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@PHDTHESIS{Tiberi:972001,
author = {Tiberi, Lorenzo},
othercontributors = {Helias, Mortiz and Honerkamp, Carsten},
title = {{T}he role of nonlinear interactions and connectivity in
shaping critical and collective network dynamics},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2023-09969},
pages = {1 Online-Ressource : Illustrationen},
year = {2023},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2023},
abstract = {Neural computation is a collective phenomenon emerging from
the complex interaction of a large number of neurons.
Through evolution and learning, neural networks organize
their structure, giving rise to rich collective dynamics
that can support complex computational tasks. Some
observables of these dynamics indeed appear to be optimally
tuned for computation. Examples include the dimensionality
and pricipal components' spectrum of neuronal activity, or
the ubiquitous presence of observables following a power-law
scaling, which suggests that the brain might tune itself
into a critical state. Understanding which structural
properties of neural networks allow the brain to optimally
tune these dynamical observables is till an open question.
Furthermore, it is not fully clear, in the very first place,
what is the computational benefit of some of the brain's
observed behaviors, such as criticality. In this thesis, we
address these questions by characterizing the dynamics of
two biologically inspired neural network models, the
stochastic Wilson-Cowan model and the stochastic
Sompolinsky-Crisanti-Sommers (SCS) model. To this end, we
adapt tools from a field that has already seen great success
in understanding collective phenomena - statistical physics.
Seeking analytical understanding and interpretability, we
focus on the two minimal and essential ingredients of neural
computation: nonlinearities and connectivity. First, we
focus on nonlinearities in the Wilson-Cowan model. We
perform the first renormalization group (RG) analysis of a
neural network model. By deriving the so-called flow of
couplings, we are able to explore the computational
implications of a fundamental property of critical systems:
the presence of nonlinear interactions across all
length-scales. This property has been so far inaccessible by
previous studies, due to the use of mean-field
approximations. We find nonlinearities to be in a
Gell-Mann-Low regime: despite vanishing at very large length
scales, they do so logarithmically slowly, thus remaining
present on practically all intermediate scales. We argue
this regime to be optimal for computation, striking a
balance between linearity, optimal for memory, and
nonlinearity, required for computation. Second, we focus on
connectivity in the linearized SCS model. We ask which
connectivity structures can directly control the network's
dynamical observables, tuning them into the computationally
optimal values observed experimentally. We develop a novel
theory for random connectivity matrices, which shows that
these structures are encoded in the shape of the
connectivity's eigenvalue distribution. In particular, the
density of nearly critical eigenvalues controls the
power-law scaling of many dynamical observable, such as the
autocorrelation, autoresponse, dimensionality, and principal
components spectrum of neuronal activity. Differently than
more traditional connectivity structures, such as motifs,
these novel structures can account for phenomena such as a
fine-tuned power-law scaling of the principal components
spectrum, as observed in V1 of mice. Third, we focus on both
nonlinearities and connectivity in the SCS model. We work on
importing the RG analysis of nonlinear interactions to
networks, especially in the general case of asymmetric
heterogeneous networks, which is of most interest to
neuroscience. This is - and still remains - an open problem,
for which, however, we provide some novel steps forward. In
the very first place, we make it formally possible to apply
the RG methods to generic networks, by noticing an analogy
with classical critical phenomena. Then, we identify new
technical challenges specific to the asymmetric,
heterogeneous case and propose formal methods to solve them,
which rely on our newly developed random matrix theory. We
also identify a novel mechanism, which causes a breakdown of
the typical power-law scaling observed in classical critical
phenomena.},
cin = {136930 ; 136920 / 130000},
ddc = {530},
cid = {$I:(DE-82)136930_20160614$ / $I:(DE-82)130000_20140620$},
pnm = {HBP SGA3 - Human Brain Project Specific Grant Agreement 3
(945539) / ACA - Advanced Computing Architectures (SO-092) /
Transparent Deep Learning with Renormalized Flows
(BMBF-01IS19077A) / Impuls- und Vernetzungsfonds
(IVF-20140101)},
pid = {G:(EU-Grant)945539 / G:(DE-HGF)SO-092 /
G:(DE-Juel-1)BMBF-01IS19077A / G:(DE-HGF)IVF-20140101},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2023-09969},
url = {https://publications.rwth-aachen.de/record/972001},
}
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