The geometry of the representation of decision variable and stimulus difficulty in the parietal cortex

Lateral intraparietal (LIP) neurons represent formation of perceptual decisions involving eye movements. In circuit models for these decisions, neural ensembles that encode actions compete to form decisions. Consequently, decision variables (DVs) are represented as partially potentiated action plans, where ensembles increase their average responses for stronger evidence supporting their preferred actions. As another consequence, DV representation and readout are implemented similarly for decisions with identical competing actions, irrespective of input and task context differences. Here, we challenge those core principles using a novel face-discrimination task, where LIP firing rates decrease with supporting evidence, contrary to conventional motion-discrimination tasks. These opposite response patterns arise from similar mechanisms in which decisions form along curved population-response manifolds misaligned with action representations. These manifolds rotate in state space based on task context, necessitating distinct readouts. We show similar manifolds in lateral and medial prefrontal cortices, suggesting a ubiquitous representational geometry across decision-making circuits.