Processing speed is an important construct in understanding cognition. This study was aimed to control task specificity for understanding the neural mechanisms underlying cognitive processing speed. Forty young adult subjects performed attention tasks of two modalities (auditory and visual) and two levels of task rules (compatible and incompatible). Block-design fMRI captured BOLD signals during the tasks. Thirteen regions of interest were defined with reference to publicly available activation maps for processing speed tasks. Cognitive speed was derived from task reaction times, which yielded six sets of connectivity measures. Mixed-effect LASSO regression revealed six significant paths suggestive of a cerebello-frontal network predicting the cognitive speed. Among them, three are long range (two fronto-cerebellar, one cerebello-frontal), and three are short range (fronto-frontal, cerebello-cerebellar, and cerebello-thalamic). The long-range connections are likely to relate to cognitive control, and the short-range connections relate to rule-based stimulus-response processes. The revealed neural network suggests that automaticity, acting on the task rules and interplaying with effortful top-down attentional control, accounts for cognitive speed. Copyright © 2020. Published by Elsevier Inc.