arXiv subjects

Wen Shen

Publications and source records attributed to Wen Shen.

At least 37 records · Page 2Linked to original sources

arXiv2026

Conservation Laws with Discontinuous Gradient-Dependent Flux: the Unstable Case

The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively. We study here the unstable case where $f(u)>g(u)$ for all $u\in {\mathbb R}$. Assuming that both $f$ and $g$ are strictly convex, solutions to the Riemann problem are constructed. Even for a smooth initial data, examples show that the Cauchy problem can have infinitely many solutions. For an initial data which is piecewise monotone, i.e., increasing or decreasing on a finite number of intervals, a solution can be constructed globally in time. It is proved that such solution is unique under the additional requirement that the number of interfaces, where the flux switches between $f$ and $g$, remains as small as possible.

math.AP↗

arXiv2026

ReasonAny: Incorporating Reasoning Capability to Any Model via Simple and Effective Model Merging

Large Reasoning Models (LRMs) with long chain-of-thought reasoning have recently achieved remarkable success. Yet, equipping domain-specialized models with such reasoning capabilities, referred to as "Reasoning + X", remains a significant challenge. While model merging offers a promising training-free solution, existing methods often suffer from a destructive performance collapse: existing methods tend to both weaken reasoning depth and compromise domain-specific utility. Interestingly, we identify a counter-intuitive phenomenon underlying this failure: reasoning ability predominantly resides in parameter regions with low gradient sensitivity, contrary to the common assumption that domain capabilities correspond to high-magnitude parameters. Motivated by this insight, we propose ReasonAny, a novel merging framework that resolves the reasoning-domain performance collapse through Contrastive Gradient Identification. Experiments across safety, biomedicine, and finance domains show that ReasonAny effectively synthesizes "Reasoning + X" capabilities, significantly outperforming state-of-the-art baselines while retaining robust reasoning performance.

cs.CL↗

arXiv2025

The Interaction Bottleneck of Deep Neural Networks: Discovery, Proof, and Modulation

Understanding what kinds of cooperative structures deep neural networks (DNNs) can represent remains a fundamental yet insufficiently understood problem. In this work, we treat interactions as the fundamental units of such structure and investigate a largely unexplored question: how DNNs encode interactions under different levels of contextual complexity, and how these microscopic interaction patterns shape macroscopic representation capacity. To quantify this complexity, we use multi-order interactions [57], where each order reflects the amount of contextual information required to evaluate the joint interaction utility of a variable pair. This formulation enables a stratified analysis of cooperative patterns learned by DNNs. Building on this formulation, we develop a comprehensive study of interaction structure in DNNs. (i) We empirically discover a universal interaction bottleneck: across architectures and tasks, DNNs easily learn low-order and high-order interactions but consistently under-represent mid-order ones. (ii) We theoretically explain this bottleneck by proving that mid-order interactions incur the highest contextual variability, yielding large gradient variance and making them intrinsically difficult to learn. (iii) We further modulate the bottleneck by introducing losses that steer models toward emphasizing interactions of selected orders. Finally, we connect microscopic interaction structures with macroscopic representational behavior: low-order-emphasized models exhibit stronger generalization and robustness, whereas high-order-emphasized models demonstrate greater structural modeling and fitting capability. Together, these results uncover an inherent representational bias in modern DNNs and establish interaction order as a powerful lens for interpreting and guiding deep representations.

cs.LG↗

arXiv2025

FOLK: Fast Open-Vocabulary 3D Instance Segmentation via Label-guided Knowledge Distillation

Open-vocabulary 3D instance segmentation seeks to segment and classify instances beyond the annotated label space. Existing methods typically map 3D instances to 2D RGB-D images, and then employ vision-language models (VLMs) for classification. However, such a mapping strategy usually introduces noise from 2D occlusions and incurs substantial computational and memory costs during inference, slowing down the inference speed. To address the above problems, we propose a Fast Open-vocabulary 3D instance segmentation method via Label-guided Knowledge distillation (FOLK). Our core idea is to design a teacher model that extracts high-quality instance embeddings and distills its open-vocabulary knowledge into a 3D student model. In this way, during inference, the distilled 3D model can directly classify instances from the 3D point cloud, avoiding noise caused by occlusions and significantly accelerating the inference process. Specifically, we first design a teacher model to generate a 2D CLIP embedding for each 3D instance, incorporating both visibility and viewpoint diversity, which serves as the learning target for distillation. We then develop a 3D student model that directly produces a 3D embedding for each 3D instance. During training, we propose a label-guided distillation algorithm to distill open-vocabulary knowledge from label-consistent 2D embeddings into the student model. FOLK conducted experiments on the ScanNet200 and Replica datasets, achieving state-of-the-art performance on the ScanNet200 dataset with an AP50 score of 35.7, while running approximately 6.0x to 152.2x faster than previous methods. All codes will be released after the paper is accepted.

cs.CV↗

arXiv2025

Classification for smooth manifolds looking like $\mathbb{CP}^3\times S^7$

In this paper, we classify simply connected closed smooth $13$-dimensional manifolds whose cohomology ring is isomorphic to that of $\mb{CP}^3\times S^7$, up to diffeomorphism, homeomorphism, and homotopy equivalence. Furthermore, if such a manifold satisfies certain conditions, either itself or its connected sum with an exotic $13$-sphere $Σ^{13}$ admits a Riemannian metric of non-negative sectional curvature. As an additional application of our classification, we classify the diagonal $S^1$-actions on $S^7\times S^7$.

math.AT↗

arXiv2025

A Multimodal Cross-View Model for Predicting Postoperative Neck Pain in Cervical Spondylosis Patients

Neck pain is the primary symptom of cervical spondylosis, yet its underlying mechanisms remain unclear, leading to uncertain treatment outcomes. To address the challenges of multimodal feature fusion caused by imaging differences and spatial mismatches, this paper proposes an Adaptive Bidirectional Pyramid Difference Convolution (ABPDC) module that facilitates multimodal integration by exploiting the advantages of difference convolution in texture extraction and grayscale invariance, and a Feature Pyramid Registration Auxiliary Network (FPRAN) to mitigate structural misalignment. Experiments on the MMCSD dataset demonstrate that the proposed model achieves superior prediction accuracy of postoperative neck pain recovery compared with existing methods, and ablation studies further confirm its effectiveness.

cs.CV↗

arXiv2025

Non-negative curvature on certain product manifolds

Let $G/H$ be a closed, simply connected homogeneous manifold. Suppose every stable class of real vector bundles over $G/H$ contains a homogeneous bundle. Then, for any closed, simply connected smooth manifold $M$ homotopy equivalent to $G/H$, there exists $n>\mathrm{dim}(M)$ such that the product manifold $M\times S^{n}$ admits a metric with non-negative sectional curvature. Many homogeneous manifolds satisfy this assumption, including simply connected compact rank-one symmetric spaces, and among others.

math.DG↗

arXiv2025

Manifold structures on highly connected Poincaré complexes

This paper constructs numerous examples of highly connected Poincaré complexes, each homotopy equivalent to a topological manifold yet not homotopy equivalent to any smooth manifold. Furthermore, we determine the homotopy type of any closed $2k$-connected framed $(4k+2)$-manifold with Kervaire invariant one for $k=7,15,31$.

math.AT↗

arXiv2025

M3-AGIQA: Multimodal, Multi-Round, Multi-Aspect AI-Generated Image Quality Assessment

The rapid advancement of AI-generated image (AIGI) models presents new challenges for evaluating image quality, particularly across three aspects: perceptual quality, prompt correspondence, and authenticity. To address these challenges, we introduce M3-AGIQA, a comprehensive framework that leverages Multimodal Large Language Models (MLLMs) to enable more human-aligned, holistic evaluation of AI-generated images across both visual and textual domains. Besides, our framework features a structured multi-round evaluation process, generating and analyzing intermediate image descriptions to provide deeper insight into these three aspects. By aligning model outputs more closely with human judgment, M3-AGIQA delivers robust and interpretable quality scores. Extensive experiments on multiple benchmarks demonstrate that our method achieves state-of-the-art performance on tested datasets and aspects, and exhibits strong generalizability in most cross-dataset settings. Code is available at https://github.com/strawhatboy/M3-AGIQA.

cs.CV↗

arXiv2025

EfficientHuman: Efficient Training and Reconstruction of Moving Human using Articulated 2D Gaussian

3D Gaussian Splatting (3DGS) has been recognized as a pioneering technique in scene reconstruction and novel view synthesis. Recent work on reconstructing the 3D human body using 3DGS attempts to leverage prior information on human pose to enhance rendering quality and improve training speed. However, it struggles to effectively fit dynamic surface planes due to multi-view inconsistency and redundant Gaussians. This inconsistency arises because Gaussian ellipsoids cannot accurately represent the surfaces of dynamic objects, which hinders the rapid reconstruction of the dynamic human body. Meanwhile, the prevalence of redundant Gaussians means that the training time of these works is still not ideal for quickly fitting a dynamic human body. To address these, we propose EfficientHuman, a model that quickly accomplishes the dynamic reconstruction of the human body using Articulated 2D Gaussian while ensuring high rendering quality. The key innovation involves encoding Gaussian splats as Articulated 2D Gaussian surfels in canonical space and then transforming them to pose space via Linear Blend Skinning (LBS) to achieve efficient pose transformations. Unlike 3D Gaussians, Articulated 2D Gaussian surfels can quickly conform to the dynamic human body while ensuring view-consistent geometries. Additionally, we introduce a pose calibration module and an LBS optimization module to achieve precise fitting of dynamic human poses, enhancing the model's performance. Extensive experiments on the ZJU-MoCap dataset demonstrate that EfficientHuman achieves rapid 3D dynamic human reconstruction in less than a minute on average, which is 20 seconds faster than the current state-of-the-art method, while also reducing the number of redundant Gaussians.

cs.CV↗

arXiv2025

On spherical fibrations and Poincare complexes

In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\mm{TOP}$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar$\mm{\acute{e}}$ complex is of the homotopy type of a topological manifold. Moreover, we present the classification for some highly connected manifolds by the homotopy types of highly connected Poincar$\mm{\acute{e}}$ complexes.

math.GT↗

arXiv2025

SeLIP: Similarity Enhanced Contrastive Language Image Pretraining for Multi-modal Head MRI

Despite that deep learning (DL) methods have presented tremendous potential in many medical image analysis tasks, the practical applications of medical DL models are limited due to the lack of enough data samples with manual annotations. By noting that the clinical radiology examinations are associated with radiology reports that describe the images, we propose to develop a foundation model for multi-model head MRI by using contrastive learning on the images and the corresponding radiology findings. In particular, a contrastive learning framework is proposed, where a mixed syntax and semantic similarity matching metric is integrated to reduce the thirst of extreme large dataset in conventional contrastive learning framework. Our proposed similarity enhanced contrastive language image pretraining (SeLIP) is able to effectively extract more useful features. Experiments revealed that our proposed SeLIP performs well in many downstream tasks including image-text retrieval task, classification task, and image segmentation, which highlights the importance of considering the similarities among texts describing different images in developing medical image foundation models.

cs.CV↗

arXiv2025

On the topology and geometry of certain $13$-manifolds

This paper gives the classifications of certain manifolds $\mathcal{M}$ of dimension $13$ up to diffeomorphism, homeomorphism, and homotopy equivalence, whose cohomology rings are isomorphic to $H^\ast(\mathrm{CP}^3\times S^7;\mathbb{Z})$. Moreover, we prove that either $\mathcal{M}$ or $\mathcal{M}\#Σ^{13}$ admits a metric of non-negative sectional curvature where $Σ^{13}$ is a certain exotic sphere of dimension 13.

math.GT↗

arXiv2024

Conservation Laws with Discontinuous Gradient-Dependent Flux: the Stable Case

The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative, respectively. We study here the stable case where $f(u)<g(u)$ for all $u\in {\mathbb R}$, with $f,g$ smooth but possibly not convex. A front tracking algorithm is introduced, proving that piecewise constant approximations converge to the trajectories of a contractive semigroup on $\mathbf{L}^1({\mathbb R})$. In the spatially periodic case, we prove that semigroup trajectories coincide with the unique limits of a suitable class of vanishing viscosity approximations.

math.AP↗

arXiv2024

Topological classification of Bazaikin spaces

Geometry of manifolds with positive sectional curvature has been a central object dates back to the beginning of Riemannian geometry. Up to homeomorphism, there are only finitely many examples of simply connected positively curved manifolds in all dimensions except in dimension 7 and 13, namely, the Aloff-Wallach spaces and the Eschenburg spaces in dimension 7, and the Bazaikin spaces in dimension 13. The topological classification modelled on the 7-dimensional examples has been carried out by Kreck-Stolz which leads to a complete topological classification for the Aloff-Wallach spaces. The main goal of this paper is to provide the topological classification of 13-dimensional manifolds modelled on the Bazaikin spaces.

math.DG↗

arXiv2024

Explaining Generalization Power of a DNN Using Interactive Concepts

This paper explains the generalization power of a deep neural network (DNN) from the perspective of interactions. Although there is no universally accepted definition of the concepts encoded by a DNN, the sparsity of interactions in a DNN has been proved, i.e., the output score of a DNN can be well explained by a small number of interactions between input variables. In this way, to some extent, we can consider such interactions as interactive concepts encoded by the DNN. Therefore, in this paper, we derive an analytic explanation of inconsistency of concepts of different complexities. This may shed new lights on using the generalization power of concepts to explain the generalization power of the entire DNN. Besides, we discover that the DNN with stronger generalization power usually learns simple concepts more quickly and encodes fewer complex concepts. We also discover the detouring dynamics of learning complex concepts, which explains both the high learning difficulty and the low generalization power of complex concepts. The code will be released when the paper is accepted.

cs.LG↗

arXiv2024

Where We Have Arrived in Proving the Emergence of Sparse Symbolic Concepts in AI Models

This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i) The high-order derivatives of the network output with respect to the input variables are all zero. (ii) The DNN can be used on occluded samples and when the input sample is less occluded, the DNN will yield higher confidence. (iii) The confidence of the DNN does not significantly degrade on occluded samples. These conditions are quite common, and we prove that under these conditions, the DNN will only encode a relatively small number of sparse interactions between input variables. Moreover, we can consider such interactions as symbolic primitive inference patterns encoded by a DNN, because we show that inference scores of the DNN on an exponentially large number of randomly masked samples can always be well mimicked by numerical effects of just a few interactions.

cs.LG↗

arXiv2024

PL cobordism and classification of PL manifolds

In this paper, we present more conclusions for $C^\ast(\mathrm{PL})$ and oriented PL cobordism, and compute the string PL bordism groups of certain dimensions. Then, we apply these results to classify certain PL manifolds of dimensions $10$ and $13$.

math.AT↗