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

A fundamental cognitive process is to map value and identity onto the objects we learn about. However, what space best embeds this mapping is not completely understood. Here we develop tools to quantify the space and organization of such a mapping in neural responses as reflected in functional MRI, to show that quick learners have a higher dimensional representation than slow learners, and hence more easily distinguishable whole-brain responses to objects of different value. Furthermore, we find that quick learners display more compact embedding of their neural responses, and hence have higher ratios of their stimuli dimension to their embedding dimension, which is consistent with greater efficiency of cognitive coding. Lastly, we investigate the neurophysiological drivers at smaller scales and study the complementary distinguishability of whole-brain responses. Our results demonstrate a spatial organization of neural responses characteristic of learning and offer geometric measures applicable to identifying efficient coding in higher-order cognitive processes.