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A fundamental cognitive process is the ability to map value and identity ontoobjects as we learn about them. Exactly how such mental constructs emerge andwhat kind of space best embeds this mapping remains incompletely understood.Here we develop tools to quantify the space and organization of such a mapping,thereby providing a framework for studying the geometric representations ofneural responses as reflected in functional MRI. Considering how human subjectslearn the values of novel objects, we show that quick learners have a higherdimensional geometric representation than slow learners, and hence more easilydistinguishable whole-brain responses to objects of different value.Furthermore, we find that quick learners display a more compact embedding oftheir neural responses and hence have a higher ratio of their task-baseddimension to their embedding dimension -- consistent with a greater efficiencyof cognitive coding. Lastly, we investigate the neurophysiological drivers ofhigh dimensional patterns at both regional and voxel levels, and we completeour study with a complementary test of the distinguishability of associatedwhole-brain responses. Our results demonstrate a spatial organization of neuralresponses characteristic of learning, and offer a suite of geometric measuresapplicable to the study of efficient coding in higher-order cognitive processesmore broadly.

Effective learning is accompanied by high dimensional and efficient representations of neural activity