Paper accepted to AAAI26 conference! [Blessing of dimensionality]

Our work on approximating functions on manifolds has been accepted to the AAAI’26 conference! This work shows that the difficulty of approximating functions depends only on the intrinsic properties of your manifold, such as the intrinsic dimension and its curvature. Moreover, it does not depend at all on the dimension of the latent space that the manifold is embedded in. This has direct applications to the manifold hypothesis, and demonstrates that such low-dimensional structures are essential for training neural networks in high dimensions. arXiv