RNCRNs are proven to universally approximate any dynamics with enough chemical neurons and fast reactions, with small instances trained for biological behaviors and shown realizable via DNA technologies.
Large Associative Memory Problem in Neurobiology and Machine Learning,
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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.
Dense associative memory retrieval converges geometrically with O(log N) time and tolerates adversarial corruptions under separation and bounded-interference conditions, achieving capacity scaling Θ(N^{n-1}).
Hierarchical Hopfield models retrieve concepts from noisy data via a strokes-concepts structure even without perfect stroke retrieval, as the second layer compensates for first-layer errors in both fixed- and variable-sized cases.
citing papers explorer
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Recurrent neural chemical reaction networks that approximate arbitrary dynamics
RNCRNs are proven to universally approximate any dynamics with enough chemical neurons and fast reactions, with small instances trained for biological behaviors and shown realizable via DNA technologies.
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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.
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Algorithmic Analysis of Dense Associative Memory: Finite-Size Guarantees and Adversarial Robustness
Dense associative memory retrieval converges geometrically with O(log N) time and tolerates adversarial corruptions under separation and bounded-interference conditions, achieving capacity scaling Θ(N^{n-1}).
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A mathematical analysis of hierarchical Hopfield models
Hierarchical Hopfield models retrieve concepts from noisy data via a strokes-concepts structure even without perfect stroke retrieval, as the second layer compensates for first-layer errors in both fixed- and variable-sized cases.