For vertebrates, there is no one-to-one correspondence between the neurons in one subject and those in another, impeding direct cross-subject mapping. Neural computations occur in a subject-specific high dimensional system, but ensemble activity patterns during a behavior are often confined to a low dimensional neural latent space. In this study we provide a method to identify universal features of neural computation by using a normalized embedding alongside a geometric framework to compare neural latent spaces across time points and subjects. We found that neural ensemble activity converges to a common geometry in different non-human primates performing similar reaching or grasping behaviors. When trained on neural activity from different subjects, across subject decoding of behavior can match or exceed within subject decoding performance. These results are consistent with the hypothesis that cortical networks in different animals operate using conserved principles of neural computation when performing similar sensorimotor tasks. Further, these results have implications for understanding computational building blocks in brain networks and to improve the function, speed, and reliability of brain-computer interfaces that rely on accurate and repeatable neural decoding.