9 papers
Optimization Geometry of Equivalent Brownian RKHS Representations
Mahdi Mohammadigohari, Gustau Camps-Valls
Equivalent finite parameterizations can represent the same functions and intrinsic norm yet induce different optimization algorithms. We study this effect in a controlled finite Br…
Brownian Heads for Deep ReLU Representations: Activation Mass and the Cost of Same-Sample Selection
Mahdi Mohammadigohari, Nicole Mücke
Deep representation learning often selects hidden features and fits the final predictor on the same sample, so fixed-feature analysis performed after selection can omit selection c…
Common Covariance Geometry and Certification for Brownian Kernel Ladders
Mahdi Mohammadigohari
A representation-adaptive kernel class produces, on a fixed sample, a union of reproducing-kernel Hilbert-space ellipsoids rather than one ellipsoid. We introduce the minimum-trace…
Trace-Norm Geometry of Composed Multitask Predictors
Mahdi Mohammadigohari
Multitask predictors apply task-specific functions to a shared representation. Penalizing the representation and task functions separately can assign different costs to equivalent…
Operator-Theoretic Generalization Bounds for Multitask Deep Learning
Mahdi Mohammadigohari, Thomas Borsani, Giuseppe Di Fatta
We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproduc…
Variation Brownian Kernel Ladders
Mahdi Mohammadigohari
Claims about the benefit of depth depend on the complexity assigned to a representation. We introduce the \emph{Variation Brownian Kernel Ladder} (VBKL), a path-atomic function-spa…
Brownian Kernel Ladders
Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia +1
We introduce Brownian kernel ladders (BKLs), a recursive hierarchy of integral reproducing kernel Hilbert spaces built from linear functionals by repeatedly integrating Brownian pu…
On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning
Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia +1
The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conv…
Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learning
Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia +1
This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework.…