selected scholarly activity
-
chapters
- Generative OrnsteinUhlenbeck Markets via Geometric Deep Learning. Lecture Notes in Computer Science. 605-614. 2023
-
conferences
- Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum. Proceedings of Machine Learning Research. 8141-8162. 2024
- NEURAL SNOWFLAKES: UNIVERSAL LATENT GRAPH INFERENCE VIA TRAINABLE LATENT GEOMETRIES. 12th International Conference on Learning Representations, ICLR 2024. 2024
- A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression. Advances in Neural Information Processing Systems. 2023
- UNIVERSAL APPROXIMATION UNDER CONSTRAINTS IS POSSIBLE WITH TRANSFORMERS. ICLR 2022 - 10th International Conference on Learning Representations. 2022
- Optimizing Optimizers: Regret-optimal gradient descent algorithms.. CONFERENCE ON LEARNING THEORY, VOL 134. 883-926. 2021
- Non-Euclidean Universal Approximation. Advances in Neural Information Processing Systems. 2020
-
journal articles
- Deep Learning: Foundations and Concepts. Quantitative Finance. 24:1725-1727. 2024
- Capacity bounds for hyperbolic neural network representations of latent tree structures. Neural Networks. 178:106420-106420. 2024
- Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation. Journal of Computational Physics. 513:113168-113168. 2024
- Designing universal causal deep learning models: The geometric (Hyper)transformer. Mathematical Finance. 34:671-735. 2024
- Universal Regular Conditional Distributions via Probabilistic Transformers. Constructive approximation. 57:1145-1212. 2023
- Instance-Dependent Generalization Bounds via Optimal Transport. Journal of machine learning research. 24. 2023
- Small Transformers Compute Universal Metric Embeddings. Journal of machine learning research. 24. 2023
- Learning sub-patterns in piecewise continuous functions. Neurocomputing. 480:192-211. 2022
- Universal Approximation Theorems for Differentiable Geometric Deep Learning. Journal of machine learning research. 23:1-73. 2022
-
WITHDRAWN: A canonical transform for strengthening the local
- The Universal Approximation Property. Annals of Mathematics and Artificial Intelligence. 89:435-469. 2021
- Lower-Estimates on the Hochschild (Co)Homological Dimension of Commutative Algebras and Applications to Smooth Affine Schemes and Quasi-Free Algebras. Mathematics. 9:251-251. 2021
- NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation. Journal of machine learning research. 22. 2021
- Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization. Risks. 8:40-40. 2020
- The entropic measure transform. Canadian Journal of Statistics, The. 48:97-129. 2020
- Regret-Optimal Transfer Learning from Pretrained Kernel Regressors – with Applications to American Option Pricing. Transactions on Machine Learning Research.
- Synchronizing pretrained kernel regressors with applications to American option pricing. Frontiers in Mathematical Finance.
-
preprints
- Guiding Two-Layer Neural Network Lipschitzness via Gradient Descent Learning Rate Constraints 2025
- Keep It Light! Simplifying Image Clustering Via Text-Free Adapters 2025
- Is In-Context Universality Enough? MLPs are Also Universal In-Context 2025
- Neural Operators Can Play Dynamic Stackelberg Games 2024
- Scalable Message Passing Neural Networks: No Need for Attention in Large Graph Representation Learning 2024
- A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression 2024
- Simultaneously Solving FBSDEs with Neural Operators of Logarithmic Depth, Constant Width, and Sub-Linear Rank 2024
- Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization 2024
- Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity 2024
- Neural Spacetimes for DAG Representation Learning 2024
- Filtered not Mixed: Stochastic Filtering-Based Online Gating for Mixture of Large Language Models 2024
- Low-dimensional approximations of the conditional law of Volterra processes: a non-positive curvature approach 2024
- Higher-Order Transformer Derivative Estimates for Explicit Pathwise Learning Guarantees 2024
- Mixture of Experts Soften the Curse of Dimensionality in Operator Learning 2024
- Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces 2024
- Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces 2024
- Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts 2024
- Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum 2024
- NEURAL SNOWFLAKES: UNIVERSAL LATENT GRAPH INFERENCE VIA TRAINABLE LATENT GEOMETRIES 2024
- Deep Kalman Filters Can Filter 2023
- A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression 2023
- Energy-Guided Continuous Entropic Barycenter Estimation for General Costs 2023
- Regret-Optimal Federated Transfer Learning for Kernel Regression with Applications in American Option Pricing 2023
- Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures 2023
- An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning 2023
- An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning 2023
- Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning 2023
- Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation 2023
- Instance-Dependent Generalization Bounds via Optimal Transport 2022
- Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis 2022
- Small Transformers Compute Universal Metric Embeddings 2022
- Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions? 2022
- Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer 2022
- Universal Approximation Under Constraints is Possible with Transformers 2021
- Universal Regular Conditional Distributions 2021
- Universal Approximation Theorems for Differentiable Geometric Deep Learning 2021
- Optimizing Optimizers: Regret-optimal gradient descent algorithms 2020
- Learning Sub-Patterns in Piecewise Continuous Functions 2020
- A Canonical Transform for Strengthening the Local $L^p$-Type Universal Approximation Property 2020
- Non-Euclidean Universal Approximation 2020
- Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices 2020
- Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization 2020
- The Universal Approximation Property 2019
- Partial Uncertainty and Applications to Risk-Averse Valuation 2019
- NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation 2018
- Optimal Stochastic Decensoring and Applications to Calibration of Market Models 2017
- Non-Euclidean Conditional Expectation and Filtering 2017
- Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization 2017
- A Lower-Bound on the Hochschild Cohomological Dimension 2016
- The Entropic Measure Transform 2015
- Hochschild Cohomological Dimension is Not Upper Semi-Continuous 2014
- Noncommutative Algebra and Noncommutative Geometry 2014
- Adjoinable Homology 2014
- Deep Kalman Filters Can Filter
-
presentations