📝 Selected Publications

Building Transformation Layers for Riemannian Neural Networks
Ziheng Chen. [Code]

• Introduces a principled generalization of fully connected and convolutional layers to Riemannian spaces.
• Instantiates the framework on three hyperbolic models, five SPD geometries, and two Grassmannian perspectives.
• Validates the framework on benchmark tasks across hyperbolic, SPD, and Grassmannian manifolds.

Riemannian Networks over Full-Rank Correlation Matrices
Ziheng Chen, Xiao-Jun Wu, Bernhard Schölkopf, Nicu Sebe. [Poster]

• Extends MLR, fully connected, and convolutional layers to the correlation manifold under five geometries.
• Develops accurate backpropagation for Riemannian computations under OLM and LSM.
• Demonstrates the effectiveness of correlation embeddings and networks through comparisons with existing SPD and Grassmannian networks.

Hyperbolic Busemann Neural Networks
Ziheng Chen, Bernhard Schölkopf, Nicu Sebe. [Code] [Slides] [Poster]

• Introduces Busemann MLR with intrinsic logits and a point-to-horosphere distance interpretation, using compact parameters, batch-efficient computation, and a Euclidean limit.
• Develops Busemann fully connected layers by generalizing FC and activation layers to both the Poincaré and Lorentz models.
• Validates BMLR and BFC across image classification, genomic sequence learning, node classification, and link prediction.

Proper Velocity Neural Networks
Ziheng Chen^*, Zihan Su^*, Bernhard Schölkopf, Nicu Sebe. [Code] [Poster]

• Establishes the complete Riemannian geometric toolkit of the proper velocity manifold with closed-form operators.
• Develops fundamental building blocks in proper velocity space, including MLR, fully connected, convolutional, activation, and batch normalization layers.
• Validates the stability and effectiveness of PVNNs on numerical stability, image classification, graph node classification, and genomic sequence learning.

Fast and Stable Riemannian Metrics on SPD Manifolds via Cholesky Product Geometry
Ziheng Chen, Yue Song, Xiao-Jun Wu, Nicu Sebe. [Code] [Slides] [Poster]

• Uncovers a product structure of Cholesky factors that enables convenient metric design.
• Introduces the Power–Cholesky Metric (PCM) and Bures–Wasserstein–Cholesky Metric (BWCM), with closed-form operators, computational efficiency, and improved numerical stability.
• Applies PCM and BWCM to Riemannian classifiers and residual blocks for SPD neural networks.

Gyrogroup Batch Normalization
Ziheng Chen, Yue Song, Xiao-Jun 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 GyroBN and instantiates it on Grassmannian and hyperbolic spaces.

Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry
Ziheng Chen, Yue Song, Xiao-Jun Wu, Gaowen Liu, Nicu Sebe. [Code]

• Explains matrix-function normalizations in global covariance pooling through Riemannian classifiers.
• Validates the analysis on ImageNet and three FGVC datasets.

RMLR: Extending Multinomial Logistic Regression into General Geometries
Ziheng Chen, Yue Song, Rui Wang, Xiao-Jun 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.

Riemannian Multinomial Logistics Regression for SPD Neural Networks
Ziheng Chen, Yue Song, Gaowen Liu, Ramana Rao Kompella, Xiao-Jun 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.

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.

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.