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A Closed-Form Formula for Consistent Lipschitz Regression on Metric Spaces with Sparse Neural Network Realizations
Ruiyang Hong, Hrad Ghoukasian, Anastasis Kratsios
Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions o…
Statistical Guarantees for Reasoning Probes on Looped Boolean Circuits
Anastasis Kratsios, Giulia Livieri, A. Martina Neuman
We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning. The underlying computation is given by…
Learning from one graph: transductive learning guarantees via the geometry of small random worlds
Nils Detering, Luca Galimberti, Anastasis Kratsios +2
Since their introduction by Kipf and Welling in , a primary use of graph convolutional networks is transductive node classification, where missing labels are inferred within…
Is In-Context Universality Enough? MLPs are Also Universal In-Context
Anastasis Kratsios, Takashi Furuya
The success of transformers is often linked to their ability to perform in-context learning. Recent work shows that transformers are universal in context, capable of approximating…
Step by Step: Adaptive Gradient Descent for Training L-Lipschitz Neural Networks
Kyle Sung, Kholood Khalil, Noah Forman +2
We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradien…
Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts
Anastasis Kratsios, Haitz Sáez de Ocáriz Borde, Takashi Furuya +1
Mixture-of-Experts (MoEs) can scale up beyond traditional deep learning models by employing a routing strategy in which each input is processed by a single "expert" deep learning m…