Optimization Geometry of Equivalent Brownian RKHS Representations
Equivalent finite parameterizations can represent the same functions and intrinsic norm yet induce different optimization algorithms. We study this effect in a controlled finite Brownian RKHS with nodal, increment, and spectral coordinates. Classical finite-element, RKHS-interpolation, Brownian-covariance, and mixed-boundary DCT identities make the shared hypothesis class, Brownian energy, approximation operator, and coordinate maps explicit. Our main results concern the optimization geometry of this fixed model. With mapped initialization, identical scalar steps, and identical minibatches, nodal and spectral GD/SGD have exactly the same mapped trajectories. Increment GD is an explicit Eu...
| Authors | Mahdi Mohammadigohari, Gustau Camps-Valls |
|---|---|
| Primary category | cs.LG |
| Published | 18 September 2026 |
| Last updated at source | 18 September 2026 |
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