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We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...
The "quasi-constant " smooth overlap of atomic position and atom-centered symmetry function fingerprint manifolds recently discovered by Parsaeifard and Goedecker [J. Chem. Phys. 156, 034302 (2022)] are closely related to the degenerate pairs of configurat ...
Programming intelligent robots requires robust controllers that can achieve desired tasks while adapting to the changes in the task and the environment. In this thesis, we address the challenges in designing such adaptive and anticipatory feedback controll ...
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...
Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...
Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...
For compact, isometrically embedded Riemannian manifolds N -> R-L, we introduce a fourth-order version of the wave maps equation. By energy estimates, we prove an a priori estimate for smooth local solutions in the energy subcritical dimension n = 1, 2. Th ...
We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunc ...
State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not straightforward. First, omn ...
In the framework of Scale Relativity Theory, by analyzing dynamics of complex system structural units based on multifractal curves, both Schrodinger and Madelung approaches are functional and complementary. The Madelung selected approach involve synchronou ...