Both the human brain and artificial neural networks organize information in low-dimensional representational spaces, yet how this geometry supports learning remains unclear. Recent theoretical results suggest that low-dimensional representations enable faster convergence of empirical to population distributions under the Wasserstein distance, meaning that fewer samples are required to accurately capture the underlying data structure, thereby improving learning efficiency and generalization. We test this hypothesis in artificial and biological systems. Across small supervised networks and large pretrained foundation models, lower intrinsic dimension is associated with smaller training–test distribution divergence and better generalization. In the human brain, this effect is region-specific: In higher-order cortical areas such as the angular gyrus, individuals with lower intrinsic dimension and more stable representational distributions across sessions showed stronger learning outcomes. Together, these findings reveal a shared geometric principle across brains and artificial intelligence (AI): Low-dimensional representational organization accelerates distributional convergence and supports efficient generalization.