Learning reshapes cortical activity, but it remains unclear whether population-level changes primarily reflect exposure to sensory statistics or reward-driven assignment of behavioral relevance. We analysed calcium imaging data from mice exposed to the same visual environment with or without reward, and used tensor component analysis to separate within-trial dynamics from across-trial learning-related structure. Rewarded learning produced a distinct reorganisation of population geometry. After learning, fewer components were sufficient to reconstruct neural activity, and variance became more concentrated in the dominant modes. This compression was not merely a nonspecific reduction in variability, but was task-aligned: the leading variance-explaining components also carried strong stimulus discriminability. These results suggest that reward does not simply enhance sensory selectivity, but reorganises visual cortical population geometry so that behaviorally relevant stimulus dimensions are embedded in the dominant modes of population activity. This micropublication was created as part of the Neuromatch Impact Scholars Program 2025. Author contribution note: Katja Kaurinkoski, Rohit Jeswanth, and Ishatpreet Singh contributed equally to this work and share second authorship. Project Website: https://impact-scholars.github.io/madrid-carvajal-2026-reward-shapes-geometry Repository: https://github.com/impact-scholars/madrid-carvajal-2026-reward-shapes-geometry