Modeling echolocation as an active pursuit of information via infotaxis

Abstract Echolocation is a closed-loop active sensing modality in which animals not only choose how they move to acquire information, but also actively modulate incoming sensory (echo) information by shaping the acoustic signals they emit to probe the environment. While many models describe how echolocating animals react to prior echoes by adjusting subsequent behavior, few explicitly model how they cognitively reason about information embedded in echoes when determining future actions. Here, we extend “infotaxis,” an information-greedy algorithm originally developed for olfactory search, to sonar sensing by formulating an echolocating agent searching for a single target under sensory uncertainty characterized by probabilities of miss and false alarm. Through analytical and computational analyses, we show that the characteristic exploration-exploitation balance of infotaxis also emerges in echolocation, and that the efficiency and reliability of infotaxis search depend strongly on sensory information quality. Compared with a maximum a posteriori agent that always directs the beam to the most probable target location, the infotaxis agent consistently completes searches with fewer pings and greater robustness to sensory uncertainty. These results highlight information as a powerful concept for understanding active sensing and developing models for sonar-guided autonomy in both biological and engineered systems. Competing Interest Statement The authors have declared no competing interest. Footnotes ↵b Also at: Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA We clarified the manuscript scope, emphasizing that our goal is to extend the infotaxis decision rule to echolocation rather than claim formal equivalence with the original olfactory observation model. We revised the Abstract, Introduction, and Discussion to better explain the analogous exploration-exploitation balance in echolocation. We also revised the Methods to clarify key model assumptions, justify the use of MAP as a belief-based exploitation baseline, refine the definition of a successful search, and add a step-by-step algorithm describing the echolocation infotaxis procedure. In the Results, we expanded the analysis to include both underestimated and overestimated sensory uncertainty, corresponding MAP analyses, and additional performance metrics, including highest posterior, entropy, and cumulative beam aim path length. In the Discussion, we described extensions needed for comparison with experimental data, cited recent robotic validation experiments, and revised the comparison with reinforcement learning. We also added a notation appendix and new supplemental simulations with beampattern-modulated sensory uncertainty. SYMBOLS - ℬs - Set of cells covered by the beam footprint - EX [Hs(K)] - Expected entropy after action s and observation X - H(K) - Entropy of the posterior of target location - Hs(K|X) - Entropy of the posterior of target location after action s and observation X - K - Random variable representing target location - k - Specific candidate target location (cell) - ℒ - Likelihood - NA - Number of cells in the search space - NB - Number of cells covered by the beam footprint - PFA - Probability of false alarm - Posterior probability of target location after ping n - PM - Probability of miss - Pmax - Maximum posterior probability of target location - pth - Search termination threshold for Pmax - rA - Radius of the search space - rB - Radius of the beam footprint - s - Agent action; consisting of beam aim and beam footprint size in single target search - X - Echo observation (X = 1 detection, X = 0 no detection) - α - Relative proportion of the beam footprint within the search space (= NB/NA) - θB - Beam aim