20 citations · 192 across the 51 of their papers we have counts for
61 papers
Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing
Gabriel Rioux, Joanna Marks, Riccardo Passeggeri +1
The Gromov-Wasserstein (GW) distance provides a principled framework for aligning metric measure (mm) spaces based solely on their intrinsic structure. Its ability to identify isom…
Probabilistic Representation and Convergence of Gromov-Wasserstein Gradient Flows
Venkatkrishna Karumanchi, Ziv Goldfeld, Kengo Kato +1
Wasserstein gradient flows are intimately connected with evolution partial differential equations and diffusion processes. We take the first step in developing such connections for…
Sliced Inner Product Gromov-Wasserstein Distances
Xiaoyun Gong, Gabriel Rioux, Ziv Goldfeld
The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling rem…
PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction
Jonathn Chang, Arya Datla, Ziv Goldfeld
Causal abstraction offers a principled framework for mechanistic interpretability, aligning a high-level causal model with low-level neural computation through interchange interven…
Estimation of Stochastic Optimal Transport Maps
Sloan Nietert, Ziv Goldfeld
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied p…
Optimal Transportation and Alignment Between Gaussian Measures
Sanjit Dandapanthula, Aleksandr Podkopaev, Shiva Prasad Kasiviswanathan +2
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment provide interpretable geometric frameworks for comparing, transforming, and aggregating heterogeneous datasets---tasks…
Performance Guarantees for Quantum Neural Estimation of Entropies
Sreejith Sreekumar, Ziv Goldfeld, Mark M. Wilde
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a…
Approximation Analysis of the Entropic Penalty in Quadratic Programming
Venkatkrishna Karumanchi, Gabriel Rioux, Ziv Goldfeld
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumv…
Robust Alignment via Partial Gromov-Wasserstein Distances
Xiaoyun Gong, Sloan Nietert, Ziv Goldfeld
The Gromov-Wasserstein (GW) problem provides a powerful framework for aligning heterogeneous datasets by matching their internal structures in a way that minimizes distortion. Howe…
Neural Estimation for Scaling Entropic Multimarginal Optimal Transport
Dor Tsur, Ziv Goldfeld, Kristjan Greenewald +1
Multimarginal optimal transport (MOT) is a powerful framework for modeling interactions between multiple distributions, yet its applicability is bottlenecked by a high computationa…
Approximation rates of entropic maps in semidiscrete optimal transport
Ritwik Sadhu, Ziv Goldfeld, Kengo Kato
Entropic optimal transport offers a computationally tractable approximation to the classical problem. In this note, we study the approximation rate of the entropic optimal transpor…
Limit Laws for Gromov-Wasserstein Alignment with Applications to Testing Graph Isomorphisms
Gabriel Rioux, Ziv Goldfeld, Kengo Kato
The Gromov-Wasserstein (GW) distance enables comparing metric measure spaces based solely on their internal structure, making it invariant to isomorphic transformations. This prope…
Gradient Flows and Riemannian Structure in the Gromov-Wasserstein Geometry
Zhengxin Zhang, Ziv Goldfeld, Kristjan Greenewald +2
The Wasserstein space of probability measures is known for its intricate Riemannian structure, which underpins the Wasserstein geometry and enables gradient flow algorithms. Howeve…
Robust Distribution Learning with Local and Global Adversarial Corruptions
Sloan Nietert, Ziv Goldfeld, Soroosh Shafiee
We consider learning in an adversarial environment, where an -fraction of samples from a distribution are arbitrarily modified (global corruptions) and the remaini…
Neural Estimation Of Entropic Optimal Transport
Tao Wang, Ziv Goldfeld
Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistic…
Information-Theoretic Generalization Bounds for Deep Neural Networks
Haiyun He, Ziv Goldfeld
Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised…
Neural Entropic Optimal Transport and Gromov-Wasserstein Alignment
Tao Wang, Ziv Goldfeld
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is…
Outlier-Robust Wasserstein DRO
Sloan Nietert, Ziv Goldfeld, Soroosh Shafiee
Distributionally robust optimization (DRO) is an effective approach for data-driven decision-making in the presence of uncertainty. Geometric uncertainty due to sampling or localiz…
Max-Sliced Mutual Information
Dor Tsur, Ziv Goldfeld, Kristjan Greenewald
Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA…
Quantum Neural Estimation of Entropies
Ziv Goldfeld, Dhrumil Patel, Sreejith Sreekumar +1
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are availabl…
Quantum Pufferfish Privacy: A Flexible Privacy Framework for Quantum Systems
Theshani Nuradha, Ziv Goldfeld, Mark M. Wilde
We propose a versatile privacy framework for quantum systems, termed quantum pufferfish privacy (QPP). Inspired by classical pufferfish privacy, our formulation generalizes and add…
Entropic Gromov-Wasserstein Distances: Stability and Algorithms
Gabriel Rioux, Ziv Goldfeld, Kengo Kato
The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact compu…
Stability and statistical inference for semidiscrete optimal transport maps
Ritwik Sadhu, Ziv Goldfeld, Kengo Kato
We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely…
Robust Estimation under the Wasserstein Distance
Sloan Nietert, Rachel Cummings, Ziv Goldfeld
We study the problem of robust distribution estimation under the Wasserstein distance, a popular discrepancy measure between probability distributions rooted in optimal transport (…