Level-Crossing Density as a Mesh-Free High-Frequency Auxiliary Loss for Implicit Neural Representations

arXiv:2607.05815v1 Announce Type: new Abstract: The Minkowski functionals of a field's excursion sets -- area, boundary measure, and Euler characteristic -- describe its level-set morphology; the Euler characteristic is the cheapest handle on topology. We derive smooth Monte-Carlo estimators for all three of a continuous neural field, evaluated at scattered points via the co-area formula and Gauss-Bonnet, using only autodiff: no grid, no complex, no persistence. The estimator is accurate to 1-3% against exact topology in 2D and 3D, and costs about 3 ms per iteration where a persistent-homology

Source: arXiv cs.LG — read the full report at the original publisher.

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