BCM theory

BCM theory (Bienenstock, Cooper, and Munro theory) is a model of synaptic plasticity that modifies Hebbian learning by introducing a sliding threshold for long-term potentiation (LTP) and long-term depression (LTD). The threshold moves as a function of the average postsynaptic activity: when neurons fire at high rates, the threshold rises, making LTD more likely; when firing is sparse, the threshold falls, making LTP dominant. This homeostatic mechanism prevents runaway excitation and ensures competitive, stable learning.

BCM theory transforms Hebbian correlation into a competitive process: inputs that are consistently active strengthen while inactive inputs weaken, producing selective receptive fields similar to those observed in visual cortex development. The theory bridges neuroscience and machine learning by showing how local, biologically plausible rules can produce structured, stable representations without external supervision.