Wahiba Taouali

No clock to rule them all.

This article introduces general concepts and definitions related to the notion of asynchronous computation in the framework of artificial neural networks. Using the dynamic field theory as an illustrative example, we explain why one may want to perform such asynchronous computation and how one can implement it since this computational scheme draws several consequences on both the trajectories and the stability of the whole system. After giving an unequivocal definition of asynchronous computation, we present a few practically usable methods and quantitative bounds that can guarantee most of the mesoscopic properties of the system.

A parsimonious computational model of visual target position encoding in the superior colliculus

The superior colliculus (SC) is a brainstem structure at the crossroad of multiple functional pathways. Several neurophysiological studies suggest that the population of active neurons in the SC encodes the location of a visual target to foveate, pursue or attend to. Although extensive research has been carried out on computational modeling, most of the reported models are often based on complex mechanisms and explain a limited number of experimental results. This suggests that a key aspect may have been overlooked in the design of previous computational models. After a careful study of the literature, we hypothesized that the representation of the whole retinal stimulus (not only its center) might play an important role in the dynamics of SC activity. To test this hypothesis, we designed a model of the SC which is built upon three well-accepted principles: the log-polar representation of the visual field onto the SC, the interplay between a center excitation and a surround inhibition and a simple neuronal dynamics, like the one proposed by the dynamic neural field theory. Results show that the retinotopic organization of the collicular activity conveys an implicit computation that deeply impacts the target selection process.

Asynchronous Evaluation as an Efficient and Natural Way to Compute Neural Networks

Several artificial neuron models are best described by a set of continuous differential equations that define the evolution of some variables over time, e.g. the membrane potential of the neuron. When these models are connected together, we obtain a differential equation system with complex inter-dependent interactions. To gain the solution of such a system, in general it requires a numerical integration since in the vast majority of cases there is no analytical solution. Regardless of the numerical method used to we would like to emphasize the fact that all these numerical methods actually require a central clock to synchronize computations. For instance, to compute the model variables at time t explicit methods use the information available on all model variables at time t −1. Since the spirit of neural networks lies in the so-called distributed property, it is rather counter-intuitive to rely implicitly on such a central clock. In this context, we would like to study the extent to which we can remove this central clock and implement asynchronous computations. This has been already studied in the case of cellular automata [1, 2, 3, 4] and parallel computations [5, 6] where different levels of numerical synchrony are considered. The highest level corresponds to the whole system being periodically evaluated and updated, while the lowest level corresponds to an undefined period of time after which a system unit is evaluated. Some proof of convergence have been proposed in the excellent work of [7] where he assumes all functions to be of type K. However this condition does not hold for differential equation systems as ours with several distinct fixed points. Consequently the convergence conditions of asynchronous calculations shown in [7] do not apply for our model and hence the convergence of the synchronous and asynchronous to the same fixed point is not guaranteed asshown in our numerical experiments. In this work, we focus on three levels, namely the synchronous, the asynchronous uniform and asynchronous non-uniform level. Firstly, we define these levels and then introduce the model under study. In the subsequent section , we present numerical experiments which reveal different aspects of the three computation schemes.