74 citations · 120 across the 41 of their papers we have counts for
46 papers
Certifiably Interpretable Training of ReLU-MLPs for Boolean Tasks with Guaranteed Truth-Table Generalization
Hrad Ghoukasian, Anastasis Kratsios
As compute scales, models evolve, and training algorithms advance, our ability to explain the increasingly powerful AI systems they enable is eroding. To help safeguard interpretab…
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…
NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes
Anastasis Kratsios, Giulia Livieri, Philipp Schmocker
We address fundamental challenges in representing and computing -valued predictable square-integrable processes over , collected in the space $\mathcal{H}^2_…
Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation
Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim +2
Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes. While powerful, this perspective is incomplete: it primarily capture…
PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable Jäckel Operator
Raeid Saqur, Yannick Limmer, Anastasis Kratsios +2
Modern option-learning systems operate in two coordinates: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and implied volatility (IV) sp…
Structure-Preserving Reconstruction of Convex Lipschitz Functionals on Hilbert Spaces from Finite Samples
Anastasis Kratsios
Convex functionals are ubiquitous in applied analysis, appearing as value functions, risk measures, super-hedging prices, and loss functionals in machine learning. In many applicat…
MEMOA: Massive Mixtures of Online Agents via Mean-Field Decentralized Nash Equilibria
Xuwei Yang, David B. Emerson, Fatemeh Tavakoli +1
In the modern age of large-scale AI, federated learning has become an increasingly important tool for training large populations of AI agents; however, its computational and commun…
Adaptivity Under Realizability Constraints: Comparing In-Context and Agentic Learning
Anastasis Kratsios, A. Martina Neuman, Philipp Petersen
We compare in-context learning with fixed queries and agentic learning with adaptive queries for uniform approximation of task families. We consider two settings: an unrestricted r…
Neural Operators Can Discover Functional Clusters
Yicen Li, Jose Antonio Lara Benitez, Ruiyang Hong +3
Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for…
Certifiable Boolean Reasoning Is Universal
Wenhao Li, Anastasis Kratsios, Hrad Ghoukasian +1
The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neur…
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…
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…
Autonomous-Flow-Based Generation
Hossein Rouhvarzi, Anastasis Kratsios
We show that using autonomous-flow-based generation, one can universally approximate orientation-preserving diffeomorphisms defined on the cube by Neural ODEs with rate $\mathcal{O…
Quantifying The Limits of AI Reasoning: Systematic Neural Network Representations of Algorithms
Anastasis Kratsios, Dennis Zvigelsky, Bradd Hart
A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting r…
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…
Neural Operators Which Certifiably Simultaneously Solve Infinitely Many Convex Programs using Logarithmic Rank and Linear Complexity
Anastasis Kratsios, Ariel Neufeld, Philipp Schmocker
Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whe…
LoRA Fine-Tuning Without GPUs: A CPU-Efficient Meta-Generation Framework for LLMs
Reza Arabpour, Haitz Sáez de Ocáriz Borde, Anastasis Kratsios
Low-Rank Adapters (LoRAs) have transformed the fine-tuning of Large Language Models (LLMs) by enabling parameter-efficient updates. However, their widespread adoption remains limit…
Generative Market Equilibrium Models with Stable Adversarial Learning via Reinforcement
Anastasis Kratsios, Xiaofei Shi, Qiang Sun +1
We present a general computational framework for solving continuous-time financial market equilibria under minimal modeling assumptions while incorporating realistic financial fric…
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…
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…
Keep It Light! Simplifying Image Clustering Via Text-Free Adapters
Yicen Li, Haitz Sáez de Ocáriz Borde, Anastasis Kratsios +1
In the era of pre-trained models, effective classification can often be achieved using simple linear probing or lightweight readout layers. In contrast, many competitive clustering…
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…
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…
Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization
Mikhail Persiianov, Arip Asadulaev, Nikita Andreev +5
Learning conditional distributions is a central problem in machine learning, which is typically approached via supervised methods with paired data .…