arXiv research

New mesh network preserves symmetries in deep learning.

DNFS trains efficient samplers for discrete distributions using locally equivariant Transformers.

This paper is devoted to apply the equivariant moving frame method to study the local equivalence problem of third order ordinarily differential equation under the pseudo-group of fiber preserving transformations.

Equivariant cohomology simplifies symplectic manifold integrals with group actions.

LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.

Proposes SE(3) equivariant graph neural networks with local frames for efficient geometric approximation.

The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical imaging problems that exhibit symmetries. Here we show how this principle can be exte…

This paper introduces equivariant hamiltonian flows, a method for learning expressive densities that are invariant with respect to a known Lie-algebra of local symmetry transformations while providing an equivariant representation of the data. We provide proof of principle demonstrations of how such flows can be learnt…

Transformation Equivariant Representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of {\em translation} equivariance underlying the success of Convolutional Neural Networks (CNNs). For this purpose, we present both deterministic AutoEncoding…

SE(3)-Transformers maintain equivariance for 3D data under rotations and translations.

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 appear (e.g. an upright face with a horizontal nose), current equivariant architect…

The effectiveness of Convolutional Neural Networks (CNNs) has been substantially attributed to their built-in property of translation equivariance. However, CNNs do not have embedded mechanisms to handle other types of transformations. In this work, we pay attention to scale changes, which regularly appear in various t…

Equivariant CNNs improve RL performance in symmetric environments.

3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the last layer of a network. Instead, an idealized model would preserve a meaningful r…

MFNs parameterize non-local interactions through matrix equivariant functions, improving graph neural network performance.

Measures equivariance in vision models using Lie derivative.

Method learns equivariances from data without custom architecture design.

The study quantifies how many objects can be linearly classified under all views.

IsoGCNs learn invariant and equivariant graph features for efficient simulations.

Equivariant diffusion model generates 3D molecules efficiently.

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the a…

A2I Transformer predicts atom energies from coordinates, avoiding heavy featurization.

In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here a so-called enhanced Burnside ring $\widehat{B}(G)$ of a finite group $G$…

Unified theorem for deep and shallow joint-equivariant machines.

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the robustness of models towards pre-defined continuous transformation groups. Throu…

An iterative SE(3)-Transformer model is developed for graph data.

New model learns graph neural networks equivariant to various transformations.

New fusion blocks improve equivariant neural networks for molecular dynamics.

Lie groupoid equivariant neural networks are a new type of neural network.

Generalizes CNNs for Lie group equivariance across various data types.

Novel CG-EGNNs learn equivariant functions from Clifford algebras.

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distributi…

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.

New translation equivariant neural processes improve spatio-temporal data modeling.

Steerable neural ODEs on homogeneous spaces for equivariant feature dynamics.

Unified framework for image restoration using equivariant denoisers.

We propose a semantic segmentation model that exploits rotation and reflection symmetries. We demonstrate significant gains in sample efficiency due to increased weight sharing, as well as improvements in robustness to symmetry transformations. The group equivariant CNN framework is extended for segmentation by introdu…

In this paper, we provide a concrete interpretation of equivariant Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant Cheeger-Müller theorem simplifies considerably when applied to locally symmetric spaces. In a companion paper, this allows us to extend recent results on torsion cohomology growth and …

New graph foundation models respect symmetries for broader applicability.

This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain conditions, the network feature naturally has the rotation-equivariance property. Rota…

Paper uses algebraic methods to prove an equivariant Poincaré-Hopf theorem.

Transformers can approximate any sequence-to-sequence function, surprising given their complexity.

L-GATr transforms high-energy physics data using geometric algebra and Lorentz symmetry.

Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural transformations to and from equivariant K-homology defined via KK-theory (the "offici…

Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.

The Witten class is derived from equivariant cohomology of a conformal loop space.

New framework for conformal equivariant cycles in KK-theory.

Coordinate-independent convolutions on manifolds avoid reference frame ambiguity.