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

Abstract

In his seminal, three-paper series, Linsker provided a mechanism for how random activity in the visual pathway could give rise to many of the features observed experimentally in the early stages of visual processing. Owing to the complexity of multilayer models, an implicit assumption in Linsker's and subsequent papers has been that propagation delay is homogeneous and, consequently, plays little functional role in neural behaviour. In this paper, we relax this assumption to examine the impact of axonal distance-dependent propagation delay on neural learning. We show that propagation delay induces low-pass filtering by dispersing the arrival times of spikes from pre-synaptic neurons, providing a natural correlation cancellation mechanism for distal connections. The cut-off frequency decreases as the radial propagation delay within a layer, relative to propagation delay between the layers, increases, introducing an upper limit on temporal resolution. Given that the post-synaptic potential (PSP) also acts as a low-pass filter, we show that the effective time constant of each should enable the processing of similar scales of temporal information. This result has implications for the visual system, in which receptive field size and, thus, radial propagation delay, increases with eccentricity. Furthermore, the network response is frequency-dependent since higher frequencies require increased input amplitude to compensate for attenuation. This concords with frequency dependent contrast sensitivity in the visual system, 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 propagation delay. Finally, we determine the eigenfunctions of both Linsker's network, and the network with propagation delay. We show that the addition of propagation delay stabilizes the leading eigenfunction to changes in homeostatic parameters, and hence stabilizes the resulting receptive field structure. It also reduces the range in the size of the spatial opponent cell's on-center size, providing stability to variations in homeostatic parameters.