Leveraging topology, geometry, and symmetries for efficient Machine Learning
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A fit-for-purpose structural and statistical model is the first major requirement in population pharmacometric model development. In this manuscript we discuss how this complex and computationally intensive task could benefit from supervised machine learni ...
This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...
The explosive growth of machine learning in the age of data has led to a new probabilistic and data-driven approach to solving very different types of problems. In this paper we study the feasibility of using such data-driven algorithms to solve classic ph ...
Neural networks have become indispensable for a wide range of applications, but they suffer from high computational- and memory-requirements, requiring optimizations from the algorithmic description of the network to the hardware implementation. Moreover, ...
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...
Neural networks (NNs) have been very successful in a variety of tasks ranging from machine translation to image classification. Despite their success, the reasons for their performance are still not well-understood. This thesis explores two main themes: lo ...
Deep neural networks have been empirically successful in a variety of tasks, however their theoretical understanding is still poor. In particular, modern deep neural networks have many more parameters than training data. Thus, in principle they should over ...
The success of deep learning may be attributed in large part to remarkable growth in the size and complexity of deep neural networks. However, present learning systems raise significant efficiency concerns and privacy: (1) currently, training systems are l ...
In the recent years, Deep Neural Networks (DNNs) have managed to succeed at tasks that previously appeared impossible, such as human-level object recognition, text synthesis, translation, playing games and many more. In spite of these major achievements, o ...