arXiv:2608.13682 2026 Regularization 1 ideas extracted · analyzed Sep 1, 2026
The paper gives a sharp pointwise bound on the pullback metric of a V-harmonic map, improving the usual quadratic dilatation estimate through a piecewise function of the generalized dilatation order. This transfers to neural encoders as a curvature-aware constraint on their local Jacobian expansion, especially for hyperbolic or other Riemannian latent spaces. A practical implementation is a spectral Jacobian regularizer that penalizes only directions exceeding the refined curvature-dependent threshold, rather than penalizing all Jacobian entries equally.
Regularize a neural encoder so its local pullback metric is bounded by the refined Schwarz-lemma constant instead of using a generic Frobenius Jacobian penalty. For an encoder into a negatively curved latent space, penalize only singular directions whose squared expansion exceeds the curvature- and dilatation-dependent threshold.