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Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examples
Yicen Li, Ruiyang Hong, Anastasis Kratsios +2
Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy…
Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity
Anastasis Kratsios, Gregory Cousins, Haitz Sáez de Ocáriz Borde +2
We show that, in a precise sense, a broad class of feedforward neural networks learn (have finite sample complexity) in the PAC model: every fixed finite feedforward architecture w…
Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data
Anastasis Kratsios, Tin Sum Cheng, Daniel Roy
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approxim…
Sharp Generalization Bounds for Foundation Models with Asymmetric Randomized Low-Rank Adapters
Anastasis Kratsios, Tin Sum Cheng, Aurelien Lucchi +1
Low-Rank Adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning (PEFT) technique for foundation models. Recent work has highlighted an inherent asymmetry…