Ziheng Chen

Ziheng Chen

Ph.D. student

“天地有正气，杂然赋流形 – 文天祥”

I am a Ph.D. student affiliated with Multimedia and Human Understanding Group (MHUG) at University of Trento, Italy, advised by Prof. Nicu Sebe. Before my Ph.D. studies, I received a B.A. degree in logistics management from Shandong University, Jinan, China, and an M.S. degree in computer science and technology from Jiangnan University, Wuxi, China, under the supervision of Prof. Xiao-Jun Wu.

My research lies in the intersection of machine learning and differential geometry, such as geometric deep learning and matrix/vector manifolds. Currently, I co-supervise several students with Rui Wang.

I am building a GitHub repo, Awesome-Riemannian-Deep-Learning, containing resources on deep learning over Riemannian spaces. 🚀

🌟 News

  • 2025.02: One paper on Riemannian batch normalization for ill-conditioned SPD matrices was accepted to CVPR 2025. It is one of the first CVPR papers with Jiangnan University as the first affiliation! Congrats Rui and Shaocheng!
  • 2025.01: Two papers were accepted to ICLR 2025!! One for Riemannian batch normalization over gyrogroups, the other for interpreting high-order pooling via Riemannian geometry.
  • 2024.09: One paper on Riemannian classifiers over general geometries was accepted to NeurIPS 2024 (final rating: 877).
  • 2024.08: One paper on adaptive Riemannian metrics for SPD matrix learning was accepted by TIP.
  • 2024.04: One paper on Grassmannian self-attention was accepted to IJCAI 2024. Congrats Rui and Chen!
  • 2024.03: Our CVPR 2024 paper on Riemannian classifiers was selected as poster to VALSE 2024.
  • 2024.03: One paper on SPD deep metric learning was early accessed in TNNLS.
  • 2024.02: One paper on Riemannian classifiers on SPD manifolds was accepted to CVPR 2024.
  • 2024.01: One paper on Riemannian batch normalization on general Lie groups was accepted to ICLR 2024.

📝 Selected Publications

(† denotes the corresponding author)

ICLR 2025
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Gyrogroup Batch Normalization
Ziheng Chen, Yue Song, Xiaojun Wu, Nicu Sebe. [Code]

  • Proposes pseudo-reductive gyrogroups, a relaxed structure of gyrogroups, with complete theoretical analyses.
  • Establishes the conditions for theoretical control over sample statistics in Riemannian batch normalization over gyrogroups, i.e., pseudo-reduction and gyroisometric gyrations.
  • Introduces a GyroBN framework for Riemannian Batch Normalization over gyrogroups, applicable to various geometries.
  • Manifests GyroBN on the Grassmannian and hyperbolic spaces.
ICLR 2025
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Understanding Matrix Function Normalizations in Covariance Pooling from the Lens of Riemannian Geometry
Ziheng Chen, Yue Song, Xiaojun Wu, Gaowen Liu, Nicu Sebe. [Code]

  • Explains the working mechanism of matrix functions in Global Covariance Pooling from the perspectives of tangent and Riemannian classifiers, and finally claims that the rationality of matrix functions should be attributed to the Riemannian classifiers they implicitly respect.
  • Validates the theoretical argument on the ImageNet and three FGVC datasets through comprehensive experiments.
NeurIPS 2024
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RMLR: Extending Multinomial Logistic Regression into General Geometries
Ziheng Chen, Yue Song, Rui Wang, Xiaojun Wu, Nicu Sebe. [Code]

  • Extends our flat SPD MLR (CVPR24) into Riemannian MLR over general geometries.
  • Proposes five families of SPD MLRs based on different geometries of the SPD manifold.
  • Proposes a novel Lie MLR for deep neural networks on rotation matrices.
ICLR 2024
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A Lie Group Approach to Riemannian Batch Normalization
Ziheng Chen, Yue Song, Yunmei Liu, Nicu Sebe. [Code]

  • Propose a Riemannian batch normalization (LieBN) framework over general Lie groups, with controllable first- and second-order statistical moments.
  • Manifests specific LieBN layers on SPD manifolds under three deformed Lie groups as well as the Lie group of rotation matrices.
CVPR 2024
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Riemannian Multinomial Logistics Regression for SPD Neural Networks
Ziheng Chen, Yue Song, Gaowen Liu, Ramana Rao Kompella, Xiaojun Wu, Nicu Sebe. [Code]

  • Extends the Euclidean Multinomial Logistic Regression (MLR) to the SPD manifold under flat Riemannian metrics.
  • Manifests the framework on the Log-Euclidean (LE) and Log-Cholesky (LC) metrics.
  • Provides the first intrinsic explanation for the widely used LogEig classifier.
Arxiv 2024
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Product Geometries on Cholesky Manifolds with Applications to SPD Manifolds
Ziheng Chen, Yue Song, Xiao-Jun Wu, Nicu Sebe. [Code]

  • Identifies the underlying product structure in the existing Cholesky metric.
  • Introduces two novel Riemannian metrics on the Cholesky manifold, along with a comprehensive analysis of their geometric properties.
  • Proposes two numerically stable Riemannian metrics on the SPD manifold, with a detailed analysis of their geometric properties.
TIP 2024
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Adaptive Log-Euclidean Metrics for SPD Matrix Learning
Ziheng Chen, Yue Song, Tianyang Xu, Zhiwu Huang, Xiao-Jun Wu, and Nicu Sebe. [Code]

  • Proposes a general framework for pullback metrics over the SPD manifold from the Euclidean space.
  • Extends the existing Log-Euclidean Metric (LEM) into ALEM.

Preprints

Conferences

Journals

🎖 Honors and Awards

  • 2023.12, Excellent Master’s Thesis of Jiangsu Association of Artificial Intelligence (江苏省人工智能学会优秀硕士论文)

💬 Invited Talks

  • 2025.03, Riemannian Deep Learning: Normalization and Classification. University of Alberta. [Slides]
  • 2024.03, Naïve Riemannian Geometry: A One Hour Tour. Jiangnan University (internal talk).

📖 Courses

To obtain basic foundations for my research, I have self-studied several math courses, most of which were done during my master studies:

  • Mathematical Analysis I, II, III, Real Analysis, Complex Analysis, Functional Analysis;
  • Advanced Algebra I, II, Abstract Algebra I;
  • Topology, Differential Geometry, Differential Manifolds, Riemannian Geometry;
  • Differential Equations, Convex Optimization, Numerical Optimization…

💻 Personal Channels