Learning rules for complex-valued patterns in networks of oscillators
Abstract
In this article, we extend learning rules from real binary to complex-valued spins. This formulation allows for a robust and natural representation of grayscale patterns, where spins behave as multi-state neurons and can be stored in a complex-valued weight matrix. We describe a rule that performs better than standard methods, such as Hebbian learning, to encode information in a suitable form for pattern retrieval with networks of oscillators. Since in neural networks it is of interest to have local and incremental learning rules, we prove the extension of a result by Diederich and Opper with our complex-valued spin formulation. We then test the behavior of the associative memory for the system of oscillators under different circumstances for both real-valued, as well as complex-valued correlated and random patterns.
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BibTeX
@misc{sbravati2026learning,
title = {{Learning rules for complex-valued patterns in networks of oscillators}},
author = {Federico Sbravati and Aida Todri-Sanial},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30800},
eprint = {2608.30800},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30800},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning rules for complex-valued patterns in networks of oscillators
AU - Federico Sbravati
AU - Aida Todri-Sanial
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30800
UR - https://arxiv.org/abs/2608.30800
AB - In this article, we extend learning rules from real binary to complex-valued spins. This formulation allows for a robust and natural representation of grayscale patterns, where spins behave as multi-state neurons and can be stored in a complex-valued weight matrix. We describe a rule that performs better than standard methods, such as Hebbian learning, to encode information in a suitable form for pattern retrieval with networks of oscillators. Since in neural networks it is of interest to have local and incremental learning rules, we prove the extension of a result by Diederich and Opper with our complex-valued spin formulation. We then test the behavior of the associative memory for the system of oscillators under different circumstances for both real-valued, as well as complex-valued correlated and random patterns.
ER -