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 and AI alignment.

Optimal Transport Theory

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, which lends itself well to analysis and method design. My work spans foundational OT theory, Wasserstein geometry, and statistical and computational OT. I am particularly interested in regularization methods for scalability in high dimensions, gradient flows in Wasserstein geometry, and robustness to outliers, with applications to testing, generative modeling, ensembling, and sampling.

Gromov-Wasserstein Alignment Theory

The Gromov-Wasserstein (GW) problem, rooted in optimal transport theory, offers a geometric framework for aligning heterogeneous datasets by modeling them as metric measure spaces and matching their internal geometry. Its quadratic structure makes GW substantially harder to analyze than classical OT, leaving many basic questions open across geometry, estimation, inference, and computation. My research develops a broad theory of GW alignment across foundations, geometry, statistics, and algorithms. Recent progress includes inaugural results on duality, empirical convergence rates, limit laws, provably convergent algorithms, and the Riemannian structure induced by the GW distance.

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 Safety, Alignment, and Interpretability

As AI capabilities continue to grow, safety, alignment, and interpretability are becoming central technical challenges. This research direction develops rigorous foundations and methods for addressing these questions, building on tools from optimal transport, information theory, and robust statistics. Topics of interest include mechanistic interpretability methods for concept localization, causal abstraction, and information-flow analysis in transformer architectures, as well as theory and algorithms for AI alignment, including gradient-based steering, tradeoffs among multiple alignment objectives, and the effects of fine-tuning on reward distributions and tail behavior.

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.