Impact of axonal delay on structure development in a multi-layered network

Abstract

The mechanisms underlying how activity in the visual pathway gives rise through neural plasticity to many features observed experimentally in early stages of visual processing was provided by Linsker in a seminal, three-paper series. Owing to the complexity of multi-layer models, an implicit assumption in Linsker’s and subsequent papers has been that propagation delay is homogeneous, playing little functional role in neural behavior. In this paper, we relax this assumption to examine the impact of distance-dependent axonal propagation delay on neural learning. We show that propagation delay induces low-pass filtering by dispersing arrival times of spikes from presynaptic neurons, providing a natural correlation cancellation mechanism for distal connections. The cut-off frequency decreases as radial propagation delay within a layer increases relative to propagation delay between layers, introducing an upper limit on temporal resolution. Given that the postsynaptic potential acts as a low-pass filter, we show that the effective time constant of each should enable processing of similar scales of temporal information. This has implications for the visual system, in which receptive field size and, thus, propagation delay, increases with eccentricity. Furthermore, network response is frequency dependent since higher frequencies require increased input amplitude to compensate for attenuation. This concords with frequency-dependent contrast sensitivity, which changes with eccentricity and receptive field size. We further show that the proportion of inhibition relative to excitation is larger where radial propagation delay is long relative to inter-laminar delay, and that delay reduces the range in on-center size, providing stability to variations in homeostatic parameters.