Geometric Deep Learning

Deep Learning Ensuring Laws of Physics

For modeling physical dynamical systems, a model associated with their geometric properties ensures the laws of physics rather than the superficial dynamics. The automatic discrete gradient algorithm makes a discrete gradient method applicable to a neural network and strictly admits the energy conservation and dissipation laws in discrete time. A representation of molecules invariant to the position and angle ensures the dynamics equivariant to the translation and rotation.

Topology-aware Data Generation

A data distribution or an object shape has its own topological structure, while a deep generative model often assumes a map from a simple distribution without regard for the difference in topology. Our proposed ChartPointFlow assigns a conditioned map to each continuous subset of a point cloud, similarly to a chart of a manifold, thereby nicely generating point clouds with different topologies.

Bayesian Deep Learning

Deep Generative Model-based Classifier

Compared to ordinary classifiers, a generative classifier extracts even detailed features for reconstruction, and thereby, it is less likely to overfit to a salient subset of features. A prior knowledge about the dependency between factors is implemented as its structure and provides interpretable results.

Uncertainty-Aware Anomaly Detection

A typical score for anomaly detection is sensitive to the apparent ambiguity of a given sample, which is indeed unrelated to the anomality. By removing it, one can detect anomalies robustly to the appearance variety.