Many animal behaviors require orientation and steering with respect to the environment. For insects, a key brain area involved in spatial orientation and navigation is the central complex. Activity in this neural circuit has been shown to track the insect's current heading relative to its environment and has also been proposed to be the substrate of path integration. However, it remains unclear how the output of the central complex is integrated into motor commands. Central complex output neurons project to the lateral accessory lobes (LAL), from which descending neurons project to thoracic motor centers. Here, we present a computational model of a simple neural network that has been described anatomically and physiologically in the LALs of male silkworm moths, in the context of odor-mediated steering. We present and analyze two versions of this network, one rate based and one based on spiking neurons. The modeled network consists of an inhibitory local interneuron and a bistable descending neuron (flip-flop) that both receive input in the LAL. The flip-flop neuron projects onto neck motor neurons to induce steering. We show that this simple computational model not only replicates the basic parameters of male silkworm moth behavior in a simulated odor plume but can also take input from a computational model of path integration in the central complex and use it to steer back to a point of origin. Furthermore, we find that increasing the level of detail within the model improves the realism of the model's behavior, leading to the emergence of looping behavior as an orientation strategy. Our results suggest that descending neurons originating in the LALs, such as flip-flop neurons, are sufficient to mediate multiple steering behaviors. This study is therefore a first step to close the gap between orientation circuits in the central complex and downstream motor centers.

While neural networks are highly effective at learning task-relevant representations from data, they typically do not learn representations with the kind of symbolic structure that is hypothesized to support high-level cognitive processes, nor do they naturally model such structures within problem domains that are continuous in space and time. To fill these gaps, this work exploits a method for defining vector representations that bind discrete (symbol-like) entities to points in continuous topological spaces in order to simulate and predict the behavior of a range of dynamical systems. These vector representations are spatial semantic pointers (SSPs), and we demonstrate that they can (1) be used to model dynamical systems involving multiple objects represented in a symbol-like manner and (2) be integrated with deep neural networks to predict the future of physical trajectories. These results help unify what have traditionally appeared to be disparate approaches in machine learning.