h1

%0 Thesis
%A Keup, Christian
%T Field theoretic approaches to computation in neuronal networks
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2022-06733
%P 1 Online-Ressource : Illustrationen, Diagramme
%D 2022
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
%Z Dissertation, RWTH Aachen University, 2022
%X This thesis is centered around the application of statistical field theory to the question of how computation is performed by neuronal networks. The spiking activity in dense networks of neurons, such as in the brain, tends to be strongly chaotic. How, then, can these circuits reliably process information? Past investigations have studied mainly weakly chaotic firing-rate models. Here we demonstrate a universal mechanism explaining how even strongly chaotic activity can support powerful computations. The calculations use a novel unified theoretical framework that allows to compare models of neural networks across scales of model complexity. Here, the framework is applied to two common model classes: binary neurons, which switch between a pulse-emitting and non-emitting state, and rate neurons, which describe just the number of pulses per second. These implement two different assumptions about the substrate of computation, commonly referred to as spike-coding vs. rate-coding. We calculate the transition to chaos in random binary networks and show that each chaotic binary network corresponds to an equivalent rate network with the same activity statistics, but with nonchaotic dynamics. Therefore results on the well-studied edge-of-chaos in firing-rate models cannot be directly transferred to spiking-type networks. Next, considering strongly chaotic regimes, we show that the activity transiently promotes the separability of different input stimuli. This effect arises because state trajectories for different inputs diverge from one another in a stereotypical, distance-dependent manner. Binary networks and pulse-coupled networks offer a particularly fast separation that can be exploited for fast, event-based computation, which, however, requires control of the initial conditions. These results provide predictions for experimental recordings in brain circuits and invite research on the use of chaotic dynamics in artificial neural networks. We further generalize the theoretical framework, which can serve as a bridge between many types of existing neural-network models and provides a systematic method to derive self-consistent, time-dependent Gaussian approximations and perturbation corrections for such systems. Furthermore, a parallel line of work is presented using the same type of techniques to study how the data representation is transformed in the process of computation by recurrent reservoir networks and trained artificial feed-forward networks. Because deep networks can exploit interactions between all scales in the data, these networks are difficult to understand based on their microscopic structure. We find that for close to Gaussian data classes, the computation can be captured by a Gaussian theory for the high-dimensional activity in each layer. Nonetheless, it remains a fundamental challenge to extend such a theory to strongly non-Gaussian distributions, and a graphical intuition to describe transformations of high-dimensional structured probability distributions is largely lacking. Therefore, inspired by our field-theoretic work we develop a graphical explanation for the transformations learned in classification tasks. We demonstrate how the transformations of the data manifold can be linked to folding operations which have a low-dimensional intuition that stays valid in the high-dimensional case, thereby opening an exiting link between the mathematics of folding algorithms and neuronal networks.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2022-06733
%U https://publications.rwth-aachen.de/record/849327