mlsanityData to 14 Oct 2026

Riemannian Self-Attention Mechanism for SPD Networks

arXiv 2311.16738 ↗First posted 28 Nov 2023cs.CVcited by 4

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Abstract (arXiv)

Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD manifold. Although there are many different ways to design network architectures for SPD matrix nonlinear learning, very few solutions explicitly mine the geometrical dependencies of features at different layers. Motivated by the great success of self-attention mechanism in capturing long-range relationships, an SPD manifold self-attention mechanism (SMSA) is proposed in this paper using some manifold-valued geometric operations, mainly the Riemannian metric, Riemannian mean, and Riemannian optimization. Then, an SMSA-based geometric learning module (SMSA-GLM) is designed for the sake of improving the discrimination of the generated deep structured representations. Extensive experimental results achieved on three benchmarking datasets show that our modification against the baseline network further alleviates the information degradation problem and leads to improved accuracy.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 22 of its 53 references that are in the map. First posted on arXiv 28 Nov 2023.

Builds on

22 of 53 references.

References · 22

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,364
  4. 2018Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognitioncited by 1,209
  5. 2016Convolutional Two-Stream Network Fusion for Video Action Recognitioncited by 384
  6. 2017First-Person Hand Action Benchmark with RGB-D Videos and 3D Hand Pose Annotationscited by 230
  7. 2016A Riemannian Network for SPD Matrix Learningcited by 162
  8. 2019H+O: Unified Egocentric Recognition of 3D Hand-Object Poses and Interactionscited by 141
  9. 2021UAV-Human: A Large Benchmark for Human Behavior Understanding with Unmanned Aerial Vehiclescited by 96
  10. 2017Interpretable 3D Human Action Analysis with Temporal Convolutional Networkscited by 89
  11. 2019Riemannian batch normalization for SPD neural networkscited by 72
  12. 2016Building Deep Networks on Grassmann Manifoldscited by 58
10 more
  1. 2019A neural network based on SPD manifold learning for skeleton-based hand gesture recognitioncited by 46
  2. 2016Dimensionality Reduction on SPD Manifolds: The Emergence of Geometry-Aware Methodscited by 29
  3. 2022Riemannian Local Mechanism for SPD Neural Networkscited by 22
  4. 2019Temporal Transformer Networks: Joint Learning of Invariant and Discriminative Time Warpingcited by 21
  5. 2016Transition Forests: Learning Discriminative Temporal Transitions for Action Recognition and Detectioncited by 18
  6. 2022O-ViT: Orthogonal Vision Transformercited by 10
  7. 2013Sparse Coding and Dictionary Learning for Symmetric Positive Definite Matrices: A Kernel Approachcited by 9
  8. 2019Analyzing Dynamical Brain Functional Connectivity As Trajectories on Space of Covariance Matricescited by 9
  9. 2019Multiple Riemannian Manifold-valued Descriptors based Image Set Classification with Multi-Kernel Metric Learningcited by 6
  10. 2013Spatio-Temporal Covariance Descriptors for Action and Gesture Recognitioncited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Subgroups of U(d) Induce Natural RNN and Transformer Architecturescited by 1
  2. 2026CliffSearch: Structured Agentic Co-Evolution over Theory and Code for Scientific Algorithm Discoverycited by 0
  3. 2026Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layerscited by 0
  4. 2026SPD-MetaFormer is what you need for small-data brain decodingcited by 0