Arie Ogranovich | Searcharxiv

arXiv2026

Oscillator-Based Associative Memory with Exponential Capacity: Theory, Algorithms, and Hardware Implementation

Associative memory systems enable content-addressable storage and retrieval of patterns, a capability central to biological neural computation and artificial intelligence. Classical implementations such as Hopfield networks face fundamental limitations in memory capacity, scaling at most linearly with network size. We present an associative memory architecture based on Kuramoto oscillator networks with honeycomb topology in which memories are encoded as stable phase-locked configurations. The honeycomb network consists of multiple cycles that share nodes in a chain-like arrangement, creating a one-dimensional lattice of chained+loops. We prove that this architecture achieves exponential memory capacity: a network of $N$ oscillators can store $(2\lceil n_c/4 \rceil - 1)^m$ distinct patterns, where $m$ honeycomb cycles each contain $n_c$ oscillators. Moreover, we fully characterize all stable configurations and prove that each memory's basin of attraction maintains a guaranteed minimum size independent of network scale. Simulations using charge-density-wave (CDW) oscillators validate predicted phase-locking behavior, demonstrating practical realizability in neuromorphic hardware.

cs.NE↗

arXiv2025

Oscillatory Associative Memory with Exponential Capacity

The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular interest is the challenge of incorporating memory efficiently into the learning process. Inspired by how human brains store and retrieve information, associative memory mechanisms provide a class of computational methods that can store and retrieve patterns in a robust, energy-efficient manner. Existing associative memory architectures, such as the celebrated Hopfield model and oscillatory associative memory networks, store patterns as stable equilibria of network dynamics. However, the capacity (i.e. the number of patterns that a network can memorize normalized by their number of nodes) of existing oscillatory models have been shown to decrease with the size of the network, making them impractical for large-scale, real-world applications. In this paper, we propose a novel associative memory architecture based on Kuramoto oscillators. We show that the capacity of our associative memory network increases exponentially with network size and features no spurious memories. In addition, we present algorithms and numerical experiments to support these theoretical findings, providing guidelines for the hardware implementation of the proposed associative memory networks.

eess.SY↗