arXiv research

Improved set prediction model using multiset-equivariant operations and approximate implicit differentiation.

Using deep neural networks that are either invariant or equivariant to permutations in order to learn functions on unordered sets has become prevalent. The most popular, basic models are DeepSets [Zaheer et al. 2017] and PointNet [Qi et al. 2017]. While known to be universal for approximating invariant functions, DeepS…

We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show t…

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…

Unified method for CNNs to approximate equivariant maps across various groups.

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

The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.

Study of equivariant movie moves for involutive links.

In this paper, we introduce the classification of equivariant principal bundles over the 2-sphere. Isotropy representations provide tools for understanding the classification of equivariant principal bundles. We consider a $Γ$-equivariant principal $G$-bundle over $S^2$ with structural group $G$ a compact connected Lie…

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 …

Universal MLPs with a single hidden layer can learn any function.

Formula for index in Lorentzian spacetimes.

Develops a theory for equivariant networks with partial domain symmetry.

We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply these inequalities to study cohomology of the fixed points set of a symplectic t…

We introduce the Convolutional Conditional Neural Process (ConvCNP), a new member of the Neural Process family that models translation equivariance in the data. Translation equivariance is an important inductive bias for many learning problems including time series modelling, spatial data, and images. The model embeds …

EquivCNP learns group symmetries for conditional data.

The work discusses equivariant asymptotic dimension (also known as "wide equivariant covers", "$N$-$\mathcal F$-amenability" or "amenability dimension", and "$d$-BLR condition") and its generalisation, transfer reducibility, which are versions of asymptotic dimension invented for the proofs of the Farrell--Jones and Bo…

Constructs equivariant spectral flow for Dirac-type operators on manifolds.

The paper proves stability in compact finite dimensional Alexandrov spaces using equivariant Gromov--Hausdorff convergence.

Constructs singular Yamabe solutions via equivariant reduction.

ExNODE uses ODE to model sets with permutation equivariance.

Permutation-equivariant neural networks improve auction mechanisms by reducing regret and sample complexity.

Equivariant neural networks improve performance and generalization in complex scalar field theory tasks.

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

We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the splitting of the extended tangent bundle, our definition of extended equivariant coho…

The paper studies geometric properties of group equivariant operators and their Riemannian structure.

Paper shows mapping class group-equivariant Teichmüller space deformation to Thurston spine.

This work introduces a method for almost equivariance in neural networks using Lie algebra convolutions.

Characterizes group-equivariant neural networks for three groups.

Generalizes Floer homotopy via Morse-Bott theory.

New rigidity results for complex and quaternionic moment-angle manifolds.

Unified framework for image restoration using equivariant denoisers.

Equivariant neural networks improve performance and generalization in lattice field theory tasks.

We formulate, for any Lie group G acting isometrically on a manifold M, the general notion of a G-equivariant elliptic operator that is invertible outside of a G-cocompact subset of M. We prove a version of the Rellich lemma for this setting and use this to define the equivariant index of such operators. We show that G…

Normal forms for equivariant maps in infinite dimensions established.

Study of equivariant scalar curvature groups for proper group actions.

This work establishes universality for deep equivariant networks, overcoming limitations of previous approaches.

We will have a deep look at the set of all $G$-equivariant maps from the factor Lie group $G$ to the under the action manifold $M$, both from "computational" and "observability" viewpoint. We will also be looking for the existence of "unique" structure on this set, in a way that the induced-action of Lie group $G$ be s…

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 $G$…

Absolute index theorem for warped product manifolds.

Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper, we consider a specific class of invariant and equivariant networks, for which we …

Getzler-Jones-Petrack introduced $A_\infty$ structures on the equivariant complex for manifold $M$ with smooth $\mathbb{S}^1$ action, motivated by geometry of loop spaces. Applying Witten's deformation by Morse functions followed by homological perturbation we obtained a new set of $A_\infty$ structures. We extend and …

Inspired by Kronheimer and Mrowka's approach to monopole Floer homology, we develop a model for $\mathbb{Z}/2$-equivariant symplectic Floer theory using equivariant almost complex structures, which admits a localization map to a twisted version of Floer cohomology in the invariant set. We then present applications to S…

In her PhD thesis Milin developed an equivariant version of the contact homology groups constructed by Eliashberg, Kim and Polterovich and used it to prove an equivariant contact non-squeezing theorem. In this article we re-obtain the same result in the setting of generating functions, starting from the homology groups…

The study shows symmetry improves machine learning generalization.

Analytic torsion behavior studied for degenerating manifolds with equivariant bundles.

Translationally equivariant neural networks improve performance and generalization in physics problems.

Proves minimization for Kähler manifolds with automorphisms.