For a complete list of publications see my Google Scholar or Orcid pages. My dissertation is published here.

Selected Topics

Click on a topic for brief descriptions of selected publications.

Bayesian Supervised Learning

Fundamental questions regarding artificial neural networks remain wide open: How do the networks learn useful representations based on the data and the task? Why do these representations generalize beyond the training task? And how is this implemented on the neuronal level? Getting reliable answers to these questions is hard because training artificial neural network is complex—there are many moving parts, from obvious ones like the network architecture to more subtle ones like initialization or step-size. And all of these parts can have a profound impact on the trained networks.

Working in a Bayesian perspective allows to circumvent all difficulties related to the training process and to focus on the trained networks, i.e., networks sampled from the Bayes posterior. For this reason, Bayesian neural networks are a promising starting point to address fundamental questions about learning in artificial neural networks. The central challenge is to understand the structure of the Bayes posterior, which mirrors the central problem in Statistical Mechanics: understanding the structure of the Gibbs distribution. Accordingly, the rich toolset of Statistical Mechanics is readily applicable to Bayesian neural networks.

Dynamics of Random Recurrent Networks

The structure of cortical networks of mammals is only known on a statistical level. Thus, they are typically modeled as random networks with the appropriate connectivity statistics. Conveniently, quite a bit about the dynamics of random networks can be deduced using tools from statistical physics.

For random networks, one can start from the N-dimensional, coupled system of differential equations which describe the dynamics of the network and arrive, through a series of systematic approximations, at an effective lower-dimensional description. This approach, called Dynamic Mean-Field Theory (DMFT) in the pioneering work by Sompolinsky, Crisanti, and Sommers, relies heavily on techniques from field theory (see the lecture notes Helias & Dahmen 2020 for an introduction). Albeit mathematically involved, the final result is intuitive: the recurrent input to a neuron is approximated as a Gaussian process with self-consistent statistics.