Experimental Setup methods were used to pre-determine sample sizes but our sample sizes are similar to those reported in previous publications 3,4 All participants were financially remunerated for their time. In the first experiment, participants were paid up to $7 for an estimated 40 minutes: $2 for completing each of the two stages, $1 for completing the entire task, and an extra $1 on each stage on which they correctly answered at least 90% of trials. Experiment 2 provided the same payment as Experiment 1, but with an estimated duration of 40 minutes. In the third experiment, subjects were paid up to $11 for an estimated 60 minutes: $3 per stage, $1 for completing the entire task, and $2 for >90% performance on each stage. Subjects performed a self-paced SRT motor response task using a keyboard. Stimuli were represented as a horizontal row of five gray squares; all five squares were shown at all times during the main phase of the experiment. To indicate a target key or pair of keys that the subject was meant to press, the corresponding squares would be outlined in red (Fig. 1A). When subjects pressed the correct key combination, the squares on the screen would immediately display the next target. If an incorrect key was pressed, or a key was left out of a two-key combination, the message “Error!” was displayed on the screen below the stimuli, and remained until the subject pressed the correct key(s). The squares corresponded spatially with keys ‘Space’, ‘H’, ‘J’, ‘K’ and ‘L’, such that the left square represented ‘Space’ and the right square represented ‘L’. These keys were chosen to ergonomically rest underneath the subject’s right hand on a QWERTY keyboard with their thumb above ‘Space’, index finger above ‘H’, and so on (Fig. 1B). The order in which stimuli were presented to the subject in Experiments 1 and 3 was prescribed by a random walk on a graph of N = 15 nodes connected by E = 30 edges. In each graph, one of the 15 one- or two-finger key combinations was randomly assigned to each node (Fig. 1A). A different graph (mapping of key presses to nodes) was generated for each random walk. For any two nodes that were not connected by an edge, the transition probability was equal to zero. For any two nodes that were connected by an edge, the transition probability was equal to 1 divided by the number of edges emanating from the pre-transition node. In Experiment 2, stage 1 consisted of a random walk as previously described. The order of stimulus presentation in stage 2 was generated by a series of Hamiltonian cycles through the graph. A single cycle consisted of every node in the graph being visited exactly once, and each cycle was followed by another Hamiltonian cycle beginning from a node adjacent from where the last cycle ended. We studied the learning of 3 different graph topologies: a modular graph, a lattice graph, and a random graph (Fig. 1C). The modular graph was characterized by 3 clusters of 5-nodes each, and a greater number of edges between nodes in a cluster than 20/29