arXiv subjects

Meng Huang

Publications and source records attributed to Meng Huang.

At least 19 recordsLinked to original sources

arXiv2026

Phase Retrieval in $\mathbb C^4$ Requires Exactly Eleven Measurements

Determining the minimal number of intensity measurements required for phase retrieval in $\mathbb{C}^4$ has been a long-standing open problem. Prior to this work, the best-known results implied that this minimum was either $10$ or $11$. In this paper, we leverage characteristic classes and cohomology groups from differential topology to prove that no family of $10$ vectors in $\mathbb{C}^4$ possesses the phase retrieval property. Combining our lower bound with Vinzant's explicit eleven-vector construction establishes that the exact minimum is $11$. Our result yields a significant consequence for pure state quantum tomography, namely, a rank-one POVM on $\mathbb{C}^4$ requires exactly $11$ elements to be informationally complete for pure states. This further implies that three orthonormal bases are insufficient to uniquely distinguish all pure states in $\mathbb{C}^4$. Because four orthonormal bases are already known to be sufficient, we conclude that exactly four bases are required, thereby completely resolving the problem left in [C. Carmeli, T. Heinosaari, J. Schultz, A. Toigo, Eur. Phys. J. D].

quant-ph↗

arXiv2026

Benchmarking Foundation and Large Language Models for Few-Shot Medical Image Segmentation

Few-shot medical image segmentation (FS-MIS) aims to segment novel regions of interest (ROIs) from a few annotated support examples. Despite rapid progress, existing FS-MIS solutions span diverse paradigms but are evaluated under inconsistent settings, leaving their relative effectiveness unclear. We introduce FAME, a unified benchmark for evaluating FS-MIS solutions, covering specialists, SAM-based methods, CLIP-based methods, and MLLM-based methods. FAME contains 14,958 test samples across 7 anatomical sites, 9 imaging modalities, and 14 ROI categories, and evaluates models under zero-shot and ten-shot settings with additional assessment of target-absence recognition and generalization under covariate and semantic shifts. Our evaluation reveals several findings. First, effective few-shot segmentation depends on how models exploit support examples: direct visual adaptation generally outperforms prompt-based strategies. Second, increasing support examples improves performance only when models can effectively utilize them. Third, semantic transfer remains substantially more challenging than imaging-domain adaptation, and strong localization ability does not necessarily imply reliable target-absence recognition. We hope FAME provides a comprehensive understanding of current FS-MIS solutions and facilitates the development of more effective and reliable few-shot medical segmentation methods.

cs.CV↗

arXiv2026

Yuvion VL: A Multimodal Foundation Model for Adversarial Content and AI Safety

General-purpose models often struggle to reliably identify and understand real-world multimodal risks, largely due to the inherent multimodal adversarial nature of content and AI safety. We present Yuvion VL, a family of multimodal large language models purpose-built for content and AI safety, with both instruction-tuned and reasoning-oriented variants. Yuvion VL addresses this gap by treating safety as an inherently adversarial and multimodal problem and designing the entire pipeline around adversarial robustness. For data construction, we develop an automated pipeline integrating adversarial-aware data synthesis with multi-stage quality control, producing large-scale, high-quality multimodal samples augmented with domain knowledge and reasoning annotations. For training, we adopt a three-stage pipeline that includes continued pretraining for risk-concept cross-modal alignment, instruct post-training for production-grade safety tasks, and reasoning post-training for enhanced interpretability and performance in complex tasks. We further introduce Confuse-then-Contrast Fine-Tuning, a contrastive framework that mines model-specific confusions and constructs multi-image contrastive groups to enforce explicit discrimination of fine-grained visual-semantic elements, enabling the model to distinguish between visually similar cases with different safety implications in adversarial safety tasks. To support rigorous evaluation, we further introduce Yuvion VL RiskEval (YVRE), a collection of benchmarks covering diverse open and internal evaluations, with a focus on content and AI safety, adversarial robustness, and real-world capability requirements. Experiments show that Yuvion VL-32B achieves industry-leading safety performance, surpassing comparably sized open-source models and best closed-source commercial models, while maintaining comparable general capabilities.

cs.CV↗

arXiv2026

Higher-order Diffusion Sampling via Chebyshev Interpolation and Gauss--Seidel Iterations

Higher-order ODE solvers have shown strong empirical promise for accelerating diffusion models through the probability flow ODE, but rigorous non-asymptotic guarantees for such acceleration remain limited. In this paper, we develop a Chebyshev--Gauss--Seidel higher-order sampler and establish a non-asymptotic convergence guarantee that allows the approximation order to grow logarithmically with the number of outer iterations. In the exact-score setting, up to logarithmic factors, the proposed sampler requires at most \[ d^{1+o_T(1)}\varepsilon^{-1/K_1} \] score functions to approximate the target distribution on $\mathbb{R}^d$ within total variation distance $\varepsilon$, where $o_T(1)\to 0$ as $T\to\infty$ and $K_1>0$ is a sufficiently large constant. The analysis assumes only a polynomial second-moment bound on the target distribution, thereby relaxing the bounded-support condition imposed in existing higher-order theory. Moreover, the guarantee is robust to score and Jacobian estimation errors and does not require higher-order smoothness assumptions on the score estimates. Numerical experiments on anisotropic Gaussian mixture benchmarks support the predicted improvement in the accuracy--cost tradeoff under finite score-evaluation budgets.

math.NA↗

arXiv2026

A Double Bind: Gendered Funding, Research Topics, and Academic Performance in the Social Sciences

While female representation in social sciences is increasing, systemic gender disparities may persist in research funding and academic performance. Some argue that female scholars now receive equal opportunities, yet evidence suggests that gender imbalances remain, particularly in specific research areas. This study examines 12,945 National Science Foundation (NSF)-funded principal investigators in social sciences from 2000 to 2019 to assess gender disparities in grant allocation, research topics, and post-award academic performance. Findings reveal a dual imbalance. First, despite similar overall funding success rates, female scholars remain underrepresented in high-impact and traditionally male-dominated research topics. Male recipients are more represented in most funded topics, especially technology- and methodology-related ones, whereas female recipients are more concentrated in a smaller set of topics related to children, family, cognition, and health. Second, post-award performance patterns suggest that females outperform males in male-dominated fields, whereas males excel in female-dominated ones, undermining any presumed advantage of female scholars in their own research areas. These patterns may be associated with gendered constraints in academic career trajectories. Furthermore, early-career experiences shape these outcomes asymmetrically. In male-dominated topics, postdoctoral experience is associated with lower publication and citation performance for women but higher publication and citation performance for men. In female-dominated topics, postdoctoral experience is positively associated with women's publications and citations and with men's publication output. These findings suggest that policy discussions should consider not just overall funding equality, but also gendered disparities across research topics and career trajectories.

cs.DL↗

arXiv2026

NS-RGS: Newton-Schulz based Riemannian gradient method for orthogonal group synchronization

Group synchronization is a fundamental task involving the recovery of group elements from pairwise measurements. For orthogonal group synchronization, the most common approach reformulates the problem as a constrained nonconvex optimization and solves it using projection-based methods, such as the generalized power method. However, these methods rely on exact SVD or QR decompositions in each iteration, which are computationally expensive and become a bottleneck for large-scale problems. In this paper, we propose a Newton-Schulz-based Riemannian Gradient Scheme (NS-RGS) for orthogonal group synchronization that significantly reduces computational cost by replacing the SVD or QR step with the Newton-Schulz iteration. This approach leverages efficient matrix multiplications and aligns perfectly with modern GPU/TPU architectures. By employing a refined leave-one-out analysis, we overcome the challenge arising from statistical dependencies, and establish that NS-RGS with spectral initialization achieves linear convergence to the target solution up to near-optimal statistical noise levels. Experiments on synthetic data and real-world global alignment tasks demonstrate that NS-RGS attains accuracy comparable to state-of-the-art methods such as the generalized power method, while achieving nearly a 2$\times$ speedup.

stat.ML↗

arXiv2026

Scaled Gradient Descent for Ill-Conditioned Low-Rank Matrix Recovery with Optimal Sampling Complexity

The low-rank matrix recovery problem seeks to reconstruct an unknown $n_1 \times n_2$ rank-$r$ matrix from $m$ linear measurements, where $m\ll n_1n_2$. This problem has been extensively studied over the past few decades, leading to a variety of algorithms with solid theoretical guarantees. Among these, gradient descent based non-convex methods have become particularly popular due to their computational efficiency. However, these methods typically suffer from two key limitations: a sub-optimal sample complexity of $O((n_1 + n_2)r^2)$ and an iteration complexity of $O(\kappa \log(1/\epsilon))$ to achieve $\epsilon$-accuracy, resulting in slow convergence when the target matrix is ill-conditioned. Here, $\kappa$ denotes the condition number of the unknown matrix. Recent studies show that a preconditioned variant of GD, known as scaled gradient descent (ScaledGD), can significantly reduce the iteration complexity to $O(\log(1/\epsilon))$. Nonetheless, its sample complexity remains sub-optimal at $O((n_1 + n_2)r^2)$. In contrast, a delicate virtual sequence technique demonstrates that the standard GD in the positive semidefinite (PSD) setting achieves the optimal sample complexity $O((n_1 + n_2)r)$, but converges more slowly with an iteration complexity $O(\kappa^2 \log(1/\epsilon))$. In this paper, through a more refined analysis, we show that ScaledGD achieves both the optimal sample complexity $O((n_1 + n_2)r)$ and the improved iteration complexity $O(\log(1/\epsilon))$. Notably, our results extend beyond the PSD setting to general low-rank matrix recovery problem. Numerical experiments further validate that ScaledGD accelerates convergence for ill-conditioned matrices with the optimal sampling complexity.

stat.ML↗

arXiv2025

Recovery Performance of PhaseLift for Phase Retrieval from Coded Diffraction Patterns

The PhaseLift algorithm is an effective convex method for solving the phase retrieval problem from Fourier measurements with coded diffraction patterns (CDP). While exact reconstruction guarantees are well-established in the noiseless case, the stability of recovery under noise remains less well understood. In particular, when the measurements are corrupted by an additive noise vector $\vw \in \R^m$, existing recovery bounds scale on the order of $\norm{\vw}$, which is conjectured to be suboptimal. More recently, Soltanolkotabi conjectured that the optimal PhaseLift recovery bound should scale with the average noise magnitude, that is, on the order of $\norm{\vw}/\sqrt m$. However, establishing this theoretically is considerably more challenging and has remained an open problem. In this paper, we focus on this conjecture and prove that under adversarial noise, the recovery error of PhaseLift is bounded by $O\xkh{ \sqrt{\frac{\norm{\vw}\log n }{\sqrt m}}}\norm{\vx_0}$. Here, $\vx_0 \in \C^n$ is the signals we aim to recover. Moreover, for mean-zero sub-Gaussian noise vector $\vw \in \R^m$, a upper error bound and its corresponding minimax lower bound are also provided. Our results represent a significant step toward Soltanolkotabi's conjecture, offering new insights into the stability of PhaseLift under noisy CDP measurements.

math.NA↗

arXiv2025

Convergence Analysis of Reshaped Wirtinger Flow with Random Initialization for Phase Retrieval

This paper investigates phase retrieval using the Reshaped Wirtinger Flow (RWF) algorithm, focusing on recovering target vector $\vx \in \R^n$ from magnitude measurements $y_i = \left| \langle \va_i, \vx \rangle \right|, \; i = 1, \ldots, m,$ under random initialization, where $\va_i \in \R^n$ are measurement vectors. For Gaussian measurement designs, we prove that when $m\ge O(n \log^2 n\log^3 m)$, the RWF algorithm with random initialization achieves $\epsilon$-accuracy within $O\big(\log n + \log(1/\epsilon)\big)$ iterations, thereby attaining nearly optimal sample and computational complexities comparable to those previously established for spectrally initialized methods. Numerical experiments demonstrate that the convergence rate is robust to initialization randomness and remains stable even with larger step sizes.

math.OC↗

arXiv2025

Sparse Signal Recovery From Quadratic Systems with Full-Rank Matrices

In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m \ll n$). This paper addresses this problem by exploiting signal sparsity. Using tools from algebraic geometry, we derive theoretical recovery guarantees for sparse quadratic systems, showing that $m\ge 2s$ (real case) and $m\ge 4s-2$ (complex case) generic measurements suffice to uniquely recover all $s$-sparse signals. Under a Gaussian measurement model, we propose a novel two-stage Sparse Gauss-Newton (SGN) algorithm. The first stage employs a support-restricted spectral initialization, yielding an accurate initial estimate with $m=O(s^2\log{n})$ measurements. The second stage refines this estimate via an iterative hard-thresholding Gauss-Newton method, achieving quadratic convergence to the true signal within finitely many iterations when $m\ge O(s\log{n})$. Compared to existing second-order methods, our algorithm achieves near-optimal sampling complexity for the refinement stage without requiring resampling. Numerical experiments indicate that SGN significantly outperforms state-of-the-art algorithms in both accuracy and computational efficiency. In particular, (1) when sparsity level $s$ is high, compared with existing algorithms, SGN can achieve the same success rate with fewer measurements. (2) SGN converges with only about $1/10$ iterations of the best existing algorithm and reach lower relative error.

cs.IT↗

arXiv2025

The Condition Number in Phase Retrieval from Intensity Measurements

This paper investigates the stability of phase retrieval by analyzing the condition number of the nonlinear map $\Psi_{\boldsymbol{A}}(\boldsymbol{x}) = \bigl(\lvert \langle {\boldsymbol{a}}_j, \boldsymbol{x} \rangle \rvert^2 \bigr)_{1 \le j \le m}$, where $\boldsymbol{a}_j \in \mathbb{H}^n$ are known sensing vectors with $\mathbb{H} \in \{\mathbb{R}, \mathbb{C}\}$. For each $p \ge 1$, we define the condition number $\beta_{\Psi_{\boldsymbol{A}}}^{\ell_p}$ as the ratio of optimal upper and lower Lipschitz constants of $\Psi_{\boldsymbol{A}}$ measured in the $\ell_p$ norm, with respect to the metric $\mathrm {dist}_\mathbb{H}\left(\boldsymbol{x}, \boldsymbol{y}\right) = \|\boldsymbol{x} \boldsymbol{x}^\ast - \boldsymbol{y} \boldsymbol{y}^\ast\|_*$. We establish universal lower bounds on $\beta_{\Psi_{\boldsymbol{A}}}^{\ell_p}$ for any sensing matrix $\boldsymbol{A} \in \mathbb{H}^{m \times d}$, proving that $\beta_{\Psi_{\boldsymbol{A}}}^{\ell_1} \ge \pi/2$ and $\beta_{\Psi_{\boldsymbol{A}}}^{\ell_2} \ge \sqrt{3}$ in the real case $(\mathbb{H} = \mathbb{R})$, and $\beta_{\Psi_{\boldsymbol{A}}}^{\ell_p} \ge 2$ for $p=1,2$ in the complex case $(\mathbb{H} = \mathbb{C})$. These bounds are shown to be asymptotically tight: both a deterministic harmonic frame $\boldsymbol{E}_m \in \mathbb{R}^{m \times 2}$ and Gaussian random matrices $\boldsymbol{A} \in \mathbb{H}^{m \times d}$ asymptotically attain them. Notably, the harmonic frame $\boldsymbol{E}_m \in \mathbb{R}^{m \times 2}$ achieves the optimal lower bound $\sqrt{3}$ for all $m \ge 3$ when $p=2$, thus serving as an optimal sensing matrix within $\boldsymbol{A} \in \mathbb{R}^{m \times 2}$. Our results provide the first explicit uniform lower bounds on $\beta_{\Psi_{\boldsymbol{A}}}^{\ell_p}$ and offer insights into the fundamental stability limits of phase retrieval.

cs.IT↗

arXiv2025

Performance analysis of tail-minimization and the linear rate of convergence of a proximal algorithm for sparse signal recovery

Recovery error bounds of tail-minimization and the rate of convergence of an efficient proximal alternating algorithm for sparse signal recovery are considered in this article. Tail-minimization focuses on minimizing the energy in the complement $T^c$ of an estimated support $T$. Under the restricted isometry property (RIP) condition, we prove that tail-$\ell_1$ minimization can exactly recover sparse signals in the noiseless case for a given $T$. In the noisy case, two recovery results for the tail-$\ell_1$ minimization and the tail-lasso models are established. Error bounds are improved over existing results. Additionally, we show that the RIP condition becomes surprisingly relaxed, allowing the RIP constant to approach $1$ as the estimation $T$ closely approximates the true support $S$. Finally, an efficient proximal alternating minimization algorithm is introduced for solving the tail-lasso problem using Hadamard product parametrization. The linear rate of convergence is established using the Kurdyka-{\L}ojasiewicz inequality. Numerical results demonstrate that the proposed algorithm significantly improves signal recovery performance compared to state-of-the-art techniques.

cs.IT↗

arXiv2024

Noisy phase retrieval from subgaussian measurements

This paper aims to address the phase retrieval problem from subgaussian measurements with arbitrary noise, with a focus on devising robust and efficient algorithms for solving non-convex problems. To ensure uniqueness of solutions in the subgaussian setting, we explore two commonly used assumptions: either the subgaussian measurements satisfy a fourth-moment condition or the target signals exhibit non-peakiness. For each scenario, we introduce a novel spectral initialization method that yields robust initial estimates. Building on this, we employ leave-one-out arguments to show that the classical Wirtinger flow algorithm achieves a linear rate of convergence for both real-valued and complex-valued cases, provided the sampling complexity $m\ge O(n \log^3 m)$, where $n$ is the dimension of the underlying signals. In contrast to existing work, our algorithms are regularization-free, requiring no truncation, trimming, or additional penalty terms, and they permit the algorithm step sizes as large as $O(1)$, compared to the $O(1/n)$ in previous literature. Furthermore, our results accommodate arbitrary noise vectors that meet certain statistical conditions, covering a wide range of noise scenarios, with sub-exponential noise as a notable special case. The effectiveness of our algorithms is validated through various numerical experiments. We emphasize that our findings provide the first theoretical guarantees for recovering non-peaky signals using non-convex methods from Bernoulli measurements, which is of independent interest.

math.OC↗

arXiv2024

Asymptotic quadratic convergence of the Gauss-Newton method for complex phase retrieval

In this paper, we introduce a Gauss-Newton method for solving the complex phase retrieval problem. In contrast to the real-valued setting, the Gauss-Newton matrix for complex-valued signals is rank-deficient and, thus, non-invertible. To address this, we utilize a Gauss-Newton step that moves orthogonally to certain trivial directions. We establish that this modified Gauss-Newton step has a closed-form solution, which corresponds precisely to the minimal-norm solution of the associated least squares problem. Additionally, using the leave-one-out technique, we demonstrate that $m\ge O( n\log^3 n)$ independent complex Gaussian random measurements ensures that the entire trajectory of the Gauss-Newton iterations remains confined within a specific region of incoherence and contraction with high probability. This finding allows us to establish the asymptotic quadratic convergence rate of the Gauss-Newton method without the need of sample splitting.

math.NA↗

arXiv2024

Forte: A Suite of Advanced Multireference Quantum Chemistry Methods

Forte is an open-source library specialized in multireference electronic structure theories for molecular systems and the rapid prototyping of new methods. This paper gives an overview of the capabilities of Forte, its software architecture, and examples of applications enabled by the methods it implements.

physics.chem-ph↗

arXiv2022

A benchmark study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group

This work examines the accuracy and precision of X-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the X-ray absorption benchmark of organic molecules (XABOOM) set, consisting of 116 transitions from mostly organic molecules [T. Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32 eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.

physics.chem-ph↗

arXiv2022

Inferring cell-specific lncRNA regulation with single-cell RNA-sequencing data in the developing human neocortex

Long non-coding RNAs (lncRNAs) are important regulators to modulate gene expression and cell proliferation in the developing human brain. Previous methods mainly use bulk lncRNA and mRNA expression data to study lncRNA regulation. However, to analyze lncRNA regulation regarding individual cells, we focus on single-cell RNA-sequencing (scRNA-seq) data instead of bulk data. Recent advance in scRNA-seq has provided a way to investigate lncRNA regulation at single-cell level. We will propose a novel computational method, CSlncR (cell-specific lncRNA regulation), which combines putative lncRNA-mRNA binding information with scRNA-seq data including lncRNAs and mRNAs to identify cell-specific lncRNA-mRNA regulation networks at individual cells. To understand lncRNA regulation at different development stages, we apply CSlncR to the scRNA-seq data of human neocortex. Network analysis shows that the lncRNA regulation is unique in each cell from the different human neocortex development stages. The comparison results indicate that CSlncR is also an effective tool for predicting cell-specific lncRNA targets and clustering single cells, which helps understand cell-cell communication.

q-bio.MN↗

arXiv2022

Unveiling interpretable development-specific gene signatures in the developing human prefrontal cortex with ICGS

In this paper, to unveil interpretable development-specific gene signatures in human PFC, we propose a novel gene selection method, named Interpretable Causality Gene Selection (ICGS), which adopts a Bayesian Network (BN) to represent causality between multiple gene variables and a development variable. The proposed ICGS method combines the positive instances-based contrastive learning with a Variational AutoEncoder (VAE) to obtain this optimal BN structure and use a Markov Blanket (MB) to identify gene signatures causally related to the development variable. Moreover, the differential expression genes (DEGs) are used to filter redundant genes before gene selection. In order to identify gene signatures, we apply the proposed ICGS to the human PFC single-cell transcriptomics data. The experimental results demonstrate that the proposed method can effectively identify interpretable development-specific gene signatures in human PFC. Gene ontology enrichment analysis and ASD-related gene analysis show that these identified gene signatures reveal the key biological processes and pathways in human PFC and have more potential for neurodevelopment disorder cure. These gene signatures are expected to bring important implications for understanding PFC development heterogeneity and function in humans.

q-bio.NC↗