From Chaos to Coherence: Effects of High-Order Synaptic Correlations on Neural Dynamics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918134625075200 |
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| author | Sherf, Nimrod Pitkow, Xaq Josić, Krešimir Bassler, Kevin E. |
| author_facet | Sherf, Nimrod Pitkow, Xaq Josić, Krešimir Bassler, Kevin E. |
| contents | Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on networks with random or simple connectivity structures. Experimental observations find that high-order cortical connectivity patterns affect the temporal patterns of network activity, but a theory that relates such complex structure to network dynamics has yet to be developed. Here, we show that third- and higher-order cyclic correlations in synaptic connectivities greatly impact neuronal dynamics. Specifically, strong cyclic correlations in a network suppress chaotic dynamics and promote oscillatory or fixed activity. This change in dynamics is related to the form of the unstable eigenvalues of the random connectivity matrix. A phase transition from chaotic to fixed or oscillatory activity coincides with the development of a cusp at the leading edge of the eigenvalue support. We also relate the dimensions of activity to the network structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00300 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Chaos to Coherence: Effects of High-Order Synaptic Correlations on Neural Dynamics Sherf, Nimrod Pitkow, Xaq Josić, Krešimir Bassler, Kevin E. Neurons and Cognition Disordered Systems and Neural Networks Biological Physics Recurrent Neural Network models have elucidated the interplay between structure and dynamics in biological neural networks, particularly the emergence of irregular and rhythmic activities in cortex. However, most studies have focused on networks with random or simple connectivity structures. Experimental observations find that high-order cortical connectivity patterns affect the temporal patterns of network activity, but a theory that relates such complex structure to network dynamics has yet to be developed. Here, we show that third- and higher-order cyclic correlations in synaptic connectivities greatly impact neuronal dynamics. Specifically, strong cyclic correlations in a network suppress chaotic dynamics and promote oscillatory or fixed activity. This change in dynamics is related to the form of the unstable eigenvalues of the random connectivity matrix. A phase transition from chaotic to fixed or oscillatory activity coincides with the development of a cusp at the leading edge of the eigenvalue support. We also relate the dimensions of activity to the network structure. |
| title | From Chaos to Coherence: Effects of High-Order Synaptic Correlations on Neural Dynamics |
| topic | Neurons and Cognition Disordered Systems and Neural Networks Biological Physics |
| url | https://arxiv.org/abs/2504.00300 |