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Riemannian Deep Learning: Modules, Networks, and Geometries
Ziheng Chen
Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximatio…
LieBN: Batch Normalization over Lie Groups
Ziheng Chen, Yue Song, Rui Wang +2
Manifold-valued measurements are prevalent in various machine learning tasks. Recent advances have extended Deep Neural Networks (DNNs) to operate on manifolds. These extensions ha…
Relative Repairability: A Calibration-Based Diagnostic for High-Sparsity Post-Pruning Allocation
Qishi Zhan, Liang He, Minxuan Hu +1
At very high sparsity, neural network pruning does more than decide which weights remain. It also determines where pruning induced damage is placed across the network, and whether…
Adaptive Signal Resuscitation: Channel-wise Post-Pruning Repair for Sparse Vision Networks
Qishi Zhan, Ziheng Chen, Minxuan Hu
One-shot magnitude pruning can cause severe accuracy collapse in the high-sparsity regime, even when the pruning mask preserves the largest weights. We argue that this failure refl…
Riemannian Networks over Full-Rank Correlation Matrices
Ziheng Chen, Xiaojun Wu, Bernhard Schölkopf +1
Representations on the Symmetric Positive Definite (SPD) manifold have garnered significant attention across different applications. In contrast, the manifold of full-rank correlat…
Intrinsic Lorentz Neural Network
Xianglong Shi, Ziheng Chen, Yunhan Jiang +1
Real-world data frequently exhibit latent hierarchical structures, which can be naturally represented by hyperbolic geometry. Although recent hyperbolic neural networks have demons…
Hyperbolic Busemann Neural Networks
Ziheng Chen, Bernhard Schölkopf, Nicu Sebe
Hyperbolic spaces provide a natural geometry for representing hierarchical and tree-structured data due to their exponential volume growth. To leverage these benefits, neural netwo…
Riemannian Batch Normalization: A Gyro Approach
Ziheng Chen, Xiao-Jun Wu, Bernhard Schölkopf +1
Normalization layers are crucial for deep learning, but their Euclidean formulations are inadequate for data on manifolds. On the other hand, many Riemannian manifolds in machine l…
Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry
Rui Wang, Shaocheng Jin, Ziheng Chen +2
Covariance matrices have proven highly effective across many scientific fields. Since these matrices lie within the Symmetric Positive Definite (SPD) manifold - a Riemannian space…
RMLR: Extending Multinomial Logistic Regression into General Geometries
Ziheng Chen, Yue Song, Rui Wang +2
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-value…
A Lie Group Approach to Riemannian Batch Normalization
Ziheng Chen, Yue Song, Yunmei Liu +1
Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and…