Research Interests | Ziv Goldfeld

Overview

My research develops mathematical and algorithmic foundations for machine learning and AI, with an emphasis on reliability, scalability, robustness, interpretability, and safety. I draw on tools from optimal transport, information theory, statistics, optimization, and applied probability to study foundational, statistical, and computational questions, as well as practical methods. Some specific research interests are outlined below, including recent directions in mechanistic interpretability, robustness, and AI safety.

Optimal Transport: Foundations, Geometry, Statistics, and Algorithms

Optimal transport (OT) provides a geometric framework for comparing and transforming complex probability distributions. It translates problems of learning from, interpolating between, or ensembling high-dimensional probability distributions into geometric questions about distances, geodesics, and barycenters in metric spaces. My work spans foundational OT theory, Wasserstein geometry, statistical and computational OT, and regularization methods for scalability in high dimensions. A central direction is the Gromov-Wasserstein (GW) problem for aligning heterogeneous datasets by modeling them as metric measure spaces and matching their internal geometry. Its quadratic structure raises fundamental questions across geometry, estimation, inference, and computation. Recent progress includes results on GW duality, empirical convergence rates, limit laws, provably convergent algorithms, and the Riemannian structure induced by the GW distance, with applications to testing, generative modeling, ensembling, sampling, and heterogeneous data alignment.

Information Theory for Learning and Privacy

Information theory complements geometric approaches through entropy, divergence, and information measures that capture uncertainty and statistical dependence. I use information-theoretic tools to study representations, abstractions, and attention patterns in deep models, including information flow and the information bottleneck perspective. I also develop scalable information measures, such as sliced mutual information (SMI), that retain key properties of Shannon mutual information while remaining efficiently estimable in high dimensions. These tools support learning and inference tasks across testing, feature extraction, generalization, fairness, and explainability. Related interests include privacy, security, and links between classical and quantum information measures.

Robust Estimation and Decision-Making

Robustness to distribution shift, outliers, and adversarial contamination is central to reliable AI. I study robust estimation and decision-making under hybrid corruption models that combine local perturbations with global outlier effects. A key direction in my work is an OT-based framework that unifies these corruption modes and supports minimax analyses, efficient estimators, and downstream decision procedures. I am particularly interested in the interface with Wasserstein DRO, where one can obtain guarantees that adapt to decision complexity and expose practical tradeoffs among robustness, statistical efficiency, and computation.

AI Mechanistic Interpretability and Safety

As AI systems become more capable, mechanistic interpretability and safety raise central technical questions about how learned representations form and how model behavior can be audited or steered. This research direction develops rigorous foundations and methods using tools from optimal transport, information theory, and robust statistics. In a recent project, we propose PLOT (Progressive Localization via Optimal Transport), a mechanistic interpretability method for causal abstraction in neural networks that achieves state-of-the-art accuracy while running one to two orders of magnitude faster than the previous best approach. Related interests include concept localization, causal abstraction, information-flow analysis in transformer architectures, and the mathematical foundations of alignment and safe model steering.

Neural Estimation of Classical and Quantum Divergences

Neural estimation provides a scalable framework for estimating divergences and information measures from samples, but its empirical success raises subtle questions about approximation, optimization, and statistical error. I develop neural methods and theory for estimating statistical divergences, including OT/GW distances and f-divergences, as well as information measures such as mutual and directed information. A central goal is to combine scalability and compatibility with modern learning pipelines with rigorous performance guarantees and a clearer understanding of statistical-computational tradeoffs. I am also interested in quantum extensions, including variational quantum-classical methods for estimating quantum divergences and related information measures.