Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909854848778240 |
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| author | Xue, Shuyue Maghrebi, Mohammad Mias, George I. Piermarocchi, Carlo |
| author_facet | Xue, Shuyue Maghrebi, Mohammad Mias, George I. Piermarocchi, Carlo |
| contents | We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycle attractors. The limit cycle phase is bounded by two critical regions: a Hopf bifurcation line and a fold bifurcation line, each with unique dynamical critical exponents and sensitivity to perturbations. A Master Equation approach numerically verifies the critical behavior predicted analytically. We discuss how these networks could model biological processes near a critical threshold of cyclic instability evolving through multi-step transitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks Xue, Shuyue Maghrebi, Mohammad Mias, George I. Piermarocchi, Carlo Disordered Systems and Neural Networks Statistical Mechanics Biological Physics Molecular Networks We study Hopfield networks with non-reciprocal coupling inducing switches between memory patterns. Dynamical phase transitions occur between phases of no memory retrieval, retrieval of multiple point-attractors, and limit-cycle attractors. The limit cycle phase is bounded by two critical regions: a Hopf bifurcation line and a fold bifurcation line, each with unique dynamical critical exponents and sensitivity to perturbations. A Master Equation approach numerically verifies the critical behavior predicted analytically. We discuss how these networks could model biological processes near a critical threshold of cyclic instability evolving through multi-step transitions. |
| title | Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Biological Physics Molecular Networks |
| url | https://arxiv.org/abs/2501.00983 |