How high dimensional neural dynamics are confined in phase space
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914988677922816 |
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| author | Wang, Shishe Huang, Haiping |
| author_facet | Wang, Shishe Huang, Haiping |
| contents | High dimensional dynamics play a vital role in brain function, ecological systems, and neuro-inspired machine learning. Where and how these dynamics are confined in the phase space remains challenging to solve. Here, we provide an analytic argument that the confinement region is an M-shape when the neural dynamics show a diversity, with two sharp boundaries and a flat low-density region in between. Despite increasing synaptic strengths in a neural circuit, the shape remains qualitatively the same, while the left boundary is continuously pushed away. However, in deep chaotic regions, an arch-shaped confinement gradually emerges. Our theory is supported by numerical simulations on finite-sized networks. This analytic theory opens up a geometric route towards addressing fundamental questions about high dimensional non-equilibrium dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How high dimensional neural dynamics are confined in phase space Wang, Shishe Huang, Haiping Neurons and Cognition Statistical Mechanics Neural and Evolutionary Computing Chaotic Dynamics High dimensional dynamics play a vital role in brain function, ecological systems, and neuro-inspired machine learning. Where and how these dynamics are confined in the phase space remains challenging to solve. Here, we provide an analytic argument that the confinement region is an M-shape when the neural dynamics show a diversity, with two sharp boundaries and a flat low-density region in between. Despite increasing synaptic strengths in a neural circuit, the shape remains qualitatively the same, while the left boundary is continuously pushed away. However, in deep chaotic regions, an arch-shaped confinement gradually emerges. Our theory is supported by numerical simulations on finite-sized networks. This analytic theory opens up a geometric route towards addressing fundamental questions about high dimensional non-equilibrium dynamics. |
| title | How high dimensional neural dynamics are confined in phase space |
| topic | Neurons and Cognition Statistical Mechanics Neural and Evolutionary Computing Chaotic Dynamics |
| url | https://arxiv.org/abs/2410.19348 |