arXiv subjects

Jianwen Zhang

Publications and source records attributed to Jianwen Zhang.

At least 19 recordsLinked to original sources

arXiv2026

The combined limits of large bulk viscosity and small angular viscosity for the 2D compressible micropolar fluid equations

This paper is concerned with the combined limits of large bulk viscosity and small angular viscosity for the two-dimensional compressible micropolar fluid equations. We first establish the global well-posedness of strong solutions to the Cauchy problem with large bulk viscosity, when the initial velocity is well-prepared in the sense that $\sqrtν\|{\rm div} u_0\|_{L^2}$ is uniformly bounded. The global a priori estimates obtained are uniform with respect to both the bulk viscosity $ν$ and the angular viscosity $\varepsilon$. Based on these uniform estimates, we then justify the combined limits as $ν\to\infty$ and $\varepsilon\to0$, and show that the solutions of the compressible micropolar system converge to those of the viscous and non-diffusive incompressible micropolar system. The convergence rates for the incompressible limit and the vanishing angular viscosity limit are also derived. In particular, the convergence rate for the incompressible limit is shown to be of order $ν^{-1/4}$ in general, and can be improved to $ν^{-1/2}$ under an additional decay condition on the initial density. Compared with previous works, the vanishing angular viscosity limit is established without the extra technical assumption $\lim_{\varepsilon\to0+}ζ/\varepsilon^α<\infty$ for some $1/2\leq α<\infty$, which extends the relevant results from the incompressible case to the compressible setting. As a by-product, the global regularity of large solutions for the 2D compressible micropolar equations with/without angular viscosity is obtained, provided the bulk viscosity is large enough.

math.AP↗

arXiv2026

NutVLM: A Self-Adaptive Defense Framework against Full-Dimension Attacks for Vision Language Models in Autonomous Driving

Vision Language Models (VLMs) have advanced perception in autonomous driving (AD), but they remain vulnerable to adversarial threats. These risks range from localized physical patches to imperceptible global perturbations. Existing defense methods for VLMs remain limited and often fail to reconcile robustness with clean-sample performance. To bridge these gaps, we propose NutVLM, a comprehensive self-adaptive defense framework designed to secure the entire perception-decision lifecycle. Specifically, we first employ NutNet++ as a sentinel, which is a unified detection-purification mechanism. It identifies benign samples, local patches, and global perturbations through three-way classification. Subsequently, localized threats are purified via efficient grayscale masking, while global perturbations trigger Expert-guided Adversarial Prompt Tuning (EAPT). Instead of the costly parameter updates of full-model fine-tuning, EAPT generates "corrective driving prompts" via gradient-based latent optimization and discrete projection. These prompts refocus the VLM's attention without requiring exhaustive full-model retraining. Evaluated on the Dolphins benchmark, our NutVLM yields a 4.89% improvement in overall metrics (e.g., Accuracy, Language Score, and GPT Score). These results validate NutVLM as a scalable security solution for intelligent transportation. Our code is available at https://github.com/PXX/NutVLM.

cs.CV↗

arXiv2025

Global regularity and incompressible limit of 2D compressible Navier-Stokes equations with large bulk viscosity

In this paper, we study the global regularity of large solutions with vacuum to the two-dimensional compressible Navier-Stokes equations on $\mathbb{T}^{2}=\mathbb{R}^{2}/\mathbb{Z}^{2}$, when the volume (bulk) viscosity coefficient $ν$ is sufficiently large. It firstly fixes a flaw in \cite[Proposition 3.3]{Danchin2023}, which concerns the $ν$-independent global $t$-weighted estimates of the solutions. Amending the proof requires non-trivially mathematical analysis. As a by-product, the incompressible limit with an explicit rate of convergence is shown, when the volume viscosity tends to infinity. In contrast to \cite[Theorem 1.3]{Danchin2019} and \cite[Corollary 1.1]{DM2017} where vacuum was excluded, the convergence rate of the incompressible limit is obtained for the global solutions with vacuum, based on some $t$-growth and singular $t$-weighted estimates.

math.AP↗

arXiv2025

Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs

We introduce Phi-4-Mini and Phi-4-Multimodal, compact yet highly capable language and multimodal models. Phi-4-Mini is a 3.8-billion-parameter language model trained on high-quality web and synthetic data, significantly outperforming recent open-source models of similar size and matching the performance of models twice its size on math and coding tasks requiring complex reasoning. This achievement is driven by a carefully curated synthetic data recipe emphasizing high-quality math and coding datasets. Compared to its predecessor, Phi-3.5-Mini, Phi-4-Mini features an expanded vocabulary size of 200K tokens to better support multilingual applications, as well as group query attention for more efficient long-sequence generation. Phi-4-Multimodal is a multimodal model that integrates text, vision, and speech/audio input modalities into a single model. Its novel modality extension approach leverages LoRA adapters and modality-specific routers to allow multiple inference modes combining various modalities without interference. For example, it now ranks first in the OpenASR leaderboard to date, although the LoRA component of the speech/audio modality has just 460 million parameters. Phi-4-Multimodal supports scenarios involving (vision + language), (vision + speech), and (speech/audio) inputs, outperforming larger vision-language and speech-language models on a wide range of tasks. Additionally, we experiment to further train Phi-4-Mini to enhance its reasoning capabilities. Despite its compact 3.8-billion-parameter size, this experimental version achieves reasoning performance on par with or surpassing significantly larger models, including DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B.

cs.CL↗

arXiv2024

Phi-3 Safety Post-Training: Aligning Language Models with a "Break-Fix" Cycle

Recent innovations in language model training have demonstrated that it is possible to create highly performant models that are small enough to run on a smartphone. As these models are deployed in an increasing number of domains, it is critical to ensure that they are aligned with human preferences and safety considerations. In this report, we present our methodology for safety aligning the Phi-3 series of language models. We utilized a "break-fix" cycle, performing multiple rounds of dataset curation, safety post-training, benchmarking, red teaming, and vulnerability identification to cover a variety of harm areas in both single and multi-turn scenarios. Our results indicate that this approach iteratively improved the performance of the Phi-3 models across a wide range of responsible AI benchmarks. Finally, we include additional red teaming strategies and evaluations that were used to test the safety behavior of Phi-3.5-mini and Phi-3.5-MoE, which were optimized for multilingual capabilities.

cs.CL↗

arXiv2024

Stability and Sharp Decay Estimates for 3D MHD Equations with Only Vertical Dissipation Near a Background Magnetic Field

This paper is concerned with the stability and large-time behavior of 3D incompressible MHD equations with only vertical dissipation near a background magnetic field. By making full use of the dissipation generated by the background magnetic field, we first establish the global stability of the solutions in $H^3$-norm. Then, the optimal decay rates of the solutions are obtained, which are consistent with the 2D classical heat equation. Moreover, some enhanced decay rates of $(u_1,b_1)$ are also achieved. In other words, the decay estimates of the second or third component of velocity/magnetic field coincide with those of 2D heat kernel, while the first component behaves like the 3D heat kernel. This is mainly due to the divergence-free condition and the anisotropic structure. The results obtained improve the previous ones due to Lin-Wu-Zhu [24,25].

math.AP↗

arXiv2021

Well-Posedness and Exponential Decay for the Navier-Stokes Equations of Viscous Compressible Heat-Conductive Fluids with Vacuum

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those proposed by Cho-Kim \cite{CK2006}, we first prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is regular. We also establish the global well-posedness of classical solutions with large oscillations and vacuum in the case when the initial total energy is suitably small. The exponential decay estimates of the global solutions are obtained.

math.AP↗

arXiv2020

Hybrid Ranking Network for Text-to-SQL

In this paper, we study how to leverage pre-trained language models in Text-to-SQL. We argue that previous approaches under utilize the base language models by concatenating all columns together with the NL question and feeding them into the base language model in the encoding stage. We propose a neat approach called Hybrid Ranking Network (HydraNet) which breaks down the problem into column-wise ranking and decoding and finally assembles the column-wise outputs into a SQL query by straightforward rules. In this approach, the encoder is given a NL question and one individual column, which perfectly aligns with the original tasks BERT/RoBERTa is trained on, and hence we avoid any ad-hoc pooling or additional encoding layers which are necessary in prior approaches. Experiments on the WikiSQL dataset show that the proposed approach is very effective, achieving the top place on the leaderboard.

cs.CL↗

arXiv2020

Vanishing shear viscosity limit and boundary layer for the one-dimensional full compressible MHD equations with large data

This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The vanishing shear viscosity limit is justified and the convergence rates are obtained. More important, to capture the behavior of the solutions at vanishing shear viscosity, both the boundary-layer thickness and the boundary-layer solution are discussed. As by-products, the global well-posedness of strong solutions with large data is established. The proofs are based on the global (uniform) estimates which are achieved by making a full use of the "effective viscous flux", the material derivatives and the structure of the one-dimensional equations.

math.AP↗

arXiv2020

Vanishing shear viscosity limit and boundary layer for the one-dimensional full compressible MHD equations with large data

This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The vanishing shear viscosity limit is justified and the convergence rates are obtained. To capture the behavior of the solutions at small shear viscosity, we also discuss the boundary-layer thickness and the boundary-layer solution. As by-products, the global well-posedness of strong solutions with large data is established. The proofs are based on the global (uniform) estimates which are achieved by making a full use of the "effective viscous flux", the material derivatives and the structure of the one-dimensional equations. Moreover, the lower positive bound of the density is obtained by using some new ideas, which are rather different from those in the existing literature.

math.AP↗

arXiv2019

Relation Discovery with Out-of-Relation Knowledge Base as Supervision

Unsupervised relation discovery aims to discover new relations from a given text corpus without annotated data. However, it does not consider existing human annotated knowledge bases even when they are relevant to the relations to be discovered. In this paper, we study the problem of how to use out-of-relation knowledge bases to supervise the discovery of unseen relations, where out-of-relation means that relations to discover from the text corpus and those in knowledge bases are not overlapped. We construct a set of constraints between entity pairs based on the knowledge base embedding and then incorporate constraints into the relation discovery by a variational auto-encoder based algorithm. Experiments show that our new approach can improve the state-of-the-art relation discovery performance by a large margin.

cs.CL↗

arXiv2017

On the infinite Prandtl number limit in two-dimensional magneto-convection

In this paper, the infinite limit of the Prandtl number is justified for the two-dimensional incompressible magneto-convection, which describes the nonlinear interaction between the Rayleigh-B$\rm\acute{e}$nard convection and an externally magnetic field. Both the convergence rates and the thickness of initial layer are obtained. Moreover, based on the method of formal asymptotic expansions, an effective dynamics is constructed to simulate the motion within the initial layer.

math.AP↗

arXiv2017

Blind Signal Detection in Massive MIMO: Exploiting the Channel Sparsity

In practical massive MIMO systems, a substantial portion of system resources are consumed to acquire channel state information (CSI), leading to a drastically lower system capacity compared with the ideal case where perfect CSI is available. In this paper, we show that the overhead for CSI acquisition can be largely compensated by the potential gain due to the sparsity of the massive MIMO channel in a certain transformed domain. To this end, we propose a novel blind detection scheme that simultaneously estimates the channel and data by factorizing the received signal matrix. We show that by exploiting the channel sparsity, our proposed scheme can achieve a DoF very close to the ideal case, provided that the channel is sufficiently sparse. Specifically, the achievable degree of freedom (DoF) has a fractional gap of only $1/T$ from the ideal DoF, where $T$ is the channel coherence time. This is a remarkable advance for understanding the performance limit of the massive MIMO system. We further show that the performance advantage of our proposed scheme in the asymptotic SNR regime carries over to the practical SNR regime. Numerical results demonstrate that our proposed scheme significantly outperforms its counterpart schemes in the practical SNR regime under various system configurations.

cs.IT↗

arXiv2016

MIMO Multiway Distributed-Relay Channel with Full Data Exchange: An Achievable Rate Perspective

We consider efficient communications over the multiple-input multiple-output (MIMO) multiway distributed relay channel (MDRC) with full data exchange, where each user, equipped with multiple antennas, broadcasts its message to all the other users via the help of a number of distributive relays. We propose a physical-layer network coding (PNC) based scheme involving linear precoding for channel alignment nested lattice coding for PNC, and lattice-based precoding for interference mitigation, We show that, with the proposed scheme, distributed relaying achieves the same sum-rate as cooperative relaying in the high SNR regime. We also show that the proposed scheme achieve the asymptotic sum capacity of the MIMO MDRC within a constant gap at high SNR. Numerical results demonstrate that the proposed scheme considerably outperforms the existing schemes including decode-and-forward and amplify-and-forward.

cs.IT↗

arXiv2016

Explicit evaluation of quadratic Euler sums

In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic Euler sums through Riemann zeta function and linear sums. The given representations are new.

math.NT↗

arXiv2016

Locally Orthogonal Training Design for Cloud-RANs Based on Graph Coloring

We consider training-based channel estimation for a cloud radio access network (CRAN), in which a large amount of remote radio heads (RRHs) and users are randomly scattered over the service area. In this model, assigning orthogonal training sequences to all users will incur a substantial overhead to the overall network, and is even impossible when the number of users is large. Therefore, in this paper, we introduce the notion of local orthogonality, under which the training sequence of a user is orthogonal to those of the other users in its neighborhood. We model the design of locally orthogonal training sequences as a graph coloring problem. Then, based on the theory of random geometric graph, we show that the minimum training length scales in the order of $\ln K$, where $K$ is the number of users covered by a CRAN. This indicates that the proposed training design yields a scalable solution to sustain the need of large-scale cooperation in CRANs. Numerical results show that the proposed scheme outperforms other reference schemes.

cs.IT↗

arXiv2015

Global solvability, non-resistive limit and magnetic boundary layer of the compressible heat-conductive MHD equations

In general, the resistivity is inversely proportional to the electrical conductivity, and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, we first establish the global well-posedness of strong solution to an initial-boundary value problem of the one-dimensional compressible, viscous, heat-conductive, non-resistive MHD equations with general heat-conductivity coefficient and large data. Then, the non-resistive limit is justified and the convergence rates are obtained, provided the heat-conductivity satisfies some growth condition. Finally, we discuss the thickness of the magnetic boundary layer, which is particularly in consistent with the Stokes-Blasius law in the classical theory of laminar boundary layer.

math.AP↗

arXiv2015

On the vanishing resistivity limit and the magnetic boundary-layers for one-dimensional compressible magnetohydrodynamics

We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic viscous and non-resistive magnetohydrodynamic flows. The global well-posedness of strong solutions with general large data is established. Moreover, the vanishing resistivity limit is justified and the thickness of magnetic boundary layers is analyzed. The proofs of these results are based on a full use of the so-called "effective viscous flux", the material derivative and the structure of the equations.

math.AP↗