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This paper presents a novel Hopfield-type associative memory model where astrocyte-modulated synaptic gains, governed by an entropy-regularized replicator equation, dynamically route information. The model's Lyapunov function guarantees convergence, and the astrocyte dynamics effectively implement a softmax-normalized allocation over pattern similarity scores, thus realizing self-attention. The proposed model demonstrates significantly improved retrieval accuracy compared to traditional Hopfield networks and recent neuron-astrocyte models, particularly under high memory load.
Self-attention can emerge naturally from the competitive dynamics of neuron-astrocyte interactions, offering a biologically plausible alternative to standard attention mechanisms.
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 attention-like computation.
