Summary of Matrix Manifold Neural Networks++, by Xuan Son Nguyen and Shuo Yang and Aymeric Histace
Matrix Manifold Neural Networks++
by Xuan Son Nguyen, Shuo Yang, Aymeric Histace
First submitted to arxiv on: 29 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Deep neural networks on Riemannian manifolds have gained popularity across various applications, including computer vision and natural language processing. The success of these networks can be attributed to the rich algebraic structures of gyrogroups and gyrovector spaces on spherical and hyperbolic manifolds. This allows for principled generalizations of successful DNNs to these manifolds. Recent works have extended these concepts to matrix manifolds, such as Symmetric Positive Definite (SPD) and Grassmann manifolds. This paper designs fully-connected and convolutional layers for SPD neural networks and develops multinomial logistic regression on Symmetric Positive Semi-definite (SPSD) manifolds. It also proposes a method for backpropagation using the Grassmann logarithmic map in the projector perspective. The proposed approach is demonstrated to be effective in human action recognition and node classification tasks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper talks about special kinds of neural networks that work well on different shapes, like spheres and hyperbolic spaces. These networks are good at solving problems like recognizing actions or classifying nodes. The key idea is that these shapes have special mathematical properties that help the networks learn better. The authors also develop new techniques for working with matrix manifolds, which are important in many applications. They show that their approach works well in two specific tasks. |
Keywords
» Artificial intelligence » Backpropagation » Classification » Logistic regression » Natural language processing
