Astrocytic gains in a Hopfield network evolve under replicator dynamics to produce emergent self-attention as softmax routing on the gain simplex at fixed points.
Consequently, the gain dy- namics are invariant under the sign flip⟨ξ µ, ϕ(x)⟩ 7→ 10 −⟨ξµ, ϕ(x)⟩
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Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics
Astrocytic gains in a Hopfield network evolve under replicator dynamics to produce emergent self-attention as softmax routing on the gain simplex at fixed points.