arXiv subjects

Shizhou Xu

Publications and source records attributed to Shizhou Xu.

10 recordsLinked to original sources

arXiv2026

Observation geometry for uncertainty-aware Hamiltonian inference and experimental design in quantum magnets

Determining microscopic interactions from spectroscopic and scattering measurements is central to understanding quantum materials, yet it often remains unclear which interactions can be reliably revealed by the available experimental data and how additional experimental modalities should be designed to resolve the remaining ambiguities. Here we present an artificial intelligence-enabled framework for uncertainty-aware Hamiltonian inference and adaptive experimental design. By combining Hamiltonian-conditioned neural surrogates with Bayesian inference and observation geometry, the framework characterizes how measurements constrain Hamiltonian parameter space, quantifies the identifiability of microscopic interactions, and propagates posterior uncertainty directly in the physical Hamiltonian parameter space rather than an abstract learned representation. Using multimodal powder and single-crystal inelastic neutron scattering measurements of the quantum magnet NiPS$_{3}$, we demonstrate physically interpretable Hamiltonian inference, modality-aware uncertainty quantification, and adaptive experimental design. The framework provides a general strategy for uncertainty-aware microscopic characterization and multimodal experimental design across quantum materials.

cond-mat.str-el↗

arXiv2026

Separation-Utility Pareto Frontier: An Information-Theoretic Characterization

We study the Pareto frontier (optimal trade-off) between utility and separation, a fairness criterion requiring predictive independence from sensitive attributes conditional on the true outcome. Through an information-theoretic lens, we prove a characterization of the utility-separation Pareto frontier, establish its concavity, and thereby prove the increasing marginal cost of separation in terms of utility. In addition, we characterize the conditions under which this trade-off becomes strict, providing a guide for trade-off selection in practice. Based on the theoretical characterization, we develop an empirical regularizer based on conditional mutual information (CMI) between predictions and sensitive attributes given the true outcome. The CMI regularizer is compatible with any deep model trained via gradient-based optimization and serves as a scalar monitor of residual separation violations, offering tractable guarantees during training. Finally, numerical experiments support our theoretical findings: across COMPAS, UCI Adult, UCI Bank, and CelebA, the proposed method substantially reduces separation violations while matching or exceeding the utility of established baseline methods. This study thus offers a provable, stable, and flexible approach to enforcing separation in deep learning.

cs.LG↗

arXiv2025

Forgetting-MarI: LLM Unlearning via Marginal Information Regularization

As AI models are trained on ever-expanding datasets, the ability to remove the influence of specific data from trained models has become essential for privacy protection and regulatory compliance. Unlearning addresses this challenge by selectively removing parametric knowledge from the trained models without retraining from scratch, which is critical for resource-intensive models such as Large Language Models (LLMs). Existing unlearning methods often degrade model performance by removing more information than necessary when attempting to ''forget'' specific data. We introduce Forgetting-MarI, an LLM unlearning framework that provably removes only the additional (marginal) information contributed by the data to be unlearned, while preserving the information supported by the data to be retained. By penalizing marginal information, our method yields an explicit upper bound on the unlearn dataset's residual influence in the trained models, providing provable undetectability. Extensive experiments confirm that our approach outperforms current state-of-the-art unlearning methods, delivering reliable forgetting and better preserved general model performance across diverse benchmarks. This advancement represents an important step toward making AI systems more controllable and compliant with privacy and copyright regulations without compromising their effectiveness.

cs.AI↗

arXiv2025

Multi-resolution Enhancement for Full Spectrum Neural Representations

Scientific data acquisition continues to outpace storage and analysis capabilities, making voxel-based representations increasingly intractable. Implicit neural representations (INRs) offer a promising solution by encoding signals through coordinate-based neural networks, serving as surrogates of data, with computational and storage requirements scaling with network complexity rather than data dimensionality. However, smaller INRs struggle to faithfully represent the multi-scale structures, high-frequency information, and fine textures that constitute a large proportion of scientific measurements. We propose WIEN-INR, a theoretically-guided hierarchical INR framework that distributes modeling across resolution scales and enables improved representation capacity through a novel enhancement network to recover subtle details. This multi-scale architecture allows smaller networks to retain the full spectrum of information while preserving training efficiency and lowering storage cost. Evaluated on distinct raw experimental measurements across scales and complexities, WIEN-INR represents a practical step toward broader adoption of neural representations in scientific workflows, delivering compact, robust, and high-fidelity representations.

cs.LG↗

arXiv2025

Machine Unlearning via Information Theoretic Regularization

How can we effectively remove or ``unlearn'' undesirable information, such as specific features or the influence of individual data points, from a learning outcome while minimizing utility loss and ensuring rigorous guarantees? We introduce a unified mathematical framework based on information-theoretic regularization to address both data-point unlearning and feature unlearning. For data-point unlearning, we introduce the \emph{Marginal Unlearning Principle}, an auditable and provable framework. Moreover, we provide an information-theoretic unlearning definition based on the proposed principle and provable guarantees on sufficiency and necessity of marginal unlearning. We then show that the proposed framework provides a natural solution to the marginal unlearning problem and yields auditable high-probability marginal-unlearning guarantees. For feature unlearning, the framework applies to deep learning with flexible training objectives. By combining flexibility in learning objectives with simplicity in regularization design, our approach is highly adaptable and practical for a wide range of machine learning and AI applications. From a mathematical perspective, we provide a unified analytic solution to the optimal feature unlearning problem with a variety of information-theoretic training objectives. Our theoretical analysis reveals intriguing connections between machine unlearning, information theory, optimal transport, and extremal sigma algebras. Numerical simulations support our theoretical findings.

cs.LG↗

arXiv2024

WHOMP: Optimizing Randomized Controlled Trials via Wasserstein Homogeneity

We investigate methods for partitioning datasets into subgroups that maximize diversity within each subgroup while minimizing dissimilarity across subgroups. We introduce a novel partitioning method called the $\textit{Wasserstein Homogeneity Partition}$ (WHOMP), which optimally minimizes type I and type II errors that often result from imbalanced group splitting or partitioning, commonly referred to as accidental bias, in comparative and controlled trials. We conduct an analytical comparison of WHOMP against existing partitioning methods, such as random subsampling, covariate-adaptive randomization, rerandomization, and anti-clustering, demonstrating its advantages. Moreover, we characterize the optimal solutions to the WHOMP problem and reveal an inherent trade-off between the stability of subgroup means and variances among these solutions. Based on our theoretical insights, we design algorithms that not only obtain these optimal solutions but also equip practitioners with tools to select the desired trade-off. Finally, we validate the effectiveness of WHOMP through numerical experiments, highlighting its superiority over traditional methods.

stat.ML↗

arXiv2024

On the (In)Compatibility between Group Fairness and Individual Fairness

We study the compatibility between the optimal statistical parity solutions and individual fairness. While individual fairness seeks to treat similar individuals similarly, optimal statistical parity aims to provide similar treatment to individuals who share relative similarity within their respective sensitive groups. The two fairness perspectives, while both desirable from a fairness perspective, often come into conflict in applications. Our goal in this work is to analyze the existence of this conflict and its potential solution. In particular, we establish sufficient (sharp) conditions for the compatibility between the optimal (post-processing) statistical parity $L^2$ learning and the ($K$-Lipschitz or $(ε,δ)$) individual fairness requirements. Furthermore, when there exists a conflict between the two, we first relax the former to the Pareto frontier (or equivalently the optimal trade-off) between $L^2$ error and statistical disparity, and then analyze the compatibility between the frontier and the individual fairness requirements. Our analysis identifies regions along the Pareto frontier that satisfy individual fairness requirements. (Lastly, we provide individual fairness guarantees for the composition of a trained model and the optimal post-processing step so that one can determine the compatibility of the post-processed model.) This provides practitioners with a valuable approach to attain Pareto optimality for statistical parity while adhering to the constraints of individual fairness.

math.ST↗

arXiv2023

Fair Data Representation for Machine Learning at the Pareto Frontier

As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. We propose a pre-processing algorithm for fair data representation via which supervised learning results in estimations of the Pareto frontier between prediction error and statistical disparity. Particularly, the present work applies the optimal affine transport to approach the post-processing Wasserstein-2 barycenter characterization of the optimal fair $L^2$-objective supervised learning via a pre-processing data deformation. Furthermore, we show that the Wasserstein-2 geodesics from the conditional (on sensitive information) distributions of the learning outcome to their barycenter characterizes the Pareto frontier between $L^2$-loss and the average pairwise Wasserstein-2 distance among sensitive groups on the learning outcome. Numerical simulations underscore the advantages: (1) the pre-processing step is compositive with arbitrary conditional expectation estimation supervised learning methods and unseen data; (2) the fair representation protects the sensitive information by limiting the inference capability of the remaining data with respect to the sensitive data; (3) the optimal affine maps are computationally efficient even for high-dimensional data.

stat.ML↗

arXiv2020

State-Driven Dynamic Graphon Model

This paper shows the equivalence class definition of graphons hinders a direct development of dynamics on the graphon space, and hence proposes a state-driven approach to obtain dynamic graphons. The state-driven dynamic graphon model constructs a time-index sequence of the permutation-invariant probability measures on the universal graph space by assigning i.i.d. state random processes to $\mathbbm{N}$ and edge random variables to each of the unordered integer pairs. The model is justified from three perspectives: graph limit definition preservation, genericity, and analysis availability. It preserves the graph limit definition of graphon by applying a bijection between the permutation-invariant probability measures on the universal graph space and the graphon space to obtain the dynamic graphon, where the existence of the bijection is proved. Also, a generalized version of the model is proved to cover the graphon space by an application of the celebrated Aldous-Hoover representation, where generalization is achieved by adding randomness to the edge-generating functions. Finally, analysis of the behavior of the dynamic graphon is shown to be available by making assumptions on the state random processes and the edge random variables.

math.PR↗

arXiv2018

Operator-Theoretical Treatment of Ergodic Theorem and Its Application to Dynamic Models in Economics

The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains that are frequently used in dynamic economic models to be ergodic. The paper reviews the time average convergence of the quasi-weakly complete continuity Markov operators to a unique projection operator. Also, it shows that a further assumption of quasi-strongly complete continuity reduces the dependence of the unique invariant measure on its corresponding initial distribution through ergodic decomposition, and therefore guarantees the Markov chain to be ergodic up to multiplication of constant coefficients. Moreover, a sufficient and practical condition is provided for the ergodicity in economic state Markov chains that are induced by exogenous random shocks and a correspondence between the exogenous space and the state space.

math.PR↗