Synthesis of Hopfield Neural Network: Novel Results

Garimella Rama Murthy

cs.NEAug 26, 2026

Synthesis of Hopfield Neural Network: Novel Results

Authors: Garimella Rama Murthy

Organizations: Professor, Department of Computer Science, Mahindra University, Bahadurpally, Hyderabad, India

Abstract

Using the logical basis of synthesizing Hopfield Neural Network with desired corners of hypercube as stable states (proposed in [1]), it is proved that more corners of hypercube can be programmed as stable states (whether the number of neurons is even or odd). The research paper presents a new perspective to the so called "Programming Problem" of Hopfield Neural Network.

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Beyond Fixed Points: Superpolynomial Capacity of Asymmetric Hopfield Networks

Aakash Kumar, Anatoly Khina, Frederik Mallmann-Trenn, Emanuele Natale

COATI, CNRS, Inria, I3S, Université Côte d’Azur, France · School of Electrical and Computer Engineering, Tel Aviv University, Israel · Department of Informatics, King’s College London, UK+1

Dynamical Systems Hopfield Networks Associative Memory

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Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical synchronous asymmetric networks, however, has remained a challenge. We present a simple and robust construction within the classical asymmetric Hopfield model with binary neurons and synchronous updates, that allows

n

neurons to support

\exp\!\big(Ω(n/(\log n)^2)\big)

distinct limit-cycle attractors, each with period

\exp\!\big(Ω(\sqrt n/\log n)\big)

and robust to random noise with flip probability up to

\frac12-o(1)

, yielding superpolynomial capacity in both the number and length of stored sequences. This is the first demonstration of such capacity for asymmetric Hopfield networks, which we obtain by combining results from combinatorics, number theory and the analysis of opinion dynamics. Our findings show that synchronous asymmetric Hopfield networks possess a sequence-memory capacity which is larger and more robust than previously recognized, demonstrating that, in both biological and artificial neural systems, robust sequence representation can be achieved through coarse architectural motifs rather than complex nonlinearities.

Abstract

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