GRaM Workshop @ ICML 2024
ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling
The workshop is co-organised by ELISE. For more information visit the workshop website.
Motivation
By recognizing that nearly all data is rooted in our physical world, and thus inherently grounded in geometry and physics, it becomes evident that representation learning should preserve this grounding in order to remain meaningful. For example, preserving group transformation laws and symmetries through equivariant layers is crucial in domains such as computational physics, chemistry, robotics, and medical imaging, and leads to effective and generalizable architectures and improved data efficiency. Similarly, in generative models applied to non-Euclidean data spaces, maintaining the manifold structure is essential in order to obtain meaningful samples. Therefore, this workshop focuses on the principle of grounding in geometry, which we define as follows:
A representation, method, or theory is grounded in geometry if it can be amenable to geometric reasoning, that is, it abides by the mathematics of geometry and physics.
Topics
We solicit submissions that present theoretical research, methodologies, applications, insightful analysis, and even open problems, within the following topics (list not exhaustive):
- Structure-preserving learning
- Preservation of symmetries; E.g., through equivariant operators.
- Dynamical systems on manifolds; Representation learning and generative modeling using ordinary, stochastic, and differential equations (ODEs, SDEs, PDEs) on manifolds.
- Computing with geometric representations; Such as the processing of multi-vectors using geometric algebra, steerable vectors using Clebsch-Gordan products, and hyperbolic features using Fréchet means.
- Structure-inducing learning
- Self-supervised learning; E.g., learning to embed data in geometric latent spaces through (geodesic) distance-based similarity metrics.
- Geometric priors; E.g., soft constraints on model weights.
- Physics-Informed Neural Networks; E.g., inducing the structure of established physical and geometric laws into neural networks through dedicated losses.
- Generative modeling and density estimation
- Geometric latent variable models; I.e., the use of latent variables that live in a manifold.
- New Methods; And adaptations of methods capable of:
- Generating geometric objects; E.g., generating atomic point clouds or shapes.
- Generating fields over manifolds; E.g., generating vector fields or spherical signals.
- Grounding in theory
- Theoretical frameworks; Unifying analyses and formulations that provide a generalizing perspective on deep learning paradigms.
- Open problems; Identifying and addressing unresolved questions and challenges that lie at the intersection of geometry and learning
