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Shu Shen

Publications and source records attributed to Shu Shen.

18 recordsLinked to original sources
arXiv2026

Test-time Adaptive Hierarchical Co-enhanced Denoising Network for Reliable Multimodal Classification

Reliable learning of multimodal data (e.g., multi-omics) is a widely concerning issue, especially in safety-critical applications such as medical diagnosis. However, low-quality data induced by multimodal noise poses a major challenge in this domain, causing existing methods to suffer from two key limitations. First, they struggle to handle heterogeneous data noise, hindering robust multimodal representation learning. Second, they exhibit limited adaptability and generalization when encountering previously unseen noise. To address these issues, we propose Test-time Adaptive Hierarchical Co-enhanced Denoising Network (TAHCD). On one hand, TAHCD introduces the Adaptive Stable Subspace Alignment and Sample-Adaptive Confidence Alignment to reliably remove heterogeneous noise. They account for noise at both global and instance levels and enable jointly removal of modality-specific and cross-modality noise, achieving robust learning. On the other hand, TAHCD introduces Test-Time Cooperative Enhancement, which adaptively updates the model in response to input noise in a label-free manner, thus improving generalization. This is achieved by collaboratively enhancing the joint removal process of modality-specific and cross-modality noise across global and instance levels according to sample noise. Experiments on multiple benchmarks demonstrate that the proposed method achieves superior classification performance, robustness, and generalization compared with state-of-the-art reliable multimodal learning approaches.

cs.CV↗
arXiv2025

Grauert's direct image theorem via superconnections and desingularizations

We give a new differential-geometric proof of Grauert's theorem on the coherence of the higher direct image of a coherent sheaf under a proper holomorphic morphism between complex analytic spaces. In the smooth case, our approach is based on the antiholomorphic superconnection introduced by Block and further developed by Bismut-Shen-Wei. The required finiteness results follow from elliptic theory. In the singular case, we reduce the problem to the smooth setting using Hironaka's desingularization.

math.AG↗
arXiv2025

AIM: Adaptive Intra-Network Modulation for Balanced Multimodal Learning

Multimodal learning has significantly enhanced machine learning performance but still faces numerous challenges and limitations. Imbalanced multimodal learning is one of the problems extensively studied in recent works and is typically mitigated by modulating the learning of each modality. However, we find that these methods typically hinder the dominant modality's learning to promote weaker modalities, which affects overall multimodal performance. We analyze the cause of this issue and highlight a commonly overlooked problem: optimization bias within networks. To address this, we propose Adaptive Intra-Network Modulation (AIM) to improve balanced modality learning. AIM accounts for differences in optimization state across parameters and depths within the network during modulation, achieving balanced multimodal learning without hindering either dominant or weak modalities for the first time. Specifically, AIM decouples the dominant modality's under-optimized parameters into Auxiliary Blocks and encourages reliance on these performance-degraded blocks for joint training with weaker modalities. This approach effectively prevents suppression of weaker modalities while enabling targeted optimization of under-optimized parameters to improve the dominant modality. Additionally, AIM assesses modality imbalance level across network depths and adaptively adjusts modulation strength at each depth. Experimental results demonstrate that AIM outperforms state-of-the-art imbalanced modality learning methods across multiple benchmarks and exhibits strong generalizability across different backbones, fusion strategies, and optimizers.

cs.CV↗
arXiv2025

Heat kernel, large-time behavior, and representation theory

Given a real reductive group $G$, the purpose of this paper is to show an asymptotic formula of the large-time behavior of the $G$-trace of the heat operator on the associated symmetric spaces. Together with Carmona's proof on Vogan's lambda map, our results provide a geometric counterpart of Vogan's minimal $K$-type theory.

math.DG↗
arXiv2025

Reliable Multimodal Learning Via Multi-Level Adaptive DeConfusion

Multimodal learning enhances the performance of various machine learning tasks by leveraging complementary information across different modalities. However, existing methods often learn multimodal representations that retain substantial inter-class confusion, making it difficult to achieve high-confidence predictions, particularly in real-world scenarios with low-quality or noisy data. To address this challenge, we propose Multi-Level Adaptive DeConfusion (MLAD), which eliminates inter-class confusion in multimodal data at both global and sample levels, significantly enhancing the classification reliability of multimodal models. Specifically, MLAD first learns class-wise latent distributions with global-level confusion removed via dynamic-exit modality encoders that adapt to the varying discrimination difficulty of each class and a cross-class residual reconstruction mechanism. Subsequently, MLAD further removes sample-specific confusion through sample-adaptive cross-modality rectification guided by confusion-free modality priors. These priors are constructed from low-confusion modality features, identified by evaluating feature confusion using the learned class-wise latent distributions and selecting those with low confusion via a Gaussian mixture model. Experiments demonstrate that MLAD outperforms state-of-the-art methods across multiple benchmarks and exhibits superior reliability.

cs.CV↗
arXiv2025

Geometric Zabrodin-Wiegmann conjecture for integer Quantum Hall states

The purpose of this article is to show a geometric version of Zabrodin-Wiegmann conjecture for an integer Quantum Hall state. Given an effective reduced divisor on a compact connected Riemann surface, using the canonical holomorphic section of the associated canonical line bundle as well as certain initial data and local normalisation data, we construct a canonical non-zero element in the determinant line of the cohomology of the $p$-tensor power of the line bundle. When endowed with proper metric data, the square of the $ L^{2} $-norm of our canonical element is the partition function associated to an integer Quantum Hall state. We establish an asymptotic expansion for the logarithm of the partition function when $ p\to +\infty$. The constant term of this expansion includes the holomorphic analytic torsion and matches a geometric version of Zabrodin-Wiegmann's prediction. Our proof relies on Bismut-Lebeau's embedding formula for the Quillen metrics, Bismut-Vasserot and Finski's asymptotic expansion for the analytic torsion associated to the higher tensor product of a positive Hermitian holomorphic line bundle.

math.DG↗
arXiv2024

Multi-QuAD: Multi-Level Quality-Adaptive Dynamic Network for Reliable Multimodal Classification

Multimodal machine learning has achieved remarkable progress in many scenarios, but its reliability is undermined by varying sample quality. This paper finds that existing reliable multimodal classification methods not only fail to provide robust estimation of data quality, but also lack dynamic networks for sample-specific depth and parameters to achieve reliable inference. To this end, a novel framework for multimodal reliable classification termed \textit{Multi-level Quality-Adaptive Dynamic multimodal network} (Multi-QuAD) is proposed. Multi-QuAD first adopts a novel approach based on noise-free prototypes and a classifier-free design to reliably estimate the quality of each sample at both modality and feature levels. It then achieves sample-specific network depth via the \textbf{\textit{Global Confidence Normalized Depth (GCND)}} mechanism. By normalizing depth across modalities and samples, \textit{\textbf{GCND}} effectively mitigates the impact of challenging modality inputs on dynamic depth reliability. Furthermore, Multi-QuAD provides sample-adaptive network parameters via the \textbf{\textit{Layer-wise Greedy Parameter (LGP)}} mechanism driven by feature-level quality. The cross-modality layer-wise greedy strategy in \textbf{\textit{LGP}} designs a reliable parameter prediction paradigm for multimodal networks with variable architecture for the first time. Experiments conducted on four datasets demonstrate that Multi-QuAD significantly outperforms state-of-the-art methods in classification performance and reliability, exhibiting strong adaptability to data with diverse quality.

cs.CV↗
arXiv2024

Anosov vector fields and Fried sections

The purpose of this paper is to prove that if $Y$ is a compact manifold, if $Z$ is an Anosov vector field on $Y$, and if $F$ is a flat vector bundle, there is a corresponding canonical nonzero section $\tau_{\nu}\left(i_{Z}\right)$ of the determinant line $\nu=\det H\left(Y,F\right)$. In families, this section is $C^{1}$ with respect to the canonical smooth structure on $\nu$. When $F$ is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on $\nu$.

math.DG↗
arXiv2021

Bismut hypoelliptic Laplacians for manifolds with boundaries

Boundary conditions for Bismut's hypoelliptic Laplacian which naturally correspond to Dirichlet and Neumann boundary conditions for Hodge Laplacians are considered. Those are related with specific boundary conditions for the differential and its various adjoints. Once the closed realizations of those operators are well understood, the commutation of the differential with the resolvent of the hypoelliptic Laplacian is checked with other properties like the PT-symmetry, which are important for the spectral analysis.

math.AP↗
arXiv2021

Dynamical Zeta Functions in the Nonorientable Case

We use a simple argument to extend the microlocal proofs of meromorphicity of dynamical zeta functions to the nonorientable case. In the special case of geodesic flow on a connected non-orientable negatively curved closed surface, we compute the order of vanishing of the zeta function at the zero point to be the first Betti number of the surface.

math.DG↗
arXiv2021

Coherent sheaves, superconnections, and RRG

Given a compact complex manifold, the purpose of this paper is to construct the Chern character for coherent sheaves with values in Bott-Chern cohomology, and to prove a corresponding Riemann-Roch-Grothendieck formula. Our paper is based on a fundamental construction of Block.

math.AG↗
arXiv2021

Morse-Smale flow, Milnor metric, and dynamical zeta function

We introduce a Milnor metric on the determinant line of the cohomology of the underlying closed manifold with coefficients in a flat vector bundle, by means of interactions between the fixed points and the closed orbits of a Morse-Smale flow. This allows us to generalise the notion of the absolute value at zero point of the Ruelle dynamical zeta function, even in the case where this value is not well defined in the classical sense. We give a formula relating the Milnor metric and the Ray-Singer metric. An essential ingredient of our proof is Bismut-Zhang's Theorem.

math.DG↗
arXiv2020

Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists

We show an equality between the analytic torsion and the absolute value at the zero point of the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises author's previous result for unitarily flat vector bundles, and the results of Bröcker, Müller, and Wotzke on closed hyperbolic manifolds.

math.DG↗
arXiv2020

Flat vector bundles and analytic torsion on orbifolds

This article is devoted to a study of flat orbifold vector bundles. We construct a bijection between the isomorphic classes of proper flat orbifold vector bundles and the equivalence classes of representations of the orbifold fundamental groups of base orbifolds. We establish a Bismut-Zhang like anomaly formula for the Ray-Singer metric on the determine line of the cohomology of a compact orbifold with coefficients in an orbifold flat vector bundle. We show that the analytic torsion of an acyclic unitary flat orbifold vector bundle is equal to the value at zero of a dynamical zeta function when the underlying orbifold is a compact locally symmetric space of the reductive type, which extends one of the results obtained by the first author for compact locally symmetric manifolds.

math.DG↗
arXiv2020

Complex valued analytic torsion and dynamical zeta function on locally symmetric spaces

We show that the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an arbitrary flat vector bundle has a meromorphic extension to the whole complex plane and that its leading term in the Laurent series at the zero point is related to the regularised determinant of the flat Laplacian of Cappell-Miller. When the flat vector bundle is close to an acyclic and unitary one, we show that the dynamical zeta function is regular at the zero point and that its value is equal to the complex valued analytic torsion of Cappell-Miller. This generalises author's previous results for unitarily flat vector bundles as well as Müller and Spilioti's results on hyperbolic manifolds.

math.DG↗
arXiv2019

Fried conjecture in small dimensions

We study the twisted Ruelle zeta function $ζ_X(s)$ for smooth Anosov vector fields $X$ acting on flat vector bundles over smooth compact manifolds. In dimension $3$, we prove Fried conjecture, relating Reidemeister torsion and $ζ_X(0)$. In higher dimensions, we show more generally that $ζ_X(0)$ is locally constant with respect to the vector field $X$ under a spectral condition. As a consequence, we also show Fried conjecture for Anosov flows near the geodesic flow on the unit tangent bundle of hyperbolic $3$-manifolds. This gives the first examples of non-analytic Anosov flows and geodesic flows in variable negative curvature where Fried conjecture holds true.

math.DG↗
arXiv2017

Analytic torsion, dynamical zeta functions, and the Fried conjecture

We prove the equality of the analytic torsion and the value at zero of a Ruelle dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold. This solves a conjecture of Fried. This article should be read in conjunction with an earlier paper by Moscovici and Stanton.

math.DG↗