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  • Open Access

Emergent self-attention from astrocyte-gated associative memory dynamics

Arnau Vivet1,* and Alex Arenas1,2,†

  • *Contact author: arnau.vivet@urv.cat
  • †Contact author: alexandre.arenas@urv.cat
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Phys. Rev. Research 8, 023276 – Published 11 June, 2026

DOI: https://doi.org/10.1103/6q3q-vfs9

Abstract

We introduce a Hopfield-type associative memory in which effective connectivity is multiplicatively modulated by astrocytic gains evolving under an entropy-regularized replicator equation. The coupled neuron-astrocyte dynamics admit a Lyapunov function, ensuring global convergence. At fixed points, astrocytic gains implement a softmax-normalized allocation over pattern similarity scores, yielding a mechanistic realization of self-attention as emergent routing on the gain simplex. In regimes of high memory load and interference, the model significantly improves retrieval accuracy relative to classical Hopfield dynamics and recent neuron-astrocyte baselines. These results establish a dynamical systems framework linking glial modulation, competitive resource allocation, and attentionlike computation.

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Phys. Rev. Research 8, 023276– Published 11 June, 2026
  • Received 1 March 2026
  • Accepted 19 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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