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Interactions across frontal cortex are critical for cognition. Animal studies suggest a role for mediodorsal thalamus (MD) in these interactions, but the computations performed and direct relevance to human decision making are unclear. Here, inspired by animal work, we extended a neural model of an executive frontal-MD network and trained it on a human decision-making task for which neuroimaging data were collected. Using a biologically-plausible learning rule, we found that the model MD thalamus compressed its cortical inputs (dorsolateral prefrontal cortex, dlPFC) underlying stimulus-response representations. Through direct feedback to dlPFC, this thalamic operation efficiently partitioned cortical activity patterns and enhanced task switching across different contingencies. To account for interactions with other frontal regions, we expanded the model to compute higher-order strategy signals outside dlPFC, and found that the MD offered a more efficient route for such signals to switch dlPFC activity patterns. Human fMRI data provided evidence that the MD engaged in feedback to dlPFC, and had a role in routing orbitofrontal cortex inputs when subjects switched behavioral strategy. Collectively, our findings contribute to the emerging evidence for thalamic regulation of frontal interactions in the human brain.