Continuous-Time Heteroassociative Memory at Biological Timescales

Associative learning in biological systems unfolds continuously in time, yet most models implicitly assume synchronized, discrete updates that instantaneously deliver the correct teaching signal to each synapse. We study a model of continuous-time heteroassociative memory neural networks in which inference and learning coevolve under coupled ODEs, and where different error-propagation topologies determine how error signals reach synapses. Longer error pathways result in propagation delays of error signals, while deeper networks result in propagation delays of cue signals. We experimentally investigate the boundary at which learning begins to fail under different combinations of propagation time constants, synaptic plasticity time constants, error signal delay $\Delta$, and cue duration $T$. We find that the plasticity time constant must substantially exceed the cue duration ($t_\text{plas}/T\approx10\text{–}50$ in our settings), a regime aligned with biological evidence. Together, these results yield testable predictions for associative memories in neuroscience, and practical design guidance for hardware implementations.