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Penghui Wang

Publications and source records attributed to Penghui Wang.

At least 19 recordsLinked to original sources

Xiaomi-TabLDM: A Tabular Foundation Model Technical Report

We introduce Xiaomi-TabLDM, a tabular large data foundation model for classification and regression via in-context learning, which delivers superior prediction accuracy without requiring task-specific fine-tuning. Pretrained exclusively on synthetic data generated from structural causal models (SCMs), our model enables more flexible context utilization and more efficient capacity scaling. i) A new performance standard. Strong regression performance across benchmarks: Xiaomi-TabLDM ranks 1st on OpenML-CTR23 and 2nd on regression across TALENT, TabArena, and BCCO, demonstrating consistently strong regression performance across four complementary benchmark suites. Favorable performance--efficiency trade-off: Xiaomi-TabLDM combines strong predictive performance with substantially lower computational cost. For example, on TabArena regression, it achieves the second-highest Elo while using 82% less training time and 68% less prediction time than the top-ranked TabFM. ii) Large-scale synthetic pretraining. Xiaomi-TabLDM expands the coverage and diversity of synthetic tabular data used for pretraining. We also adopt a three-stage training strategy together with dual-stream feature grouping, lightweight Attention Residual, and sparse Mixture-of-Experts, enabling Xiaomi-TabLDM to learn richer feature interactions and expert specialization across diverse tabular tasks. iii) Test-time scaling. Xiaomi-TabLDM further extends tabular prediction through test-time compute scaling, where allocating additional computation at inference time consistently improves predictive performance over the base model.

cs.AI

Numerical Analysis on Backward Stochastic Differential Equations by Finite Transposition Method

In this paper, we propose a finite transposition method to solve backward stochastic differential equations (BSDEs, for short). Based on the transposition solution theory for BSDEs, our method offers a promising way of efficiently computing solutions, which can be regarded as an analogous method for BSDEs as the classical finite element method for partial differential equations. Our method has the advantage of easily computable conditional expectations.

math.PR

Arveson's Gauss-Bonnet-Chern Formula for Hilbert Modules in the Multiplier-Algebra Framework

The present paper continues Arveson's program on curvature, Euler characteristic, and Gauss-Bonnet-Chern type formulae for Hilbert modules. For regular unitarily invariant complete Nevanlinna--Pick spaces on the unit ball in \(\mathbb{C}^d\), we prove that Arveson's Gauss-Bonnet-Chern formula holds unconditionally over the full multiplier algebra. Together with the polynomial-ring case, this shows that the validity of the formula depends essentially on the coefficient algebra. We then solve Arveson's finite defect problem in the same framework by giving a sharp classification of finite defect submodules. This problem is natural in curvature theory, since both curvature and Euler characteristic are governed by the defect structure. Finally, using commutative-algebra methods, we apply this classification to unitary-equivalence rigidity for finite-codimensional submodules of vector-valued reproducing kernel Hilbert modules.

math.FA

Second order necessary conditions for quantum stochastic optimal control problems

This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum stochastic differential equations driven by fermionic Brownian motion, where the control enters both the drift and diffusion terms. This result provides a theoretical foundation for further exploration of optimization problems and their practical applications in the field of quantum stochastic control.

math.OC

The norms for symmetric and antisymmetric tensor products of the weighted shift operators

In the present paper, we study the norms for symmetric and antisymmetric tensor products of weighted shift operators. By proving that for $n\geq 2$, $$\|S_{\alpha}^{l_1}\odot\cdots \odot S_{\alpha}^{l_k}\odot S_{\alpha}^{*l_{k+1}}\odot\cdots \odot S_{\alpha}^{*l_{n}}\| =\mathop{\prod}_{i=1}^n\left \| S_{\alpha}^{{l_{i}}}\right\|, \text{ for any} \ (l_1,l_2\cdots l_n)\in\mathbb N^n$$ if and only if the weight satisfies the regularity condition, we partially solve \cite[Problem 6 and Problem 7]{GA}. It will be seen that most weighted shift operators on function spaces, including weighted Bergman shift, Hardy shift, Dirichlet shift, etc, satisfy the regularity condition. Moreover, at the end of the paper, we solve \cite[Problem 1 and Problem 2]{GA}.

math.FA

Arveson's version of the Gauss-Bonnet-Chern formula for Hilbert modules over the polynomial rings

In this paper, we refine the framework of Arveson's version of the Gauss-Bonnet-Chern formula by proving that a submodule in the Drury-Arveson module being locally algebraic is equivalent to Arveson's version of the Gauss-Bonnet-Chern formula holding true for the associated quotient module. Moreover, we establish the asymptotic Arveson's curvature invariant and the asymptotic Euler characteristic for contractive Hilbert modules over polynomial rings in infinitely many variables, and obtain the infinitely-many-variables analogue of Arveson's version of Gauss-Bonnet-Chern formula. Finally, we solve the finite defect problem for submodules of the Drury-Arveson module $H^2$ in infinitely many variables by proving that $H^2$ has no nontrivial submodules of finite rank.

math.FA

Just a Few Glances: Open-Set Visual Perception with Image Prompt Paradigm

To break through the limitations of pre-training models on fixed categories, Open-Set Object Detection (OSOD) and Open-Set Segmentation (OSS) have attracted a surge of interest from researchers. Inspired by large language models, mainstream OSOD and OSS methods generally utilize text as a prompt, achieving remarkable performance. Following SAM paradigm, some researchers use visual prompts, such as points, boxes, and masks that cover detection or segmentation targets. Despite these two prompt paradigms exhibit excellent performance, they also reveal inherent limitations. On the one hand, it is difficult to accurately describe characteristics of specialized category using textual description. On the other hand, existing visual prompt paradigms heavily rely on multi-round human interaction, which hinders them being applied to fully automated pipeline. To address the above issues, we propose a novel prompt paradigm in OSOD and OSS, that is, \textbf{Image Prompt Paradigm}. This brand new prompt paradigm enables to detect or segment specialized categories without multi-round human intervention. To achieve this goal, the proposed image prompt paradigm uses just a few image instances as prompts, and we propose a novel framework named \textbf{MI Grounding} for this new paradigm. In this framework, high-quality image prompts are automatically encoded, selected and fused, achieving the single-stage and non-interactive inference. We conduct extensive experiments on public datasets, showing that MI Grounding achieves competitive performance on OSOD and OSS benchmarks compared to text prompt paradigm methods and visual prompt paradigm methods. Moreover, MI Grounding can greatly outperform existing method on our constructed specialized ADR50K dataset.

cs.CV

Fredholm index of Toeplitz pairs with $H^{\infty}$ symbols

In the present paper, we characterize the Fredholmness of Toeplitz pairs on Hardy space over the bidisk with the bounded holomorphic symbols, and hence we obtain the index formula for such Toeplitz pairs. The key to obtain the Fredholmness of such Toeplitz pairs is the $L^p$ solution of Corona Problem over $\mathbb{D}^2$.

math.FA

Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II)

In the present paper, by using the relaxed transposition method[29], we solve the second-order adjoint equations, corresponding to the optimal control of quantum stochastic systems in fermion fields, which plays the fundamental roles in the study of the Pointryagin-type maximum principle in quantum stochastic optimal control. The second-order adjoint equation is a backard operator valued quantum stochastic differential equation, which has no definition in the algebra of bounded operators, and the solution derived from the relaxed transposition method makes sense in W*-topology.

math.OC

Essential normality of quotient modules vs. Hilbert-Schmidtness of submodules in $H^2(\mathbb D^2)$

In the present paper, we prove that all the quotient modules in $H^2(\mathbb D^2)$, associated to the finitely generated submodules containing a distinguished homogenous polynomial, are essentially normal, which is the first result on the essential normality of non-algebraic quotient modules in $H^2(\mathbb D^2)$. Moreover, we obtain the equivalence of the essential normality of a quotient module and the Hilbert-Schmidtness of its associated submodule in $H^2(\mathbb D^2)$, in the case that the submodule contains a distinguished homogenous polynomial. As an application, we prove that each finitely generated submodule containing a polynomial is Hilbert-Schmidt, which partially gives an affirmative answer to the conjecture of Yang \cite{Ya3}.

math.FA

Optimal control of quantum system in fermion fields: Pontryagin-type maximum principle(I)

In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical chemistry to multi-dimensional nuclear magnetic resonance experiments. Furthermore, we establish the existence and uniqueness of solutions to backward quantum stochastic differential equations driven by fermion Brownian motion. The application of noncommutative martingale inequalities and the martingale representation theorem enables this achievement.

math.OC

$L^p$-solutions of QSDE driven by Fermion fields with nonlocal conditions under non-Lipschitz coefficients

The main purpose of this paper is to obtain the existence and uniqueness of $L^p$-solution to quantum stochastic differential equation driven by Fermion fields with nonlocal conditions in the case of non-Lipschitz coefficients for $p>2$. The key to our technique is to make use of the Burkholder-Gundy inequality given by Pisier and Xu and Minkowski-type inequality to iterate instead of the fixed point theorem commonly used for nonlocal problems. Moreover, we also obtain the self-adjointness of the $L^p$-solution which is important in the study of optimal control problems.

math.PR

Essentially normal quotient weighted Bergman modules over the bidisk and distinguished varieties

We introduce a Grassmannian structure for a class of quotient Hilbert modules and attack the polydisc version of Arveson-Douglas conjecture associated to distinguished varieties. More interestingly, we obtain an operator-theoretic characterization of distinguished varieties in the bidisk in terms of essential normality of the quotient modules. As an application, we study the K-homology of the boundary of distinguished variety.

math.OA

DSE-GAN: Dynamic Semantic Evolution Generative Adversarial Network for Text-to-Image Generation

Text-to-image generation aims at generating realistic images which are semantically consistent with the given text. Previous works mainly adopt the multi-stage architecture by stacking generator-discriminator pairs to engage multiple adversarial training, where the text semantics used to provide generation guidance remain static across all stages. This work argues that text features at each stage should be adaptively re-composed conditioned on the status of the historical stage (i.e., historical stage's text and image features) to provide diversified and accurate semantic guidance during the coarse-to-fine generation process. We thereby propose a novel Dynamical Semantic Evolution GAN (DSE-GAN) to re-compose each stage's text features under a novel single adversarial multi-stage architecture. Specifically, we design (1) Dynamic Semantic Evolution (DSE) module, which first aggregates historical image features to summarize the generative feedback, and then dynamically selects words required to be re-composed at each stage as well as re-composed them by dynamically enhancing or suppressing different granularity subspace's semantics. (2) Single Adversarial Multi-stage Architecture (SAMA), which extends the previous structure by eliminating complicated multiple adversarial training requirements and therefore allows more stages of text-image interactions, and finally facilitates the DSE module. We conduct comprehensive experiments and show that DSE-GAN achieves 7.48\% and 37.8\% relative FID improvement on two widely used benchmarks, i.e., CUB-200 and MSCOCO, respectively.

cs.CV

Spatial Location Constraint Prototype Loss for Open Set Recognition

One of the challenges in pattern recognition is open set recognition. Compared with closed set recognition, open set recognition needs to reduce not only the empirical risk, but also the open space risk, and the reduction of these two risks corresponds to classifying the known classes and identifying the unknown classes respectively. How to reduce the open space risk is the key of open set recognition. This paper explores the origin of the open space risk by analyzing the distribution of known and unknown classes features. On this basis, the spatial location constraint prototype loss function is proposed to reduce the two risks simultaneously. Extensive experiments on multiple benchmark datasets and many visualization results indicate that our methods is superior to most existing approaches.

cs.CV

Adversarial Motorial Prototype Framework for Open Set Recognition

Open set recognition is designed to identify known classes and to reject unknown classes simultaneously. Specifically, identifying known classes and rejecting unknown classes correspond to reducing the empirical risk and the open space risk, respectively. First, the motorial prototype framework (MPF) is proposed, which classifies known classes according to the prototype classification idea. Moreover, a motorial margin constraint term is added into the loss function of the MPF, which can further improve the clustering compactness of known classes in the feature space to reduce both risks. Second, this paper proposes the adversarial motorial prototype framework (AMPF) based on the MPF. On the one hand, this model can generate adversarial samples and add these samples into the training phase; on the other hand, it can further improve the differential mapping ability of the model to known and unknown classes with the adversarial motion of the margin constraint radius. Finally, this paper proposes an upgraded version of the AMPF, AMPF++, which adds much more generated unknown samples into the training phase. In this paper, a large number of experiments prove that the performance of the proposed models is superior to that of other current works.

cs.CV

Numerics for Stochastic Distributed Parameter Control Systems: a Finite Transposition Method

In this chapter, we present some recent progresses on the numerics for stochastic distributed parameter control systems, based on the \emph{finite transposition method} introduced in our previous works. We first explain how to reduce the numerics of some stochastic control problems in this respect to the numerics of backward stochastic evolution equations. Then we present a method to find finite transposition solutions to such equations. At last, we give an illuminating example.

math.OC

A note on "Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions"

The eigenvalue problem of stochastic Hamiltonian systems with boundary conditions was studied by Peng \cite{peng} in 2000. For one-dimensional case, denoting by $\{λ_n\}_{n=1}^{\infty}$ all the eigenvalues of such an eigenvalue problem, Peng proved that $λ_n\to +\infty$. In this short note, we prove that the growth order of $λ_n$ is the same as $n^2$ as $n\to +\infty$. Apart from the interesting of its own, by this result, the statistic period of solutions of FBSDEs can be estimated directly by corresponding coefficients and time duration.

math.PR