arXiv subjects

Anthony N Burkitt

Publications and source records attributed to Anthony N Burkitt.

3 recordsLinked to original sources

arXiv2023

Eigenvalue spectral properties of sparse random matrices obeying Dale's law

This paper examines the relationship between sparse random network architectures and neural network stability by examining the eigenvalue spectral distribution. Specifically, we generalise classical eigenspectral results to sparse connectivity matrices obeying Dale's law: neurons function as either excitatory (E) or inhibitory (I). By defining sparsity as the probability that a neutron is connected to another neutron, we give explicit formulae that shows how sparsity interacts with the E/I population statistics to scale key features of the eigenspectrum, in both the balanced and unbalanced cases. Our results show that the eigenspectral outlier is linearly scaled by sparsity, but the eigenspectral radius and density now depend on a nonlinear interaction between sparsity, the E/I population means and variances. Contrary to previous results, we demonstrate that a non-uniform eigenspectral density results if any of the E/I population statistics differ, not just the E/I population variances. We also find that 'local' eigenvalue-outliers are present for sparse random matrices obeying Dale's law, and demonstrate that these eigenvalues can be controlled by a modified zero row-sum constraint for the balanced case, however, they persist in the unbalanced case. We examine all levels of connection (sparsity), and distributed E/I population weights, to describe a general class of sparse connectivity structures which unifies all the previous results as special cases of our framework. Sparsity and Dale's law are both fundamental anatomical properties of biological neural networks. We generalise their combined effects on the eigenspectrum of random neural networks, thereby gaining insight into network stability, state transitions and the structure-function relationship.

q-bio.NC↗

arXiv2023

Understanding visual processing of motion: Completing the picture using experimentally driven computational models of MT

Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of neural computation. Computational modeling of the neuronal pathways of the visual cortex has been successful in developing theories of biological motion processing. This review describes a range of computational models that have been inspired by neurophysiological experiments. Theories of local motion integration and pattern motion processing are presented, together with suggested neurophysiological experiments designed to test those hypotheses.

q-bio.NC↗

arXiv2020

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

The mechanisms underlying how activity in the visual pathway may give rise through neural plasticity to many of the features observed experimentally in the early stages of visual processing was provided by Linkser 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 and plays little functional role in neural behaviour. 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 the arrival times of spikes from presynaptic neurons, providing a natural correlation cancellation mechanism for distal connections. The cut-off frequency decreases as the radial propagation delay within a layer increases relative to propagation delay between the layers, introducing an upper limit on temporal resolution. Given that the 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. We show that the addition of propagation delay reduces the range in the cell's on-center size, providing stability to variations in homeostatic parameters.

q-bio.NC↗