Replay builds an efficient cognitive map offline to avoid computation online

How do humans integrate fragmented experiences into a coherent structure that supports novel inferences? Addressing this question requires tracking learning from the very first encounters. Using magnetoencephalography, we recorded human neural activity throughout the full process - from initial learning to inference. Participants first learned one-dimensional, pairwise rank relationships that collectively formed a two-dimensional (2D) conceptual map, and then inferred unobserved relationships. During rest, offline replay integrated piecemeal memories into a coherent 2D representation, predicting the emergence of a grid-cell-like code that reflected a generalizable task schema. This schema reduced the need for effortful computations during subsequent inference. During inference, two types of on-task replay emerged: a fast replay, resembling offline replay and representing the full map, and a slow replay, focused on trial-specific details. Notably, slow replay negatively correlated with both grid-like coding and inference performance. Together, these results suggest that replay builds an efficient cognitive map offline, thereby reducing reliance on deliberate computation online.