Artificial neural networks - computing systems fundamental to Machine Learning - can be mathematically viewed as graphs. SPECTRUM aims at exploiting the graph structure of neural networks to improve their performance, by using Spectral Graph Theory (SGT). In particular, the goals of SPECTRUM are: (G1) to provide an original framework for optimizing existing neural network architectures by modifying the graphs underlying their structure; (G2) to design and optimize a novel architecture based on the theory of Markov chains on graphs and inspired by the mechanism of signal transmission in the human brain during the learning process. For both G1 and G2, SGT will provide tools to quantify the dependence of the neural network efficiency on the structure of the graph underlying it and, hence, methods to improve efficiency. The main challenges of SPECTRUM are: (CH1) solving open problems in SGT related to the optimization of quantities such as the algebraic connectivity and Kemeny’s constant over certain families of graphs and to the use of Matrix Theory and Algebraic Graph Theory to speed up the computation of those quantities for graphs associated with neural networks, by exploiting their hierarchical structure; (CH2) solving technical issues concerning the implementation of the novel neural network architecture of G2. The PM will carry out the project at EPFL for the first two years and at UiO for the final year. The training at EPFL and the collaboration with Prof. Marcus will be crucial to address CH2; Prof. Dahl will support the rest of the team mainly for the aspects related to CH1. In the final stage of the project, the PM will organize scientific activities at UiO to disseminate the findings of SPECTRUM and to transfer the knowledge acquired in Switzerland to the Norwegian research community. He will also attend a pedagogical training program and a research leadership program at UiO. They will enhance the necessary skills to foster his future academic career.
Project leader: Lorenzo Ciardo
Institution: Matematisk institutt