Operator-Theoretic Generalization Bounds for Multitask Deep Learning
We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces. In vector-valued Sobolev RKHSs, we derive Rademacher complexity bounds for invertible and width-expanding injective architectures. The estimates separate the output-coupling contribution, represented by the trace of the task matrix, from the layerwise operator norms, Sobolev symbol ratios, determinant factors, and restriction constants generated by the linear maps. We then analyze a distinct one-dimensional Brownian/Cameron--Martin regime. Using the exact anchored derivative-norm chara...
| Authors | Mahdi Mohammadigohari, Thomas Borsani, Giuseppe Di Fatta |
|---|---|
| Primary category | cs.LG |
| Published | 17 August 2026 |
| Last updated at source | 17 August 2026 |
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