Compensating for Neural Transmission Delay Using Extrapolatory Neural Activation in Evolutionary Neural Networks Heejin Lim and Yoonsuck Choe Department of Computer Science, Texas A&M University 3112 TAMU, College Station, TX 77843-3112, USA Email: hjlim@cs.tamu.edu, choe@tamu.edu (Submitted on December 20, 2005; Accepted on March 20, 2006) Abstract — In an environment that is temporal as well as spatial in nature, the nervous system of agents needs to deal with various forms of delay, internal or external. Neural (or internal) delay can cause serious problems because by the time the central nervous system receives an input from the periphery, the environmental state is already updated. To be in touch with reality in the present rather than in the past, such a delay has to be compensated. Our ob- servation is that facilitatory dynamics found in synapses can effectively deal with delay by activating in an extrapolatory mode. The idea was tested in a modi ed 2D pole-balancing problem which included sensory delays. Within this domain, we tested the behavior of recur- rent neural networks with facilitatory neural dynamics trained via neuroevolution. Analysis of the performance and the evolved network parameters showed that, under various forms of delay, networks utilizing facilitatory dynamics are at a signi cant competitive advantage compared to networks with other dynamics. Keywords — Neural delay, delay compensation, extrapolation, pole balancing, evolutionary neural networks 1. Introduction Delay is an unavoidable problem for a living organism, which has physical limits in the speed of signal transmission within its system. Such a delay can cause serious problems as shown in Fig. 1. During the time a signal travels from a peripheral sensor (such as the photoreceptor) to the central nervous system (e.g. the visual cortex), a moving object in the environment can cover a signi cant distance which can lead to critical errors in the motor output based on that input. For example, the neural latency from visual stimulus onset to the motor output can be no less than 100 ms up to several hundred milliseconds [1, 2, 3]: An object moving at 40 mph can cover about 9 m in 500 ms (Fig. 1b). However, the problem can be overcome if the central nervous system can take into account the neural trans- mission delay (Δt) and generate action based on the estimated current state S(t +Δt) rather than that at its periphery at time t (S(t), Fig. 1c). Such a compensatory mechanism can be built into a system at birth, but such a x ed solution is not feasible because the organism grows in size during development, resulting in increased de- lay. For example, consider that the axons are stretched to become longer during growth. How can the developing nervous system cope with such a problem? This is the main question investigated in this paper. Psychophysical experiments such as ash-lag effect showed that extrapolation can take place in the nervous system. In visual ash-lag effect, the position of a moving object is perceived to be ahead of a brie y ashed object when they are physically co-localized at the time of the ash [4, 5, 6, 7, 8]. One interesting hypothesis arising from ash-lag effect is that of motion extrapolation: Extrapolation of state information over time can compensate for delay, and ash-lag effect may be caused by such a mechanism [5, 9, 10, 11]. According to the motion extrapolation model, a moving object’s location is extrapolated so that the perceived location of the object at a given instant is the same as the object’s actual location in the environment at that precise Neural Information Processing – Letters and Reviews Vol. 10, Nos. 4-6, April-June 2006 147