74 citations · 120 across the 41 of their papers we have counts for
23 papers · 1 filter
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…
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…
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…
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…
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…
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…
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 .…
Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity
Ruiyang Hong, Anastasis Kratsios
The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that nee…
Neural Spacetimes for DAG Representation Learning
Haitz Sáez de Ocáriz Borde, Anastasis Kratsios, Marc T. Law +2
We propose a class of trainable deep learning-based geometries called Neural Spacetimes (NSTs), which can universally represent nodes in weighted directed acyclic graphs (DAGs) as…
Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
Anastasis Kratsios, A. Martina Neuman, Gudmund Pammer
Machine learning models with inputs in a Euclidean space , when implemented on digital computers, generalize, and their generalization gap converges to at a rate…
Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries
Haitz Sáez de Ocáriz Borde, Anastasis Kratsios
The inductive bias of a graph neural network (GNN) is largely encoded in its specified graph. Latent graph inference relies on latent geometric representations to dynamically rewir…
Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures
Anastasis Kratsios, Ruiyang Hong, Haitz Sáez de Ocáriz Borde
We study the representation capacity of deep hyperbolic neural networks (HNNs) with a ReLU activation function. We establish the first proof that HNNs can -isometrical…
Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation
J. Antonio Lara Benitez, Takashi Furuya, Florian Faucher +3
Despite their remarkable success in approximating a wide range of operators defined by PDEs, existing neural operators (NOs) do not necessarily perform well for all physics problem…
Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?
Anastasis Kratsios, Behnoosh Zamanlooy
We study the problem of approximating compactly-supported integrable functions while implementing their support set using feedforward neural networks. Our first main result transcr…
Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer
Beatrice Acciaio, Anastasis Kratsios, Gudmund Pammer
Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless,…
Optimizing Optimizers: Regret-optimal gradient descent algorithms
Philippe Casgrain, Anastasis Kratsios
The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as…
A Canonical Transform for Strengthening the Local -Type Universal Approximation Property
Anastasis Kratsios, Behnoosh Zamanlooy
Most -type universal approximation theorems guarantee that a given machine learning model class is dense in $L^p_μ(\mathbb{…
Non-Euclidean Universal Approximation
Anastasis Kratsios, Eugene Bilokopytov
Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks. However, the impact of such change…