132,257 research outputs found
Geometric deep learning
The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas
Geometric deep learning: going beyond Euclidean data
Many scientific fields study data with an underlying structure that is a
non-Euclidean space. Some examples include social networks in computational
social sciences, sensor networks in communications, functional networks in
brain imaging, regulatory networks in genetics, and meshed surfaces in computer
graphics. In many applications, such geometric data are large and complex (in
the case of social networks, on the scale of billions), and are natural targets
for machine learning techniques. In particular, we would like to use deep
neural networks, which have recently proven to be powerful tools for a broad
range of problems from computer vision, natural language processing, and audio
analysis. However, these tools have been most successful on data with an
underlying Euclidean or grid-like structure, and in cases where the invariances
of these structures are built into networks used to model them. Geometric deep
learning is an umbrella term for emerging techniques attempting to generalize
(structured) deep neural models to non-Euclidean domains such as graphs and
manifolds. The purpose of this paper is to overview different examples of
geometric deep learning problems and present available solutions, key
difficulties, applications, and future research directions in this nascent
field
Geometric Multi-Model Fitting by Deep Reinforcement Learning
This paper deals with the geometric multi-model fitting from noisy,
unstructured point set data (e.g., laser scanned point clouds). We formulate
multi-model fitting problem as a sequential decision making process. We then
use a deep reinforcement learning algorithm to learn the optimal decisions
towards the best fitting result. In this paper, we have compared our method
against the state-of-the-art on simulated data. The results demonstrated that
our approach significantly reduced the number of fitting iterations
Molecular geometric deep learning
Geometric deep learning (GDL) has demonstrated huge power and enormous
potential in molecular data analysis. However, a great challenge still remains
for highly efficient molecular representations. Currently, covalent-bond-based
molecular graphs are the de facto standard for representing molecular topology
at the atomic level. Here we demonstrate, for the first time, that molecular
graphs constructed only from non-covalent bonds can achieve similar or even
better results than covalent-bond-based models in molecular property
prediction. This demonstrates the great potential of novel molecular
representations beyond the de facto standard of covalent-bond-based molecular
graphs. Based on the finding, we propose molecular geometric deep learning
(Mol-GDL). The essential idea is to incorporate a more general molecular
representation into GDL models. In our Mol-GDL, molecular topology is modeled
as a series of molecular graphs, each focusing on a different scale of atomic
interactions. In this way, both covalent interactions and non-covalent
interactions are incorporated into the molecular representation on an equal
footing. We systematically test Mol-GDL on fourteen commonly-used benchmark
datasets. The results show that our Mol-GDL can achieve a better performance
than state-of-the-art (SOTA) methods. Source code and data are available at
https://github.com/CS-BIO/Mol-GDL
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