The defense will also be live streamed using Zoom. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.
The event opens for participation just before it starts, and closes for new participants approximately 15 minutes after it has begun.
Trial lecture: 'Dimension reduction of higher dimensional data'
Time and place: Sep. 10, 2024 10:15 AM, Nucleus, Bikuben, Kristine Bonnevies hus
Main research findings:
The question of how minds and brains interact with the external world has puzzled humanity for thousands of years. Following recent advancements in computational and neural recording technology we are now able to study the activity of populations of thousands of neurons. Despite our recent ability to illuminate this “black box”, this abundance of data has led to the need for more interpretable models.
In this thesis, tools from topology are applied to the analysis of neural networks, with the goal of understanding the way in which they transform manifolds of stimuli. This transformation can be described by the way in which manifold homology changes during propagation through the layers of a network. The thesis extends persistent homology by using geodesic distances, with which we reliably discover that rotating images induce a circular topology in the activity of primary visual cortex. We further discuss the experimental conditions for this analysis to be successful. Following this, we introduce the idea of a rank decomposition, which allows us to study the topology of networks with piecewise-linear activation functions and show that trained networks are highly topologically destructive. Finally, we study how the toroidal structure of a population of grid cells is determined by the distribution of their phases.
Adjudication committee
Prof. Kenneth Harris, University College London
Prof. Nils Baas, Norwegian University of Science and Technology (NTNU)
Prof. Eivind Valen, Department of Biosciences, University of Oslo
Chair of defense
Assoc. Prof. Jonas Paulsen, Department of Biosciences, University of Oslo
Supervisors
Prof. Gaute Einevoll, Norwegian University of Life Sciences & University of Oslo
Prof. Marianne Fyhn, Department of Biosciences, University of Oslo
Prof. Anders Malthe-Sørenssen, Department of Physics, University of Oslo