Oscillator-Based Associative Memory with Exponential Capacity: Theory, Algorithms, and Hardware Implementation
This addresses a fundamental bottleneck in associative memory for AI and neuromorphic computing, offering a scalable solution with exponential capacity, though it is incremental in improving upon existing oscillator-based methods.
The paper tackles the limited memory capacity of classical associative memory systems like Hopfield networks by proposing an architecture based on Kuramoto oscillator networks with honeycomb topology, achieving exponential memory capacity with proven stable configurations and guaranteed basin sizes, validated through simulations with charge-density-wave oscillators.
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.