Behavior is sloppy: a multitude of cognitive strategies can produce similar behavioral read-outs. An underutilized approach is to combine multifaceted behavioral analyses with neural recordings to resolve cognitive strategies. Here we show that rats performing a decision-making task exhibit distinct strategies over training, and these cognitive strategies are decipherable from orbitofrontal cortex (OFC) neural dynamics. We trained rats to perform a temporal wagering task with hidden reward states. While naive rats passively adapted to reward statistics, expert rats inferred reward states. Electrophysiological recordings and novel methods for characterizing population dynamics identified latent neural factors that reflected inferred states in expert but not naive rats. In experts, these factors showed abrupt changes following single trials that were informative of state transitions. These dynamics were driven by neurons whose firing rates reflected single trial inferences, and OFC inactivations showed they were causal to behavior. These results reveal the neural signatures of inference.