Abstract: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. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension $D$. Experiments on synthetic and real data confirm LHSD's superior robustness and its utility in detecting memorization in large-scale diffusion models.
| Comments: | Accepted at ICML 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.01221 [cs.LG] |
| (or arXiv:2605.01221v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.01221 arXiv-issued DOI via DataCite (pending registration) |
From: Genki Osada [view email]
[v1]
Sat, 2 May 2026 03:30:55 UTC (27,115 KB)
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