Parietal top-down projections balance flexibility and stability in adaptive learning

Rapid behavioral adaptation requires the brain to solve a fundamental computational dilemma: how to flexibly update learned rules while maintaining stable motor performance. This flexibility-stability trade-off is central to cognitive function and artificial intelligence, yet its neural circuit basis is poorly understood. Here, we identify the circuit architecture that coordinates this balance. Using a within-session auditory reversal learning task combined with circuit-specific manipulations in mice, we demonstrate that the posterior parietal cortex (PPC) orchestrates adaptive learning through two parallel, anatomically distinct pathways to the auditory cortex (AC) and inferior colliculus (IC). These two circuits perform a double dissociation of function: the PPC-to-AC circuit facilitates flexible rule updating by encoding dynamic stimulus-outcome contingencies, while the PPC-to-IC circuit preserves stable action execution across changing rules. A feedforward network model further demonstrates that segregated stable and flexible top-down projections are necessary and sufficient for rapid reversal learning. This parallel architecture segregates adaptive and stable computations into distinct circuits, providing a mechanistic framework for cognitive flexibility and offering potential insight into conditions where this balance is disrupted, such as obsessive-compulsive disorder and schizophrenia.