Physical neural networks (PNNs) leverage intrinsic device dynamics for energy-efficient computing by mapping neural network operations onto physical parameters. However, practical PNN deployment faces critical challenges: cumulative non-idealities during signal propagation and the mismatch between conventional training algorithms and physical hardware. Biological systems overcome similar limitations through synaptic plasticity combining local learning with homeostatic regulation. The Bienenstock-Cooper-Munro (BCM) rule, a prominent model of synaptic plasticity, addresses these challenges by integrating Hebbian learning with a history-dependent sliding threshold that provides intrinsic stability.
This review systematically examines BCM rules from three perspectives: theoretical foundations, hardware implementation, and PNN applications. The BCM rule exhibits three essential features: spike-rate dependent plasticity (SRDP), threshold sliding, and non-monotonic enhanced depression effect (EDE). At the device level, first-order memristors naturally emulate SRDP through flux-controlled conductance modulation. Threshold sliding requires second-order dynamics, demonstrated in WO_x, HfO_x, and STO-based devices where additional state variables modulate competition between potentiation and decay. EDE realization follows two approaches: external coding strategies (e.g., triplet-STDP) that induce non-monotonic behavior through precisely timed spikes, and intrinsic dynamics strategies leveraging competing physical processes in two-terminal devices to achieve EDE under natural spike-rate coding without external circuitry. At the system level, BCM enables unsupervised learning in single-layer, multi-layer, and convolutional networks, approaching backpropagation performance in certain tasks while offering biological plausibility and energy efficiency. The sliding threshold mechanism provides homeostatic regulation that prevents weight divergence, mitigates catastrophic forgetting, and enables self-repair in fault-tolerant systems.
Despite progress, challenges remain: theoretical gaps between frequency-based BCM and observed spike-timing plasticity, reliance on external coding schemes compromising device simplicity, and parameter sensitivity in complex networks. Future directions include deepening theoretical understanding of BCM dynamics, developing intrinsic device strategies fully capturing BCM features under natural coding, and fostering interdisciplinary collaboration among materials, circuits, and algorithms to enable large-scale robust PNN implementations.