Local dynamic interactions in the collicular motor map: a neural network model

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In this paper we explore the possibility that some of the dynamic properties of the neural activity in the gaze-related motor map (located in the intermediate layers of the superior colliculus) might be mediated by local interactions between movement-related neurons and fixation neurons. More specifically, the goal of this research is to demonstrate, from a computational standpoint, which classes of dynamic behaviour of the collicular neurons can be obtained without the intervention of feedback signals, and hence to begin to explore the extent to which the gaze system needs feedback in order to operate. We modelled: (i) the collicular motor map as dynamical system realized with a recurrent neural network: (ii) the dynamics of the neural activity in the map as the trnnsients of that system towards an equilibrium configuration which the network learnt with a recurrent learning algorithm (recurrent backpropagation). The results of our simulations demonstrate the following. (i) The transients of the trained network are hill-flattening patterns as observed by some experimenters in the burst-neuron layer of the superior colliculus of rhesus monkeys. This result was obtained despite the fact that the learning algorithm did not specify what the network's transients should be. (ii) The connections in the trained network are excitatory within the fixation zone of the motor map and inhibitory elsewhere. (iii) The results of the learning are robust in the face of changes in the connectivity pattern and the initialization of the weights, but a local connectivity pattern favours the network's stability. (iv) Nonlinearity is required in order to obtain meaningful dynamic behaviours. (v) The trained network is robust to abnormal stimulation patterns, such as noisy and multiple stimuli, and when multiple stimuli are utilized the response of the network remains a stereotyped flattening one.The results of the learning point to the possibility that the dynamics of the burst-neuron layer of the superior colliculus might be locally regulated rather than feedback-driven, and that the action of the feedback is confined to the layer of the buildup neurons. The results of the multiple-stimulation experiment support the hypothesis asserted by one of the authors in an earlier work (Massone 1994), that the averaging of the direction of movement following double stimulation of the motor map (Robinson 1972) does not occur at the level of the motor map. This paper also constitutes a study of the properties and responses of recurrent backpropagation subject to various choices for the parameters of the network and the algorithm.