arXiv:2603.28288v1 Announce Type: new
Abstract: Kolmogorov-Arnold Networks (KAN) employ B-spline bases on a fixed grid, providing no intrinsic multi-scale decomposition for non-smooth function approximation. We introduce Fractal Interpolation KAN (FI-…
arXiv:2603.27859v1 Announce Type: new
Abstract: Large language models fragment Kazakh text into many more tokens than equivalent English text, because their tokenizers were built for high-resource languages. This tokenizer tax inflates compute, shorte…
arXiv:2603.27137v1 Announce Type: cross
Abstract: We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics gam…
arXiv:2603.27936v1 Announce Type: cross
Abstract: Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE…
arXiv:2603.28448v1 Announce Type: cross
Abstract: We propose Yau’s Affine Normal Descent (YAND), a geometric framework for smooth unconstrained optimization in which search directions are defined by the equi-affine normal of level-set hypersurfaces. T…
arXiv:2306.02192v3 Announce Type: replace
Abstract: Does the use of auto-differentiation yield reasonable updates for deep neural networks (DNNs)? Specifically, when DNNs are designed to adhere to neural ODE architectures, can we trust the gradients p…
arXiv:2603.28324v1 Announce Type: cross
Abstract: We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the condi…
arXiv:2510.27643v2 Announce Type: replace
Abstract: This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Baye…
arXiv:2402.07153v3 Announce Type: replace-cross
Abstract: This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation. We provide bounds for the generalization and training error in terms o…
arXiv:2603.26517v1 Announce Type: cross
Abstract: Since the earliest stages of human civilization, advances in technology have been tightly linked to our ability to understand and predict the mechanical behavior of materials. In recent years, this cha…