Exponential history integration with diverse temporal scales in retrosplenial cortex supports hyperbolic behavior

Animals use past experience to guide future choices. The integration of experiences typically follows a hyperbolic, rather than exponential, decay pattern with a heavy tail for distant history. Hyperbolic integration affords sensitivity to both recent environmental dynamics and long-term trends. However, it is unknown how the brain implements hyperbolic integration. We found that mouse behavior in a foraging task showed hyperbolic decay of past experience, but the activity of cortical neurons showed exponential decay. We resolved this apparent mismatch by observing that cortical neurons encode history information with heterogeneous exponential time constants that vary across neurons. A model combining these diverse timescales recreated the heavy-tailed, hyperbolic history integration observed in behavior. In particular, the time constants of retrosplenial cortex (RSC) neurons best matched the behavior, and optogenetic inactivation of RSC uniquely reduced behavioral history dependence. These results indicate that behavior-relevant history information is maintained across multiple timescales in parallel and that RSC is a critical reservoir of information guiding decision-making.