Abstract
To flexibly adapt to new situations, our brains must understand the regularities in the world, as well as those in our own patterns of behaviour. A wealth of findings is beginning to reveal the algorithms that we use to map the outside world(1-6). However, the biological algorithms that map the complex structured behaviours that we compose to reach our goals remain unknown. Here we reveal a neuronal implementation of an algorithm for mapping abstract behavioural structure and transferring it to new scenarios. We trained mice on many tasks that shared a common structure (organizing a sequence of goals) but differed in the specific goal locations. The mice discovered the underlying task structure, enabling zero-shot inferences on the first trial of new tasks. The activity of most neurons in the medial frontal cortex tiled progress to goal, akin to how place cells map physical space. These 'goal-progress cells' generalized, stretching and compressing their tiling to accommodate different goal distances. By contrast, progress along the overall sequence of goals was not encoded explicitly. Instead, a subset of goal-progress cells was further tuned such that individual neurons fired with a fixed task lag from a particular behavioural step. Together, these cells acted as task-structured memory buffers, implementing an algorithm that instantaneously encoded the entire sequence of future behavioural steps, and whose dynamics automatically computed the appropriate action at each step. These dynamics mirrored the abstract task structure both on-task and during offline sleep. Our findings suggest that schemata of complex behavioural structures can be generated by sculpting progress-to-goal tuning into task-structured buffers of individual behavioural steps.