Michael Murray
Michael Murrray is a Lecturer in Mathematics at the University of Bath. Prior to this he completed a postdoc at UCLA and received a DPhil from Oxford. His research is focused on developing theory for machine learning: in particular, understanding optimization, generalization and feature learning in the context of neural networks.
Project
Recent experiments have shown classical Hopfield networks, trained via energy flow minimisation, can store the isomorphism class of a graph given vanishingly few examples. This observation suggests, at least in the case of certain graph or group structured datasets, that classical Hopfield networks possess a far greater capacity compared with their ability to store random data. Moreover, empirical findings indicate that the learned Hopfield parameters exhibit at least approximate graph isomorphism invariance and that only a vanishingly small sampling ratio is necessary for strict memorization of the full orbit. This raises a number of important questions: how does invariance emerge when minimizing the energy flow given only a few examples from the orbit? Which types of graph can be strictly memorized by these invariant Hopfield networks? What is the critical sampling ratio required for reliably storing the entire orbit and how does this ratio depend on the properties of the graph in question? In addition, the potential algorithmic significance of these results is underexplored, particularly in the context of solving challenging combinatorial, group and graph theoretic problems.
