• Room 4472, Academic Building, HKUST (Lifts 25-26)
• Zoom (online)
Abstract
Neural networks are highly complex dynamical systems consisting of large numbers of neurons interacting through synapses. How can we formulate adequate theoretical frameworks for understanding such systems from static to dynamics, and from macroscopic to microscopic? In this thesis, we analyse two paradigms, RBM and Hopfield model, one is the cornerstone of unsupervised learning , and another is fundamental of theoretical neuroscience studied by tools originated from disorder statistical mechanics. In the first part , we analyse the permutation symmetry of RBM with two hidden units, revealing the series of continuous phase transitions driven by data. In the second part , we study a popular correlated Hopfield model which is used as a prototype of lots of neuroscience experiments and investigate the model from a dynamics perspective using random matrices and its equilibrium properties by the replica theory. From these two angles, we get more insights about the temporal and spatial correlations in neural circuits.
To request for meeting link, please write to phjacma@ust.hk.