The Interconnection Tensor Rank and the Neural Network Storage Capacity

2025/04/08 by Boris Kryzhanovsky, Kryzhanovsky, Boris V.
Computer Science · #94-10 #Advanced Statistical Modeling Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #I.5.1 #Neural Networks Stability and Synchronization #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2504.05926

openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Neural network properties are considered in the case of the interconnection tensor rank being higher than two. This sort of interconnection tensor occurs in realization of crossbar-based neural networks. It is intrinsic for a crossbar design to suffer from parasitic currents. It is shown that the interconnection tensor of a certain form makes the neural network much more efficient: the storage capacity and basin of attraction of the network increase considerably. A network like the Hopfield one is used in the study.

Citations

• 4K-Memristor Analog-Grade Passive Crossbar Circuit
• Implementation of Multilayer Perceptron Network with Highly Uniform Passive Memristive Crossbar Circuits
• Neuromorphic computing with multi-memristive synapses
• Vowel recognition with four coupled spin-torque nano-oscillators
• Dense Associative Memory is Robust to Adversarial Inputs
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• A Practical Guide to Training Restricted Boltzmann Machines

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