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
7 Pith papers cite this work. Polarity classification is still indexing.
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DLAM extends Hopfield networks with dreaming and multi-layer coupling to enhance retrieval and pattern separation, analyzed via replica-symmetric free energy and Monte Carlo simulations.
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.
CRHNs integrate convolutional extraction with subspace attractor retrieval trained via Subspace Rotation Algorithm and report order-of-magnitude lower reconstruction error than MHNs and PCNs on STL data under adversarial perturbations.
Thesis uses statistical mechanics to study DAM and RBM models for understanding memorization, low-dimensional learning, and adversarial robustness in neural networks.
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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.