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Article Dans Une Revue PLoS Computational Biology Année : 2022

The impact of sparsity in low-rank recurrent neural networks

Résumé

Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces. How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics. This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are known to be highly sparse. Here we investigate the dynamics of low-rank recurrent networks in which the connections are randomly sparsified, which makes the network connectivity formally full-rank. We first analyse the impact of sparsity on the eigenvalue spectrum of low-rank connectivity matrices, and use this to examine the implications for the dynamics. We find that in the presence of sparsity, the eigenspectra in the complex plane consist of a continuous bulk and isolated outliers, a form analogous to the eigenspectra of connectivity matrices composed of a low-rank and a full-rank random component. This analogy allows us to characterise distinct dynamical regimes of the sparsified low-rank network as a function of key network parameters. Altogether, we find that the low-dimensional dynamics induced by low-rank connectivity structure are preserved even at high levels of sparsity, and can therefore support rich and robust computations even in networks sparsified to a biologically-realistic extent.
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Dates et versions

hal-03797582 , version 1 (14-10-2022)

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Elizabeth Herbert, Srdjan Ostojic. The impact of sparsity in low-rank recurrent neural networks. PLoS Computational Biology, 2022, 18 (8), pp.e1010426. ⟨10.1371/journal.pcbi.1010426⟩. ⟨hal-03797582⟩
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