**Rapid learning of higher-order statistics in implicit sequence learning**

K. R. Thompson & P. J. Reber

Implicit learning involves extracting experienced regularities and statistical variation from the environment in order to improve behavior. Because knowledge of environmental structure is acquired outside of awareness, it is challenging to determine the precise nature of the information that is obtained from experience. A commonly used paradigm to study this implicit learning process is perceptual-motor sequence learning in which a covertly embedded sequence is used to create statistical structure across sequences of actions. It is somewhat intuitive to hypothesize that participants acquire the simplest possible statistics, which should be the least computationally demanding to track across time. In most sequence learning experiments, this means learning second-order conditional probabilities (or trigrams). In the current experiments, we manipulated the statistical information available to participants during training on an implicit sequence learning task. Participants were either trained with a traditional 12-item repeating sequence, or with probabilistic, pseudo-randomly mixed 6-item fragments of that sequence constructed to match the lower-order (trigram) statistics of the repeating sequence condition. If only the simplest necessary statistics are learned, we would expect participants to display equal sequence learning across conditions. We found that participants who trained on full repetitions of the sequence exhibited robustly better sequence learning than participants who completed fragment training. This implies that some higher-order statistics are acquired rapidly during repeating sequence practice. We built a computational simulation model to test specific hypotheses about candidate learning processes. The best-fitting statistical learning model incorporated immediate acquisition of fourth-order conditional probabilities, two orders of magnitude more complex than strictly necessary to learn the sequence. A third behavioral experiment confirmed that fragments training led to equivalent learning as repeated sequence training when fourth-order information was matched. This is particularly striking considering the exponential increase in storage capacity necessary to compute higher-order statistics among all elements of the environment. While our results do not rule out other approaches to the computationally difficult problem (e.g., chunking mechanisms), both the behavioral and modeling data suggest that participants rapidly learn higher-order statistics from sequential information.