A central goal in neuroscience is to interpret neural activation and, moreover, to do so in a way that captures universal principles by generalizing across individuals. Recent research in multivoxel pattern-based fMRI analysis has led to considerable success at decoding within individual subjects. However, the goal of being able to decode across subjects is still challenging: It has remained unclear what population-level regularities of neural representation there might be. Here, we present a novel and highly accurate solution to this problem, which decodes across subjects between eight different stimulus conditions. The key to finding this solution was questioning the seemingly obvious idea that neural decoding should work directly on neural activation patterns. On the contrary, to decode across subjects, it is beneficial to abstract away from subject-specific patterns of neural activity and, instead, to operate on the similarity relations between those patterns: Our new approach performs decoding purely within similarity space. These results demonstrate a hitherto unknown population-level regularity in neural representation and also reveal a striking convergence between our empirical findings in fMRI and discussions in the philosophy of mind addressing the problem of conceptual similarity across neural diversity.