Brownian Kernel Ladders
We introduce Brownian kernel ladders (BKLs), a recursive hierarchy of integral reproducing kernel Hilbert spaces built from linear functionals by repeatedly integrating Brownian pullback kernels indexed by functions from the preceding layer. The nonnegative 1-homogeneity of the Brownian kernel yields a kernel-preserving canonical spherical normalization and propagates square-root regularity through the hierarchy. Allowing all canonical ladder measures to vary produces a full adaptive BKL envelope with an infimal complexity. For this envelope, we prove depth-dependent Hölder and pointwise estimates, quasi-Banach structure, nestedness, and, under a geometric trace condition, strict growth w...
| Authors | Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia et al. |
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| Primary category | cs.LG |
| Published | 14 June 2026 |
| Last updated at source | 10 August 2026 |
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