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A bstract The efficient coding hypothesis presents a compelling success story for theoretical and systems neu-roscience. It marshals a unifying idea, that neural codes can be understood as efficient encodings of natural stimuli, to explain phenomena from across sensory systems, sometimes with exquisite precision. However, similar normative assaults on cognitive representations, such as those in prefrontal or entorhinal cortex, have been less comprehensively successful. We argue that this reflects efficient coding’s focus on encoded variables, overlooking the computations that neural circuits implement. Here, instead, we develop an efficient computing theory that studies optimal implementations of recurrent cognitive computations. We apply this framework to the prefrontal cortex, in particular, to a rich vein of neural recordings: structured working memory tasks, such as recalling a sequence. Despite using near-identical tasks, the literature has reported two distinct coding schemes: one contextual, with neurons active only in a particular sequence, the other compositional, with neurons tuned to a single sequence element. Just as efficient coding links stimuli statistics to optimal representation, our theory relates task structure and statistics to optimal representation. In so doing, we find that compositional and contextual codes can be understood as two extremes of a spectrum of optimal representations, with the correlations amongst sequence elements determining a task’s position on this spectrum. Our theory highlights previously underappreciated discrepancies between measured representations, explaining them via subtle task differences; and allows us to infer the algorithm underlying otherwise ambiguous neural data. In sum, we demonstrate an efficient computing approach that makes normative statements about cognitive representations, and serves as a tool for understanding a swathe of neural data.