arXiv:2608.05433 2026 Regularization 1 ideas extracted · analyzed Aug 31, 2026
The paper proves a strict sign-truncation principle for the spectral fractional Dirichlet energy: for fractional orders between 1 and 3/2, replacing a sign-changing function u by its absolute value strictly lowers its spectral fractional Laplacian energy. The transferable asset is the energy gap Q_s[u] - Q_s[|u|], which detects oscillatory sign structure through fractional powers of a Laplacian spectrum. A practical neural adaptation is a graph- or token-domain regularizer that penalizes this gap for hidden feature channels, encouraging smooth magnitude structure without forcing features to become constant. The continuum theorem motivates the construction, while the finite-graph version should be validated empirically because strict positivity is not guaranteed for every graph discretization.
Add a spectral fractional energy-gap regularizer to hidden features defined on a graph, image grid, or token interaction graph. The penalty is large when a channel has sign changes that create high-frequency fractional energy, while preserving the feature magnitude after applying elementwise absolute-value truncation.