arXiv subjects

Lu Wei

Publications and source records attributed to Lu Wei.

At least 19 recordsLinked to original sources

arXiv2026

Difference equations of average entropies

Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this work, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.

math-ph↗

arXiv2026

Grounding Spatial Relations in a Compact World Model: Instruction Leakage and a Goal-Free Dynamics Fix

Compact world models that condition on a language goal promise to ground relations such as ``put the red block left of the blue block'' using a sparse set of explicit \emph{reference anchors}. We ask when such references actually ground a relation, and identify a trap: a goal-conditioned predictor reaches a striking $0.90$ relation-readout accuracy, yet this is \emph{instruction transcription}, not perception. Withholding the goal collapses it to chance ($0.90\!\to\!0.27$, three seeds) and a counterfactual instruction makes the predicted anchors follow the \emph{false} instruction $94.5\%$ of the time (true scene $2.3\%$; $N{=}256$). Tested across three settings and a within-task ablation, our central claim characterizes the confound: \textbf{instruction leakage occurs when the scored quantity is transcribable from the instruction (when the instruction names the answer) and is essentially independent of how predictive the non-instruction inputs are.} Our tabletop and the external BabyAI benchmark leak, whereas a Language-Table forward-dynamics world model whose instruction names \emph{referents} does not, until the instruction is augmented to name the direction; and degrading the action never increases leakage, the opposite of what predictor-competition predicts. The diagnosis prescribes the fix: keep the goal out of the dynamics (it belongs to the planner's cost) and supervise the \emph{read} path, recovering genuine, instruction-independent grounding ($0.88$, identical with and without the goal). The detection protocol and remedy apply to any goal-conditioned world model whose instruction names the scored quantity.

cs.AI↗

arXiv2026

Average entropy of Bogoliubov-Kubo-Mori random state ensemble

Random states play a foundational role in different branches of modern quantum science. In this work, we study a recently proposed random state ensemble induced from von Neumann entropy through the Bogoliubov-Kubo-Mori (BKM) metric. In particular, we derive an exact yet explicit formula of average entanglement entropy over BKM ensemble. In obtaining the formula, we only make use of properties of normalization constant of the ensemble in the absence of its correlation kernel, contrary to average entropy computation of other ensembles. This new framework paves the way for calculating higher-order cumulants of BKM ensemble beyond the average.

math-ph↗

arXiv2026

Conservative Discrete Structure Stabilizes Autoregressive Rollouts in a 1D Drift Diffusion Poisson Benchmark

Learned plasma transport surrogates can match short horizon states while failing over long rollouts because charge accounting, density admissibility, and Poisson compatible field reconstruction are not enforced. We study this issue in a controlled nondimensional one dimensional drift diffusion Poisson benchmark with Dirichlet electrostatic potential boundaries and zero species wall fluxes. The benchmark is a conservation and rollout test, not a complete sheath wall model. We compare Conservative FluxNet, a structure preserving flux correction model with a conservative finite volume update and positivity aware limiting, against direct next state regressors, direct variants with Poisson recomputation, charge projection, and rollout training, and a classical conservative core without learned correction. The central result is that the classical finite volume core alone achieves near roundoff rollout error, so the paper is primarily about conservative discrete structure rather than learned closure. On the headline experiment, the conservative model achieves rollout MSE $7.35\times 10^{-9}$ versus $4.23\times 10^{1}$ for the unconstrained baseline, $2.53\times 10^{1}$ with Poisson recomputation, $6.72\times 10^{1}$ with charge projection, and $2.71\times 10^{1}$ with four step rollout training. Across $64$ prespecified configurations, it wins rollout mean squared error in $60/64$ cases despite winning one step mean squared error in only $19/64$. These results show that, for this controlled benchmark and comparison class, local conservative finite volume structure is more important than one step neural regression accuracy for stable autoregressive rollout.

cs.CE↗

arXiv2026

Spectral moments of Bures-Hall ensemble and applications to entanglement entropy

We study spectral moments of the Bures-Hall random matrices ensemble. The main result establishes a recurrence relation for the $k$-th spectral moment valid for a real-valued $k$, in contrast to prevailing results in the literature of different ensembles of assuming an integer $k$. The key to establish the recurrence relation is the obtained Christoffel-Darboux formulas of correlation kernels of the ensemble that avoid tedious summations. As an application of our spectral moment results, we re-derive the formulas of average von Neumann entropy and quantum purity of Bures-Hall ensemble conjectured by Ayana Sarkar and Santosh Kumar. This work is dedicated to the memory of Santosh Kumar.

math-ph↗

arXiv2026

Non-intersecting Squared Bessel Process: Spectral Moments and Dynamical Entanglement Entropy

Statistical ensembles of reduced density matrices of bipartite quantum systems play a central role in entanglement estimation, but do not capture the non-stationary nature of entanglement relevant to realistic quantum information processing. To address this limitation, we propose a dynamical extension of the Hilbert-Schmidt ensemble, a baseline statistical model for entanglement estimation, arising from non-intersecting squared Bessel processes and perform entanglement estimation via average entanglement entropy and quantum purity. The investigation is enabled by finding spectral moments of the proposed dynamical ensemble, which serves as a new approach for systematic computation of entanglement metrics. Along the way, we also obtain new results for the underlying multiple orthogonal polynomials of modified Bessel weights, including structure and recurrence relations, and a Christoffel-Darboux formula for the correlation kernels.

math-ph↗

arXiv2026

Towards accurate predictions of bond-selective fluorescence spectra

Vibrational-encoded fluorescence spectro-microscopies are emerging as powerful tools for studying molecular vibrations with the unparalleled sensitivity of fluorescence spectroscopy. We recently described one such technique, termed bond-selective fluorescence-detected infrared-excited (BonFIRE) spectro-microscopy. Currently, prospects of BonFIRE towards rational molecular design are limited, but they have the potential to be assisted by computational tools. In this Perspective, we provide a brief overview of the theory of BonFIRE spectroscopy. We then describe a fully automated computational pipeline for calculating BonFIRE spectra, reproducing key features of experimental results. Finally, we highlight a few potential applications of computational methods for vibrational-encoded fluorescence spectro-microscopies and their broader implications for chemistry and biology.

physics.chem-ph↗

arXiv2026

How well can off-the-shelf LLMs elucidate molecular structures from mass spectra using chain-of-thought reasoning?

Mass spectrometry (MS) is a powerful analytical technique for identifying small molecules, yet determining complete molecular structures directly from tandem mass spectra (MS/MS) remains a long-standing challenge due to complex fragmentation patterns and the vast diversity of chemical space. Recent progress in large language models (LLMs) has shown promise for reasoning-intensive scientific tasks, but their capability for chemical interpretation is still unclear. In this work, we introduce a Chain-of-Thought (CoT) prompting framework and benchmark that evaluate how LLMs reason about mass spectral data to predict molecular structures. We formalize expert chemists' reasoning steps-such as double bond equivalent (DBE) analysis, neutral loss identification, and fragment assembly-into structured prompts and assess multiple state-of-the-art LLMs (Claude-3.5-Sonnet, GPT-4o-mini, and Llama-3 series) in a zero-shot setting using the MassSpecGym dataset. Our evaluation across metrics of SMILES validity, formula consistency, and structural similarity reveals that while LLMs can produce syntactically valid and partially plausible structures, they fail to achieve chemical accuracy or link reasoning to correct molecular predictions. These findings highlight both the interpretive potential and the current limitations of LLM-based reasoning for molecular elucidation, providing a foundation for future work that combines domain knowledge and reinforcement learning to achieve chemically grounded AI reasoning.

cs.CL↗

arXiv2025

EMMA: Concept Erasure Benchmark with Comprehensive Semantic Metrics and Diverse Categories

The widespread adoption of text-to-image (T2I) generation has raised concerns about privacy, bias, and copyright violations. Concept erasure techniques offer a promising solution by selectively removing undesired concepts from pre-trained models without requiring full retraining. However, these methods are often evaluated on a limited set of concepts, relying on overly simplistic and direct prompts. To test the boundaries of concept erasure techniques, and assess whether they truly remove targeted concepts from model representations, we introduce EMMA, a benchmark that evaluates five key dimensions of concept erasure over 13 metrics. EMMA goes beyond standard metrics like image quality and time efficiency, testing robustness under challenging conditions, including indirect descriptions, visually similar non-target concepts, and potential gender and ethnicity bias, providing a socially aware analysis of method behavior. Using EMMA, we analyze five concept erasure methods across five domains (objects, celebrities, art styles, NSFW, and copyright). Our results show that existing methods struggle with implicit prompts (i.e., generating the erased concept when it is indirectly referenced) and visually similar non-target concepts (i.e., failing to generate non-target concepts resembling the erased one), while some amplify gender and ethnicity bias compared to the original model. Code and prompts are available at https://github.com/lobsterlulu/EMMA.

cs.CV↗

arXiv2025

Privacy Loss of Noise Perturbation via Concentration Analysis of A Product Measure

Noise perturbation is one of the most fundamental approaches for achieving $(\epsilon,\delta)$-differential privacy (DP) guarantees when releasing the result of a query or function $f(\cdot)\in\mathbb{R}^M$ evaluated on a sensitive dataset $\mathbf{x}$. In this approach, calibrated noise $\mathbf{n}\in\mathbb{R}^M$ is used to obscure the difference vector $f(\mathbf{x})-f(\mathbf{x}')$, where $\mathbf{x}'$ is known as a neighboring dataset. A DP guarantee is obtained by studying the tail probability bound of a privacy loss random variable (PLRV), defined as the Radon-Nikodym derivative between two distributions. When $\mathbf{n}$ follows a multivariate Gaussian distribution, the PLRV is characterized as a specific univariate Gaussian. In this paper, we propose a novel scheme to generate $\mathbf{n}$ by leveraging the fact that the perturbation noise is typically spherically symmetric (i.e., the distribution is rotationally invariant around the origin). The new noise generation scheme allows us to investigate the privacy loss from a geometric perspective and express the resulting PLRV using a product measure, $W\times U$; measure $W$ is related to a radius random variable controlling the magnitude of $\mathbf{n}$, while measure $U$ involves a directional random variable governing the angle between $\mathbf{n}$ and the difference $f(\mathbf{x})-f(\mathbf{x}')$. We derive a closed-form moment bound on the product measure to prove $(\epsilon,\delta)$-DP. Under the same $(\epsilon,\delta)$-DP guarantee, our mechanism yields a smaller expected noise magnitude than the classic Gaussian noise in high dimensions, thereby significantly improving the utility of the noisy result $f(\mathbf{x})+\mathbf{n}$. To validate this, we consider convex and non-convex empirical risk minimization (ERM) problems in high dimensional space and apply the proposed product noise to achieve privacy.

cs.CR↗

arXiv2025

Higher-order spectral form factors of circular unitary ensemble

Spectral form factor (SFF), one of the key quantity from random matrix theory, serves as an important tool to probe universality in disordered quantum systems and quantum chaos. In this work, we present exact closed-form expressions for the second- and third-order SFFs in the circular unitary ensemble (CUE), valid for all real values of the time parameter, and analyze their asymptotic behavior in different regimes. In particular, for the second-order SFF, we derive an exact closed-form expression in terms of polygamma functions. In the limit of infinite matrix size, and when the time parameter is restricted to integer values, the second-order SFF reproduces the standard result established in earlier studies. When the time parameter is of order one relative to the matrix size, we demonstrate that the second-order SFF grows logarithmically with the ensemble dimension. For the third-order SFFs, a closed-form result in a special case is obtained by exploiting the translational invariance of CUE.

math-ph↗

arXiv2025

Average relative entropy of random states

Relative entropy serves as a cornerstone concept in quantum information theory. In this work, we study relative entropy of random states from major generic state models of Hilbert-Schmidt and Bures-Hall ensembles. In particular, we derive exact yet explicit formulas of average relative entropy of two independent states of arbitrary dimensions from the same ensemble as well as from two different ensembles. One ingredient in obtaining the results is the observed factorization of ensemble averages after evaluating the required unitary integral. The derived exact formula in the case of Hilbert-Schmidt ensemble complements the work by Kudler-Flam (2021 Phys Rev Lett 126 171603), where the corresponding asymptotic formula for states of equal dimensions was obtained based on the replica method.

math-ph↗

arXiv2025

Spectra-to-Structure and Structure-to-Spectra Inference Across the Periodic Table

X-ray Absorption Spectroscopy (XAS) is a powerful technique for probing local atomic environments, yet its interpretation remains limited by the need for expert-driven analysis, computationally expensive simulations, and element-specific heuristics. Recent advances in machine learning have shown promise for accelerating XAS interpretation, but many existing models are narrowly focused on specific elements, edge types, or spectral regimes. In this work, we present XAStruct, a learning-based system capable of both predicting XAS spectra from crystal structures and inferring local structural descriptors from XAS input. XAStruct is trained on a large-scale dataset spanning over 70 elements across the periodic table, enabling generalization to a wide variety of chemistries and bonding environments. The framework includes the first machine learning approach for predicting neighbor atom types directly from XAS spectra, as well as a generalizable regression model for mean nearest-neighbor distance that requires no element-specific tuning. By combining deep neural networks for complex structure property mappings with efficient baseline models for simpler tasks, XAStruct offers a scalable and extensible solution for data-driven XAS analysis and local structure inference. The source code will be released upon paper acceptance.

cs.LG↗

arXiv2025

Skewness of von Neumann entropy over Bures-Hall random states

We study the degree of entanglement, as measured by von Neumann entropy, of bipartite systems over the Bures-Hall ensemble. Closed-form expressions of the first two cumulants of von Neumann entropy over the ensemble have been recently derived in the literature. In this paper, we focus on its skewness by calculating the third cumulant that describes the degree of asymmetry of the distribution. The main result is an exact closed-form formula of the third cumulant, which leads to a more accurate approximation to the distribution of von Neumann entropy. The key to obtaining the result lies on finding a dozen of new summation identities in simplifying a large number of finite summations involving polygamma functions.

math-ph↗

arXiv2025

Cracking the Code: Enhancing Implicit Hate Speech Detection through Coding Classification

The internet has become a hotspot for hate speech (HS), threatening societal harmony and individual well-being. While automatic detection methods perform well in identifying explicit hate speech (ex-HS), they struggle with more subtle forms, such as implicit hate speech (im-HS). We tackle this problem by introducing a new taxonomy for im-HS detection, defining six encoding strategies named codetypes. We present two methods for integrating codetypes into im-HS detection: 1) prompting large language models (LLMs) directly to classify sentences based on generated responses, and 2) using LLMs as encoders with codetypes embedded during the encoding process. Experiments show that the use of codetypes improves im-HS detection in both Chinese and English datasets, validating the effectiveness of our approach across different languages.

cs.CL↗

arXiv2025

XDIP: A Curated X-ray Absorption Spectrum Dataset for Iron-Containing Proteins

Earth-abundant iron is an essential metal in regulating the structure and function of proteins. This study presents the development of a comprehensive X-ray Absorption Spectroscopy (XAS) database focused on iron-containing proteins, addressing a critical gap in available high-quality annotated spectral data for iron-containing proteins. The database integrates detailed XAS spectra with their corresponding local structural data of proteins and enables direct comparison between spectral features and structural motifs. Utilizing a combination of manual curation and semi-automated data extraction techniques, we developed a comprehensive dataset via extensive literature review, ensuring the quality and accuracy of data, which contains 437 protein structures and 1954 XAS spectrums. Our methods included careful documentation and validation processes to ensure accuracy and reproducibility. This dataset not only centralizes information on iron-containing proteins but also supports advanced data-driven discoveries, such as machine learning, to predict and analyze protein structure and functions. This work underscores the potential of integrating detailed spectroscopic data with structural biology to advance the field of biological chemistry and catalysis.

q-bio.BM↗

arXiv2025

Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems

The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter physics. In this work, we propose the \textit{transformer density operator ansatz} for determining the steady states of dissipative quantum many-body systems. By vectorizing the density operator as a many-body state in a doubled Hilbert space, the transformer encodes the amplitude and phase of the state's coefficients, with its parameters serving as variational variables. Our design preserves translation invariance while leveraging attention mechanisms to capture diverse long-range correlations. We demonstrate the effectiveness of our approach by numerically calculating the steady states of dissipative Ising and Heisenberg spin chain models, showing that our method achieves excellent accuracy in predicting mixed steady states.

quant-ph↗

arXiv2025

Cumulant Structures of Entanglement Entropy

We present a new method to derive exact cumulant expressions of any order of von Neumann entropy over Hilbert-Schmidt ensemble. The new method uncovers hidden cumulant structures that decouple each cumulant in a summation-free manner into its lower-order joint cumulants involving families of ancillary statistics. Importantly, the new method is able to avoid the seemingly inevitable task of simplifying nested summations of increasing difficulty that prevents the existing method in the literature to obtain higher-order cumulants.

math-ph↗