Christodoulou, Georgia; Vogels, Tim PISTA ; Agnes, Everton J.
Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes.
PLoS Computational Biology
We thank Friedemann Zenke for his comments, especially on the effect of the self loops on the spectrum. We also thank Ken Miller and Bill Podlaski for helpful comments. This research was funded by a Wellcome Trust and Royal Society Henry Dale Research Fellowship (WT100000; TPV), a Wellcome Senior Research Fellowship (214316/Z/18/Z; GC, EJA, and TPV), and a Research Project Grant by the Leverhulme Trust (RPG-2016-446; EJA and TPV).
Christodoulou G, Vogels TP, Agnes EJ. Regimes and mechanisms of transient amplification in abstract and biological neural networks. PLoS Computational Biology. 2022;18(8). doi:10.1371/journal.pcbi.1010365
Christodoulou, G., Vogels, T. P., & Agnes, E. J. (2022). Regimes and mechanisms of transient amplification in abstract and biological neural networks. PLoS Computational Biology. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1010365
Christodoulou, Georgia, Tim P Vogels, and Everton J. Agnes. “Regimes and Mechanisms of Transient Amplification in Abstract and Biological Neural Networks.” PLoS Computational Biology. Public Library of Science, 2022. https://doi.org/10.1371/journal.pcbi.1010365.
G. Christodoulou, T. P. Vogels, and E. J. Agnes, “Regimes and mechanisms of transient amplification in abstract and biological neural networks,” PLoS Computational Biology, vol. 18, no. 8. Public Library of Science, 2022.
Christodoulou G, Vogels TP, Agnes EJ. 2022. Regimes and mechanisms of transient amplification in abstract and biological neural networks. PLoS Computational Biology. 18(8), e1010365.
Christodoulou, Georgia, et al. “Regimes and Mechanisms of Transient Amplification in Abstract and Biological Neural Networks.” PLoS Computational Biology, vol. 18, no. 8, e1010365, Public Library of Science, 2022, doi:10.1371/journal.pcbi.1010365.
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