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Recent work has highlighted that many types of variables are represented in each neocortical area. How can these many neural representations be organized together without interference, and coherently maintained/updated through time? We recorded from large neural populations in posterior cortices as mice performed a complex, dynamic task involving multiple interrelated variables. The neural encoding implied that correlated task variables were represented by uncorrelated modes in an information-coding subspace. We show via theory that this can enable optimal decoding directions to be insensitive to neural noise levels. Across posterior cortex, principles of efficient coding thus applied to task-specific information, with neural-population modes as the encoding unit. Remarkably, this encoding function was multiplexed with rapidly changing, sequential neural dynamics, yet reliably followed slow changes in task-variable correlations through time. We can explain this as due to a mathematical property of high-dimensional spaces that the brain might exploit as a temporal scaffold.