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Jinxin Wang

Publications and source records attributed to Jinxin Wang.

17 recordsLinked to original sources

Science Edge Evaluation: SEE the Missing Step Toward Real Scientific Discovery

Large language models (LLMs) are increasingly involved in scientific discovery, yet it remains unclear whether they can support complex real laboratory science. Here we introduce Science Edge Evaluation (SEE), a multimodal benchmark of expert-curated questions grounded in peer-reviewed literature and experimental practice in chemistry, biology, and materials science. Evaluation of 19 multimodal large language models (MLLMs) shows that even the best-performing model reaches only 48.7% accuracy. Moreover, general-purpose models outperform science-specialized models on average. In the visual-agent evaluation, the use of tools increases the best accuracy to 52.7%. Tool use can expand the information available to models, but more information does not necessarily lead to reliable scientific reasoning. The key challenge is whether models can manage tool-derived information within the boundaries of the original experimental evidence. Together, these findings reveal that current MLLMs still cannot reliably make justified and evidence-bounded inferences from experimental results, which is an essential capability in real scientific discovery. Bridging this gap requires MLLMs to transition from explaining established scientific concepts to deriving novel and evidence-based insights from experimental data.

cs.AI

Gaussian fluctuations for the parabolic Anderson model with L\'evy white noise

In this article, we consider the parabolic Anderson model driven by a L\'evy white noise with finite variance in dimension 1, and we study the asymptotic behaviour of the spatial average of the solution. The main result shows that, with appropriate normalization and centering, the spatial integral converges in distribution to the standard normal distribution, and gives an estimate for the rate of this convergence in the Wasserstein distance, the Kolmogorov distance, and the Fortet-Mourier distance. We also prove the functional limit theorem corresponding to this result.

math.PR

Restarted Accelerated Primal-Dual Algorithms with Adaptive Stepsizes for Nonlinear Conic Constrained Convex Optimization

We propose restarted accelerated primal-dual algorithms with (non-monotone) backtracking (rAPDB) for convex nonlinear conic programs, with quadratically constrained quadratic programs (QCQPs) as a special case. Unlike linear and quadratic programs, these problems give rise to convex-concave minimax reformulations with non-bilinear coupling terms; therefore, the existing primal-dual methods for bilinear couplings are not applicable. To address this challenge, we build on the accelerated primal-dual method with adaptive stepsize search -- as it adapts to the local curvature -- and develop both fixed-frequency and adaptive restart schemes, incorporating both monotone and non-monotone adaptive step-size search strategies. The resulting algorithms require only first-order information and matrix-vector products, making them suitable for large-scale and GPU-accelerated implementation. Under metric subregularity of the KKT mapping, we prove a quadratic growth property for a self-centered smoothed duality gap and establish global linear convergence of the proposed restarted methods. We also establish sufficient conditions under which the metric subregularity holds even for general nonconvex problems over convex polyhedral cones. These results are new and may be of independent interest. Numerical experiments on random QCQPs and kernel matrix learning instances show that the proposed methods, especially with non-monotone adaptive stepsizes and GPU acceleration, achieve strong practical performance.

math.OC

TriP: A Triangle Puzzle Approach to Robust Translation Averaging

Translation averaging aims to recover camera locations from pairwise relative translation directions and is a fundamental component of global Structure-from-Motion pipelines. The problem is challenging because direction measurements contain no distance information, making the estimation problem highly ill-conditioned and highly sensitive to corrupted observations. In this paper, we propose TriP, a triangle-based framework for robust translation averaging. TriP first infers local relative edge scales from triangle geometry, and then synchronizes the scales of overlapping triangles in the logarithmic domain to recover globally consistent edge lengths and camera locations. By leveraging higher-order consistency across triangles, the proposed method is robust to adversarial, cycle-consistent, and other structured corruptions. In addition, TriP avoids the collapse issue without requiring any extra anti-collapse constraints, since log-scale synchronization excludes the degenerate zero-scale solution by construction. These structural advantages enable a particularly strong theory for exact location recovery. On the practical side, TriP is fully parallelizable, computationally efficient, and naturally scalable to graphs with millions of cameras. Moreover, it outperforms all previous translation averaging methods by a large margin on both synthetic and real datasets.

cs.CV

SPDEs with time-independent L\'evy colored noise

In this article, we introduce a time-independent version of the L\'evy colored noise considered in Balan (2015) and Balan and Jim\'enez (2026). We study the existence of the solution of a linear stochastic partial differential equation with this type of noise, and we identify some necessary conditions which guarantee that the solution has finite $p$-th order moments. Using tools from Malliavin calculus, we investigate the existence of the solution for the equation with multiplicative noise. As examples, we consider the stochastic heat and wave equations in any dimension $d \geq 1$.

math.PR

StegoNGP: 3D Cryptographic Steganography using Instant-NGP

Recently, Instant Neural Graphics Primitives (Instant-NGP) has achieved significant success in rapid 3D scene reconstruction, but securely embedding high-capacity hidden data, such as an entire 3D scene, remains a challenge. Existing methods rely on external decoders, require architectural modifications, and suffer from limited capacity, which makes them easily detectable. We propose a novel parameter-free 3D Cryptographic Steganography using Instant-NGP (StegoNGP), which leverages the Instant-NGP hash encoding function as a key-controlled scene switcher. By associating a default key with a cover scene and a secret key with a hidden scene, our method trains a single model to interweave both representations within the same network weights. The resulting model is indistinguishable from a standard Instant-NGP in architecture and parameter count. We also introduce an enhanced Multi-Key scheme, which assigns multiple independent keys across hash levels, dramatically expanding the key space and providing high robustness against partial key disclosure attacks. Experimental results demonstrated that StegoNGP can hide a complete high-quality 3D scene with strong imperceptibility and security, providing a new paradigm for high-capacity, undetectable information hiding in neural fields. The code can be found at https://github.com/jiang-wenxiang/StegoNGP.

cs.CV

Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization

Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has been limited, and until very recently essentially no worst-case complexity bounds were available. Recently, Cao et al. provided a sharp error bound for linear interpolation and extrapolation and derived a worst-case complexity result for a basic simplex-type method. Motivated by this, we propose a practical and provable algorithm -- the regular simplicial search method (RSSM), that incorporates reflection and shrinking steps, akin to the original method of Spendley et al. We establish worst-case complexity bounds in nonconvex, convex, and strongly convex cases. These results provide guarantees on convergence rates and lay the groundwork for future complexity analysis of more advanced simplex-type algorithms.

math.OC

Molecular HDD Logic for Encrypted Massive Data Storage

Organic memories, with small dimension, fast speed and long retention features, are considered as promising candidates for massive data archiving. In order to satisfy the re-quirements for ultra-low power and high-security information storage, we design a concep-tual molecular hard-disk (HDD) logic scheme that is capable to execute in-situ encryption of massive data in pW/bit power-consumption range. Beneficial from the coupled mechanism of counter-balanced redox reaction and local ion drifting, the basic HDD unit consisting of ~ 200 self-assembled RuXLPH molecules in a monolayer (SAM) configuration undergoes unique conductance modulation with continuous, symmetric and low-power switching char-acteristics. 96-state memory performance, which allows 6-bit data storage and single-unit one-step XOR operation, is realized in the RuXLPH SAM sample. Through single-unit XOR manipulation of the pixel information, in-situ bitwise encryption of the Mogao Grottoes mural images stored in the molecular HDD is demonstrated.

cs.ET

Randomized Submanifold Subgradient Method for Optimization over Stiefel Manifolds

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain challenging, particularly when the objective function is nonsmooth. In this paper, we propose a novel coordinate-type algorithm, named \emph{randomized submanifold subgradient method} (RSSM), for minimizing a possibly nonsmooth weakly convex function over the Stiefel manifold and study its convergence behavior. Similar to coordinate-type algorithms in the Euclidean setting, RSSM exhibits low per-iteration cost and is suitable for high-dimensional problems. We prove that RSSM has an iteration complexity of $\mathcal O(\varepsilon^{-4})$ for driving a natural stationarity measure below $\varepsilon$, both in expectation and in almost-sure senses. To the best of our knowledge, this is the first convergence guarantee for coordinate-type algorithms for nonsmooth optimization over the Stiefel manifold. To establish the said guarantee, we develop two new theoretical tools, namely a Riemannian subgradient inequality for weakly convex functions on proximally smooth matrix manifolds and an averaging operator that induces an adaptive metric on the ambient Euclidean space, which could be of independent interest. Lastly, we present numerical results on robust subspace recovery and orthogonal dictionary learning to demonstrate the viability of our proposed method.

math.OC

Weighted Spectral Filters for Kernel Interpolation on Spheres: Estimates of Prediction Accuracy for Noisy Data

Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect approximation performance. However, in dealing with noisy data, kernel interpolation frequently behaves not so well due to the large condition number of the kernel matrix and instability of the interpolation process. In this paper, we introduce a weighted spectral filter approach to reduce the condition number of the kernel matrix and then stabilize kernel interpolation. The main building blocks of the proposed method are the well developed spherical positive quadrature rules and high-pass spectral filters. Using a recently developed integral operator approach for spherical data analysis, we theoretically demonstrate that the proposed weighted spectral filter approach succeeds in breaking through the bottleneck of kernel interpolation, especially in fitting noisy data. We provide optimal approximation rates of the new method to show that our approach does not compromise the predicting accuracy. Furthermore, we conduct both toy simulations and two real-world data experiments with synthetically added noise in geophysical image reconstruction and climate image processing to verify our theoretical assertions and show the feasibility of the weighted spectral filter approach.

cs.LG

On the Estimation Performance of Generalized Power Method for Heteroscedastic Probabilistic PCA

The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In this paper, to estimate the underlying low-dimensional linear subspace (simply called \emph{ground truth}) from available heterogeneous data samples, we consider the associated non-convex maximum-likelihood estimation problem, which involves maximizing a sum of heterogeneous quadratic forms over an orthogonality constraint (HQPOC). We propose a first-order method -- generalized power method (GPM) -- to tackle the problem and establish its \emph{estimation performance} guarantee. Specifically, we show that, given a suitable initialization, the distances between the iterates generated by GPM and the ground truth decrease at least geometrically to some threshold associated with the residual part of certain "population-residual decomposition". In establishing the estimation performance result, we prove a novel local error bound property of another closely related optimization problem, namely quadratic optimization with orthogonality constraint (QPOC), which is new and can be of independent interest. Numerical experiments are conducted to demonstrate the superior performance of GPM in both Gaussian noise and sub-Gaussian noise settings.

math.OC

Projected Tensor Power Method for Hypergraph Community Recovery

This paper investigates the problem of exact community recovery in the symmetric $d$-uniform $(d \geq 2)$ hypergraph stochastic block model ($d$-HSBM). In this model, a $d$-uniform hypergraph with $n$ nodes is generated by first partitioning the $n$ nodes into $K\geq 2$ equal-sized disjoint communities and then generating hyperedges with a probability that depends on the community memberships of $d$ nodes. Despite the non-convex and discrete nature of the maximum likelihood estimation problem, we develop a simple yet efficient iterative method, called the \emph{projected tensor power method}, to tackle it. As long as the initialization satisfies a partial recovery condition in the logarithmic degree regime of the problem, we show that our proposed method can exactly recover the hidden community structure down to the information-theoretic limit with high probability. Moreover, our proposed method exhibits a competitive time complexity of $\mathcal{O}(n\log^2n/\log\log n)$ when the aforementioned initialization condition is met. We also conduct numerical experiments to validate our theoretical findings.

math.OC

Decentralized Weakly Convex Optimization Over the Stiefel Manifold

We focus on a class of non-smooth optimization problems over the Stiefel manifold in the decentralized setting, where a connected network of $n$ agents cooperatively minimize a finite-sum objective function with each component being weakly convex in the ambient Euclidean space. Such optimization problems, albeit frequently encountered in applications, are quite challenging due to their non-smoothness and non-convexity. To tackle them, we propose an iterative method called the decentralized Riemannian subgradient method (DRSM). The global convergence and an iteration complexity of $\mathcal{O}(\varepsilon^{-2} \log^2(\varepsilon^{-1}))$ for forcing a natural stationarity measure below $\varepsilon$ are established via the powerful tool of proximal smoothness from variational analysis, which could be of independent interest. Besides, we show the local linear convergence of the DRSM using geometrically diminishing stepsizes when the problem at hand further possesses a sharpness property. Numerical experiments are conducted to corroborate our theoretical findings.

math.OC

Morphological effects of leading-edge serrations on the acoustic signatures of mixed flow fan analyzed using novel CFD-informed methods

Leading-edge (LE) noise is a common source of broadband noise for fans that can be suppressed using appended LE serrations. We conduct an integrated study of the morphological effects of interval, length, and inclination angle of owl-inspired LE serrations on the aeroacoustic characteristics of a mixed flow fan using experiments, computational fluid dynamics (CFD), and the Ffowcs Williams-Hawkings (FWH) analogy. A novel method for surface noise strength (SNS) visualization was developed based on the FWH analogy with large-eddy simulations, and a CFD-informed index SAPG is proposed to evaluate the severity of flow separation with pressure gradient, which are verified to be effective in examining the acoustic sources and chordwise separation. Acoustic measurements show the robust tradeoff solving capability of the serrations under various morphologies and the SNS visualizations indicate that the separation-induced LE noise is suppressed considerably. One-third octave analyses suggest that extending serration length can lower separation noise more effectively than shrinking the interval over 100-3k Hz. A smaller interval is more desirable while an optimal length exists in association with tonal noise. Moreover, small inclination angles (below 20 degrees) enable the deceleration of oncoming flows with stagnation relieved, and consequently, further suppress the LE noise, by a flow-buffering effect. Heavy inclination angles (over 40 degrees) induce an additional tip vortex, causing high-coherence turbulence impingement noise and resulting in a drastic increase in broadband noise at frequencies exceeding 4k Hz. Our study thus clarifies the morphological effects of LE serrations on aeroacoustic signatures of rotary devices while providing useful methods for acoustic analyses.

physics.flu-dyn

Orthogonal Group Synchronization with Incomplete Measurements: Error Bounds and Linear Convergence of the Generalized Power Method

Group synchronization refers to estimating a collection of group elements from the noisy pairwise measurements. Such a nonconvex problem has received much attention from numerous scientific fields including computer vision, robotics, and cryo-electron microscopy. In this paper, we focus on the orthogonal group synchronization problem with general additive noise models under incomplete measurements, which is much more general than the commonly considered setting of complete measurements. Characterizations of the orthogonal group synchronization problem are given from perspectives of optimality conditions as well as fixed points of the projected gradient ascent method which is also known as the generalized power method (GPM). It is well worth noting that these results still hold even without generative models. In the meantime, we derive the local error bound property for the orthogonal group synchronization problem which is useful for the convergence rate analysis of different algorithms and can be of independent interest. Finally, we prove the linear convergence result of the GPM to a global maximizer under a general additive noise model based on the established local error bound property. Our theoretical convergence result holds under several deterministic conditions which can cover certain cases with adversarial noise, and as an example we specialize it to the setting of the Erdös-Rényi measurement graph and Gaussian noise.

math.OC

Sparse High-Order Portfolios via Proximal DCA and SCA

In this paper, we aim at solving the cardinality constrained high-order portfolio optimization, i.e., mean-variance-skewness-kurtosis model with cardinality constraint (MVSKC). Optimization for the MVSKC model is of great difficulty in two parts. One is that the objective function is non-convex, the other is the combinational nature of the cardinality constraint, leading to non-convexity as well dis-continuity. Based on the observation that cardinality constraint has the difference-of-convex (DC) property, we transform the cardinality constraint into a penalty term and then propose three algorithms including the proximal difference of convex algorithm (pDCA), pDCA with extrapolation (pDCAe) and the successive convex approximation (SCA) to handle the resulting penalized MVSK (PMVSK) formulation. Moreover, theoretical convergence results of these algorithms are established respectively. Numerical experiments on the real datasets demonstrate the superiority of our proposed methods in obtaining high utility and sparse solutions as well as efficiency in terms of time usage.

q-fin.PM

Joint Bandwidth Allocation and Path Selection in WANs with Path Cardinality Constraints

In this paper, we study a joint bandwidth allocation and path selection problem via solving a multi-objective minimization problem under the path cardinality constraints, namely MOPC. Our problem formulation captures various types of objectives including the proportional fairness, the total completion time, as well as the worst-case link utilization ratio. Such an optimization problem is very challenging since it is highly non-convex. Almost all existing works deal with such a problem using relaxation techniques to transform it to be a convex optimization problem. However, we provide a novel solution framework based on the classic alternating direction method of multipliers (ADMM) approach for solving this problem. Our proposed algorithm is simple and easy to be implemented. Each step of our algorithm consists of either finding the maximal root of a single-cubic equation which is guaranteed to have at least one positive solution or solving a one-dimensional convex subproblem in a fixed interval. Under some mild assumptions, we prove that any limiting point of the generated sequence under our proposed algorithm is a stationary point. Extensive numerical simulations are performed to demonstrate the advantages of our algorithm compared with various baselines.

eess.SP