Amplitude equations of associative memory patterns in spatially distributed systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914097513103360 |
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| author | Houben, Akke Mats |
| author_facet | Houben, Akke Mats |
| contents | Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the spatio-temporal dynamics of memory recall. They capture pattern completion and selection, and show that short-range connections can sustain spatio-temporal memory pattern dynamics in the form of propagating patterning fronts. The derived amplitude equations are of the same form as those describing classical pattern-forming instabilities, indicating a universality of the dynamics of memory recall and pattern formation in non-equilibrium systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_13576 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Amplitude equations of associative memory patterns in spatially distributed systems Houben, Akke Mats Neurons and Cognition Disordered Systems and Neural Networks Pattern Formation and Solitons Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the spatio-temporal dynamics of memory recall. They capture pattern completion and selection, and show that short-range connections can sustain spatio-temporal memory pattern dynamics in the form of propagating patterning fronts. The derived amplitude equations are of the same form as those describing classical pattern-forming instabilities, indicating a universality of the dynamics of memory recall and pattern formation in non-equilibrium systems. |
| title | Amplitude equations of associative memory patterns in spatially distributed systems |
| topic | Neurons and Cognition Disordered Systems and Neural Networks Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2506.13576 |