What's so hard about hierarchical control? Pinpointing processing constraints within cue-based and serial-order control structures.

Most task spaces require a hierarchical structure, where decisions on one level are contingent on previous decisions made on one or more higher levels. While it is a truism that increasing the number of hierarchical levels makes it harder to solve a given task, the exact nature of this "number-of-levels" effect is not clear. On the one hand, processing costs might be strictly "local," incurred only when higher-level settings need to be updated, while otherwise lower-level decisions are insulated from the presence of higher-level settings (local updating costs with ballistic control). On the other hand, maintaining and integrating more complex hierarchical structures could require overall greater representational resources, negatively affecting each individual decision within the represented task space (global integration/maintenance costs). Further, navigation through hierarchical structures can be guided either through prompts in the environment (cue-based), or through sequential plans (serial-order based), with potentially distinct maintenance and updating demands. In two experiments, we assessed performance as a function of hierarchical level and format (serial-order vs. cue-based). Model comparisons showed that the pattern of costs in the serial-order format was consistent with a global maintenance/integration account. In contrast, in the cue-based format, costs arose at updating points and when one additional relevant level beyond the current decision was relevant, while additional levels produced no further costs. This overall constellation of costs can be explained by assuming that each decision requires checking the immediately relevant higher-level context for that decision. For cue-based control, this context involves the "next-level-up" rule, whereas in the serial-order format, each trial requires updating of the current position within the sequence, which in turn requires integration across all relevant hierarchical levels.