7 papers
Mixtures of Neural Operators Reduce Active Complexity in Operator Learning
Anastasis Kratsios, Takashi Furuya, Jose Antonio Lara Benitez +2
Operator-learning systems are not governed solely by total parameter count; for one query, the relevant bottleneck can be the model that must be loaded and evaluated. We study this…
Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs
Takashi Furuya, Anastasis Kratsios
Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model disco…
Approximation Theory for Lipschitz Continuous Transformers
Takashi Furuya, Davide Murari, Carola-Bibiane Schönlieb
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz const…
One model to solve them all: 2BSDE families via neural operators
Takashi Furuya, Anastasis Kratsios, Dylan Possamaï +1
We introduce a mild generative variant of the classical neural operator model, which leverages Kolmogorov--Arnold networks to solve infinite families of second-order backward stoch…
Approximation theory for 1-Lipschitz ResNets
Davide Murari, Takashi Furuya, Carola-Bibiane Schönlieb
1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) b…
Approximation Rates in Besov Norms and Sample-Complexity of Kolmogorov-Arnold Networks with Residual Connections
Anastasis Kratsios, Bum Jun Kim, Takashi Furuya
Inspired by the Kolmogorov-Arnold superposition theorem, Kolmogorov-Arnold Networks (KANs) have recently emerged as an improved backbone for most deep learning frameworks, promisin…