Capacity of the Ant Navigation System

Insects such as ants exhibit impressive navigational abilities despite possessing compact nervous systems. This study investigates the computational principles underlying visual memory and route navigation in ants, focusing on the mushroom body (MB), a sparse and plastic neural architecture known to be an important learning center in insects brain. We construct a biologically inspired neural network model and develop a theoretical framework to analyze how the statistical properties of visual inputs affect memory capacity. In the MB, sensory information is encoded by a large population of Kenyon Cells (KCs), each receiving sparse input from projection neurons and activating only when a threshold is crossed. To reflect the biological realism of continuous learning in navigating insects, we model synaptic plasticity as an online learning process, where updates occur step by step as new inputs are presented. Within this framework, in order to study the functioning of the network and in particular its maximum capacity, we reinterpret the KC activity as a stochastic threshold-crossing event, allowing us to model memory saturation using first passage time (FPT) theory. We explore both uncorrelated and structured naturalistic inputs, modeling KC dynamics as autoregressive processes and validating analytical predictions through simulations. Incorporating realistic image statistics via Gaussian random fields, we show how spatial and temporal correlations prolong memory lifetime. Mapping simulation time to physical distance using data from empirical neuroscience studies, we estimate a maximum memorized path length consistent with behavioral observations. This work bridges neural computation, statistical physics, and biological plausibility, providing a description of memory encoding in insect-inspired networks and offering insights for the design of efficient artificial learning systems.