11 citations · 26 across the 26 of their papers we have counts for
30 papers
DYSANOS Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces
Hans Buehler, Blanka Horvath, Anastasis Kratsios +1
This article presents with DYSANOS the first generative market model for smooth SANOS option surfaces for all strikes and expiries which are free of static arbitrage. Our model is…
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…
SANOS Smooth strictly Arbitrage-free Non-parametric Option Surfaces
Hans Buehler, Blanka Horvath, Anastasis Kratsios +2
We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitr…
Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators
Dena Firoozi, Anastasis Kratsios, Xuwei Yang
Traditional mean-field game (MFG) solvers operate on an instance-by-instance basis, which becomes infeasible when many related problems must be solved (e.g., for seeking a robust d…
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…
Online Federation For Mixtures of Proprietary Agents with Black-Box Encoders
Xuwei Yang, Fatemeh Tavakoli, David B. Emerson +1
Most industry-standard generative AIs and feature encoders are proprietary, offering only black-box access: their outputs are observable, but their internal parameters and architec…
Neural Operators Can Play Dynamic Stackelberg Games
Guillermo Alvarez, Ibrahim Ekren, Anastasis Kratsios +1
Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately…
Scalable Message Passing Neural Networks: No Need for Attention in Large Graph Representation Learning
Haitz Sáez de Ocáriz Borde, Artem Lukoianov, Anastasis Kratsios +2
We propose Scalable Message Passing Neural Networks (SMPNNs) and demonstrate that, by integrating standard convolutional message passing into a Pre-Layer Normalization Transformer-…
A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression
Tin Sum Cheng, Aurelien Lucchi, Anastasis Kratsios +1
This paper conducts a comprehensive study of the learning curves of kernel ridge regression (KRR) under minimal assumptions. Our contributions are three-fold: 1) we analyze the rol…
Filtered not Mixed: Stochastic Filtering-Based Online Gating for Mixture of Large Language Models
Raeid Saqur, Anastasis Kratsios, Florian Krach +5
We propose MoE-F - a formalized mechanism for combining pre-trained Large Language Models (LLMs) for online time-series prediction by adaptively forecasting the best weighting…
Higher-Order Transformer Derivative Estimates for Explicit Pathwise Learning Guarantees
Yannick Limmer, Anastasis Kratsios, Xuwei Yang +2
An inherent challenge in computing fully-explicit generalization bounds for transformers involves obtaining covering number estimates for the given transformer class . Crude est…
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…
Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum
Tin Sum Cheng, Aurelien Lucchi, Anastasis Kratsios +1
We derive new bounds for the condition number of kernel matrices, which we then use to enhance existing non-asymptotic test error bounds for kernel ridgeless regression (KRR) in th…
A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression
Tin Sum Cheng, Aurelien Lucchi, Ivan Dokmanić +2
Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in sev…
Transformers Can Solve Non-Linear and Non-Markovian Filtering Problems in Continuous Time For Conditionally Gaussian Signals
Blanka Horvath, Anastasis Kratsios, Yannick Limmer +1
The use of attention-based deep learning models in stochastic filtering, e.g. transformers and deep Kalman filters, has recently come into focus; however, the potential for these m…
Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing
Xuwei Yang, Anastasis Kratsios, Florian Krach +2
We propose an optimal iterative scheme for federated transfer learning, where a central planner has access to datasets for the same learning model $f_…
An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning
Anastasis Kratsios, Chong Liu, Matti Lassas +2
Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces and $\m…
Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning
Anastasis Kratsios, Cody Hyndman
We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an in…
Small Transformers Compute Universal Metric Embeddings
Anastasis Kratsios, Valentin Debarnot, Ivan Dokmanić
We study representations of data from an arbitrary metric space in the space of univariate Gaussian mixtures with a transport metric (Delon and Desolneux 2020). We de…
Universal Approximation Under Constraints is Possible with Transformers
Anastasis Kratsios, Behnoosh Zamanlooy, Tianlin Liu +1
Many practical problems need the output of a machine learning model to satisfy a set of constraints, . Nevertheless, there is no known guarantee that classical neural network ar…
Universal Regular Conditional Distributions
Anastasis Kratsios
We introduce a deep learning model that can universally approximate regular conditional distributions (RCDs). The proposed model operates in three phases: first, it linearizes inpu…
Universal Approximation Theorems for Differentiable Geometric Deep Learning
Anastasis Kratsios, Leonie Papon
This paper addresses the growing need to process non-Euclidean data, by introducing a geometric deep learning (GDL) framework for building universal feedforward-type models compati…