## 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

## Call for papers

The workshop solicits submissions to the

**Proceedings track**: 8 page paper submissions (excluding appendices and references). Submissions will be peer-reviewed. Accepted papers will be published in PMLR as part of our workshop proceedings.**Extended abstract track**: 4 page paper submissions (excluding appendices and references). Submissions will be peer-reviewed. Accepted papers can be viewed on openreview.**Blogpost track**: blog posts that have tutorial value and act as explainers for (previously) published papers or important topics in the field. In this track, we further encourage blog posts that present opinion pieces, open problems,etc in provided markdown format. Submissions will be peer-reviewed and accepted submissions will be hosted on GRaM wesbite.**Tutorial track**: Tutorials with easy-to-use and understand code for topics of important to GRaM audience submitted as a collab file. Submissions will be peer-reviewed and accepted submissions will be hosted on GRaM website.**TAG challenge**: We team up with TAG and host a*ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain*challenge.

## Organizers

- Sharvaree Vadgama
- Erik Bekkers
- Alison Pouplin
- Hannah Lawrence
- Sékou-Oumar Kaba
- Robin Walters
- Jakub M. Tomczak
- Stefanie Jegelka
- Henry Kvinge
- Tegan Emerson