Related papers: Equivariant Manifold Neural ODEs and Differential …
Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for…
We study smooth higher symmetry groups and moduli $\infty$-stacks of generic higher geometric structures on manifolds. Symmetries are automorphisms which cover non-trivial diffeomorphisms of the base manifold. We construct the smooth higher…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
Neural ordinary differential equations (NODEs) presented a new paradigm to construct (continuous-time) neural networks. While showing several good characteristics in terms of the number of parameters and the flexibility in constructing…
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit…
Equivariance is a nice property to have as it produces much more parameter efficient neural architectures and preserves the structure of the input through the feature mapping. Even though some combinations of transformations might never…
We give a unified method for the general equivalence problem of extrinsic geometry, on the basis of our formulation of a general extrinsic geometry as that of an osculating map $\varphi\colon (M,\mathfrak f) \to L/L^0 \subset…
Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as…
Despite the successes of deep learning in computer vision, difficulties persist in recognizing objects that have undergone group-symmetric transformations rarely seen during training$\unicode{x2013}$for example objects seen in unusual…
Most current deep learning models equivariant to $O(n)$ or $SO(n)$ either consider mostly scalar information such as distances and angles or have a very high computational complexity. In this work, we test a few novel message passing graph…
Geometric deep learning enables the encoding of physical symmetries in modeling 3D objects. Despite rapid progress in encoding 3D symmetries into Graph Neural Networks (GNNs), a comprehensive evaluation of the expressiveness of these…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that may limit their accessibility, or are tied…
Content and image generation consist in creating or generating data from noisy information by extracting specific features such as texture, edges, and other thin image structures. We are interested here in generative models, and two main…
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…
Equivariance encodes known symmetries into neural networks, often enhancing generalization. However, equivariant networks cannot break symmetries: the output of an equivariant network must, by definition, have at least the same…
This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on applications to ordinary cohomology and to…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…