Learning and analysis of rotations in SE(3) environments

Co-Supervised by: Francesco Leonardi

If you are interested in this topic or have further questions, do not hesitate to contact francesco.leonardi@unibe.ch.

Background / Context

In the field of graphs, the generation of molecules with specific properties represents one of the most promising and rapidly evolving areas of research. However, the state of the art is still in its early stages and requires, in addition to advanced generative models, the inclusion of features intrinsic to the problem, such as equivariance with respect to the SE(3) group. In other words, molecular rotations and translations must be consistently handled by the model. Mathematics and differential geometry have provided a solid theoretical foundation, enabling the development of generative models that respect these constraints. Given the complexity of the problem, this thesis will focus on a single aspect: the handling of rotations.

Research Question(s) / Goals

  • How do SE(3)-equivariant models learn and manage rotations?
  • What differences emerge in the latent space between an SE(3) model and a standard generative model?

Approach / Methods

To address these questions, the project involves designing two generative models (one standard and one SE(3)-equivariant) based on the same architecture (e.g., a VAE), in which, in addition to molecular reconstruction, a rotation-conditioning component will be incorporated. This approach will allow an analysis of how the models represent and manage information related to geometric transformations.

Expected Contributions / Outcomes

  • Development of two generative models for molecules.
  • Comparative analysis of the latent spaces, highlighting the main differences between the models.
  • Evaluation of model convergence speed and their ability to generate out-of-distribution (OOD) molecules.

Required Skills / Prerequisites

  • Good programming skills, with a preference for PyTorch.
  • Strong mathematical background
  • Languages: English, French, Italian. 

Further Reading / Starting Literature