AI RESEARCH
Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation
arXiv CS.LG
•
ArXi:2605.01221v1 Announce Type: new While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions.