Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size

תקציר מקורי באנגליתarXiv:2510.04440v2 Announce Type: replace Abstract: We develop a source-driven fractional heat-kernel framework for semi-super\-vised graph learning that combines nonlocal propagation with sustained label information. A fixed nonzero label source compatible with the Laplacian null space prevents asymptotic collapse into that space, providing a mechanism for mitigating oversmoothing at long diffusion times. The fractional order controls the relative modal attenuation and the spectral weighting of the sustained response, while the diffusion time sets the propagation horizon. We characterize conservation laws and equilibria on normalized and disconnected graphs, develop a null-space deflation, and analyze the approximation of the propagators. On Two-Moon, fractional orders improve source-free