Publications and Preprints

2025

• Saqur, R., Kratsios, A., Krach†, F., Limmer†, Y., Tian, J. J., Willes, J., Horvarth, B., and Rudzicz, F., Filtered not Mixed: Stochastic Filtering-Based Online Gating for Mixture of Large Language Models, International Conference on Learning (2025)
• Borde, H., Kratsios, A., Law, M. T., Dong, X., and Bronstein, M., Neural Spacetimes for DAG Representation Learning, International Conference on Learning (2025)
• Kratsios, A., Sáez de Ocáriz Borde, H., Furuya, T., and Law, M. T., Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts, Transactions on Machine Learning Research (2025)
• Kratsios, T., Furuya, Is In-Context Universality Enough? MLPs are Also Universal In-Context, ArXiV (2025)
• Sung†, K.., Kratsios, A., Forman, N., Guiding Two-Layer Neural Networks toward Lipschitzness via Gradient Descent Learning Rate Constraints, ArXiV (2025)
• Li, Y.., Sáez de Ocáriz Borde, H., Kratsios, A., McNicholas, P., Keep it Light! Simplifying Image Clustering via Text-Free Adapters, ArXiV (2025)

2024

• Kratsios, A., Sáez de Ocáriz Borde, Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries, NeurIPS (2024)
• Cheng†, T. S., Lucchi, A., Kratsios, A., and Belius, D., A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression, NeurIPS (2024)
• Kolesov, A., Mokrov, P., Udovichenko, I., Gazdieva, M., Pammer, G., A. Kratsios, Korotin, A., and Burnaev, E., Energy-Guided Continuous Entropic Barycenter Estimation for General Costs, NeurIPS (2024), Award: Spotlight
• Cheng†, T. S., Lucchi, A., Kratsios, A., and Belius, D., Characterizing Overfitting in Kernel Ridgeless Regression through the Eigenspectrum, International Conference on Learning (2024)
• Benitez†, J. A. L., Furuya, T., Faucher, F., Kratsios, A., Tricoche, X., and de Hoop, M. V., Out-of-distributional Risk Bounds for Neural Operators with Applications to the Helmholtz Equation. Journal of Computational Physics, 113168
• Kratsios, A., Hong†, R., and de Ocáriz Borde, H., Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures. Neural Networks, 106420
• G. A. Alvarez, I. Ekren, A. Kratsios, X. Yang, Neural Operators Can Play Dynamic Stackelberg Games, ArXiV: 2411.09644
• Borde, H., Lukoianov, A., Kratsios, A., Law, M. T., Dong, X., and Bronstein, M., Scalable Message Passing Neural Networks: No Need for Attention in Large Graph Representation Learning, ArXiV: 2408.13885
• Persiianov, M., Asadulaev, A., Andreev, N., Starodubcev, N., Baranchuk, D., Kratsios, A., Burnaev, E. and Korotin, A., Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization, ArXiV: 2410.02628
• Hong†, R., and Kratsios, A., Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity, ArXiV: 2409.12335
• Arabpour†, R., Armstrong, J., Galimberti, L., Kratsios, A., and Livieri, G., Low-dimensional Approximations of the Conditional Law of Volterra Processes: A Non-positive Curvature Approach, ArXiV: 2405.20094
• Limmer†, Y., Kratsios, A., Yang†, X., Saqur, R., and Horvath, B., Reality Only Happens Once: Single-Path Generalization Bounds for Transformers, ArXiV: 2405.16563
• Kratsios, A., Furuya, T., Lara Benitez†, J.A., Lassas, M., and de Hoop, M., Mixture of Experts Soften the Curse of Dimensionality in Operator Learning, ArXiV: 2404.09101
• Kratsios, A., Neuman, A. M., and Pammer, G., Tighter Generalization Bounds on Digital Computers via Discrete Optimal Transport, ArXiV: 2402.05576

2023

• Kassraie, P., Hou, S., Kratsios, A., Krause, A., and Rothfuss, J., Instance-Dependent Generalization Bounds via Optimal Transport. Journal of Machine Learning Research, 24, 349
• Cheng, T. S., Kratsios, A., Lucchi, A., Dokmanic, I., and Belius, D., A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression. Advances in Neural Information Processing Systems, 36, 4767-4798
• Kratsios, A., Debarnot, V., and Dokmanić I., Small Transformers Compute Universal Metric Embeddings. Journal of Machine Learning Research, 24(170), 1-48
• Acciaio, B., Kratsios, A., and Pammer, G., Designing Universal Causal Deep Learning Models: The Geometric (Hyper) Transformer, Mathematical Finance - Special Issue on Machine Learning in Finance
• Kratsios, A., Universal Regular Conditional Distributions via Probabilistic Transformers. Constructive Approximation, 57(3), 1145-1212
• Herrera, C., Krach, F., Kratsios, A., Ruyssen, P., and Teichmann, J., Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices. Transactions on Machine Learning Research
• Hovart, B., Kratsios, A., Limmer†, Y., and Yang†, X., Deep Kalman Filters Can Filter. ArXiV: 2310.19603
• Kratsios, A., Liu, C., Lassas, M., de Hoop, M. V., and Dokmanić, I., An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning, ArXiV: 2304.12231
• Yang†, X., Kratsios, A., Krach, F., Grasselli, M., and Lucchi, A., Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing, ArXiV: 2309.04557

2022

• Papon†, L., and Kratsios, A., Universal Approximation Theorems for Differentiable Geometric Deep Learning. Journal of Machine Learning Research, 23(196), 1-73
• Kratsios, A., Zamanlooy†, B., Dokmanic, I., and Liu†, T., Universal Approximation under Constraints Is Possible with Transformers. In ICLR, International Conference on Learning Representations., Award: Spotlight
• Zamanlooy†, B., and Kratsios, A., Do ReLU Networks Have an Edge When Approximating Compactly-Supported Functions? Transactions on Machine Learning Research
• Zamanlooy†, B., and Kratsios, A., Learning Sub-patterns in Piecewise Continuous Functions. Neurocomputing, 480, 192-211
• Galimberti, L., Kratsios, A., and Livieri, G., Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis. ArXiV: 2210.13300

2021

• Hyndman, C., and Kratsios, A., NEU: A Meta-algorithm for Universal UAP-invariant Feature Representation. Journal of Machine Learning Research, 22(92), 1-51
• Casgrain, P., and Kratsios, A., Optimizing Optimizers: Regret-optimal Gradient Descent Algorithms. In Conference on Learning Theory (pp. 883-926). PMLR
• Kratsios, A., Lower-estimates on the Hochschild (Co

Who we are

Past and present group members.

Deep Learning Seminar 2025 - Talks

• Feb 7 - Eric Moulines (Learning Theory) - Rates of convergence for density estimation with generative adversarial networks
• Feb 14 - Saber Jararpour (Deep Learning Theory) - Robust Implicit Networks via Non-Euclidean Constraints
• Feb 28 - Haotian Jian (Deep Learning Theory) - Approximation Rate of the Transformer Architecture for Sequence Modeling
• March 7 - Christopher Salvi (Geometric Deep Learning) - Scaling Limits of GNNs
• March 28 - Florian Rossmannek - TBD
• Arpil 11 - Mary Letey - (Learning Theory) - Asymptotic theory of in-context learning by linear attention
• April 18 - Michael Choi - (Information Geometry and Optimization) - Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression
• April 25 - Weigutian Ou - (Approximation Theory) - Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression
• May 2 - Haizhao Yang - (Learning Theory) - Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
• May 23 - Giovanni Ballarin - (Approximation Theory) - Memory of Recurrent Networks: Do We Compute It Right?
• May 23 - Anotnio Lara - (Operator Theory) - TBD