Hippocampal theta frequency as a readout of path-integration recalibration

Understanding how the brain represents hidden variables is a fundamental challenge. In navigation, the internal path-integration gain is often masked by external landmarks that override the path integrator. Path integration can recalibrate its gain when allothetic and idiothetic cues conflict, but the real-time dynamics of this process are hidden to direct observation. Here, we demonstrate that theta frequency provides an error signal between the observable hippocampal gain and the internal path-integration gain. Theta frequency decreased as conflict between landmark-driven hippocampal gain and path-integration gain increased and recovered as the path-integration gain recalibrated to the new gain. A continuous attractor model replicated these dynamics, suggesting that the theta-frequency drop is driven by the misalignment of allothetic and idiothetic inputs, reducing the excitatory drive to the network. Thus, theta frequency provides a real-time readout of internal gain-error signals, offering a novel methodology to estimate hidden cognitive variables through observable physiological oscillations.