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

TL;DR

This paper introduces a novel oscillator-based associative memory architecture with honeycomb topology that achieves exponential storage capacity and is validated through simulations, surpassing classical linear-capacity models.

Contribution

The authors propose a new associative memory design using Kuramoto oscillators with honeycomb topology, achieving exponential capacity and providing a complete stability analysis.

Findings

Achieves exponential memory capacity: $(2 ext{ceil}(n_c/4)-1)^m$ patterns.

Fully characterizes stable configurations and basins of attraction.

Validates phase-locking behavior with charge-density-wave oscillators.

Abstract

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.