Path integration — a network model

Abstract

Abstract. Path integration is a primary means of navigation for a number of animals. We present a model which performs path integration with a neural network. This model is based on a neural structure called a sinusoidal array, which allows an efficient representation of vector information with neurons. We show that exact path integration can easily be achieved by a neural network. Thus deviations from the direct home trajectory, found previously in experiments with ants, can not be explained by computational limitations of the nervous system. Instead we suggest that the observed deviations are caused by a strategy to simplify landmark navigation.

Path integration in mammals

“…In recent times, a number of attempts have been made to describe PI in terms of arithmetical models (Fujita et al, 1990), flow diagrams (Mittelstaedt, 2000), and especially neural networks (Hartmann and Wehner, 1995;Guazzelli et al, 2001;Wittman and Schwegler, 1995;McNaughton et al, 1996;Samsonovich and McNaughton, 1997;Maurer, 1998;Arleo and Gerstner, 2000;Stringer et al, 2002). Most network models take into account available evidence that external references as well as PI are needed to complement each other, suggesting the binding process discussed in the next section.…”

Evolving neural models of path integration

“…Secondly, even the classes of description may change when implementing a model neurally. Wittmann and Schwegler (1995) note how their geocentric polar HV, represented in their network using a sinusoidal array (see below), becomes equivalent to Mittelstaedt's geocentric Cartesian bicomponent model (Mittelstaedt, 1985) for a specific set of parameters.…”

“…If we believe they are capable, we still have options (1), (2) and (3) available: (2) cannot be ruled out since selection may still only have produced an approximate system, provided it is sufficiently good. Wittmann and Schwegler (1995) present a system that can perform accurate PI using only simple and relatively few model neurons, suggesting that the reason is not a limitation of neural processing. Kim and Hallam's neural PI model supports this conclusion (Kim and Hallam, 2000).…”

“…Wehner, 1988, 1994). Neural models of C. fortis PI were presented by Hartmann and Wehner (1995) and Wittmann and Schwegler (1995). Both are based on different methods of encoding the HV chosen by the modeller, since no neurophysiological data are available to suggest the actual mechanism employed.…”

“…Hartmann and Wehner (1995) present a neural network PI model that shares the property of only producing observable errors after certain journey shapes. However, now that the system is built using neurons, the model is no longer any simpler than an exact PI system (Wittmann and Schwegler, 1995). …”