This thesis first proposes an integration of quaternions to state-of-the-art models such as : deep, recurrents, convolutionals, and adversarials neural networks. This integration rely on adapted and well-suited algorithms to fit the quaternion algebra specificities, and on a GPU implementation of quaternion neural networks. Then, a new type of neural network expressly designed for hyper-complex numbers wil be investigated, including a specific learning process and a well-adapted structure. This method has already reached promissing results that will be reported on my ResearchGate homepage and below.

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