arXiv research

Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.

The paper develops methods for calculating equivariant homology from Morse functions.

Study stabilizes Morse-Bott cohomology for equivariant manifolds.

An impossibility result shows limitations in learning symmetries and equivariant functions.

Guillemin trace formula adapted for group actions.

We use contact geometry to describe the monoid of projectively equivariant meromorphic differential operators on a complex curve, quantization of which generalizes known constructions of classical equivariants to non-commutative function algebras in several variables.

The paper computes metrics and Einstein tensors on even-dimensional manifolds.

Equivariant CNNs improve RL performance in symmetric environments.

In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$. Especially, for a given $G$-invariant/equivariant function, we construct its universal approximator by deep neural network whose layers equip $G$-actions and each affine t…

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

Develops a theory for equivariant networks with partial domain symmetry.

Machine learning uses invariant theory to restrict function classes.

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…

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

New neural networks respect symmetries in symmetric tensors, improving efficiency and generalization.

Equivariant neural networks use symmetry to interpret complex data.

Characterizes a specific type of neural network for alternating group equivariance.

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

New method uses scalars to approximate physics functions.

New equivariant filters improve graph classification.

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic…

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 $G$…

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 paper introduces $μ$K-stability for polarized schemes and develops equivariant calculus.

Paper develops equivariant basic cohomology for Lie groupoids.

New method breaks symmetry in neural networks, improving sample efficiency.

This work uses action equivariance to learn structured latent spaces for reinforcement learning.

Novel CG-EGNNs learn equivariant functions from Clifford algebras.

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 …

Study of mean curvature flow in warped products preserving equivariance.

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

We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked out, one of them yielding a quantum length element on $S^3$.

L-CNNs preserve gauge symmetry in lattice simulations.

The paper develops tensor learning methods exploiting symmetries of tensor functions.

In this paper we continue our study of equivariant minimal Lagrangian surfaces in $\mathbb{C} P^2$, characterizing the rotationally equivariant cases and providing explicit formulae for relevant geometric quantities of translationally equivariant minimal Lagrangian surfaces in terms of Weierstrass elliptic functions.

In this paper, we first define the equivariant infinitesimal $η$-form, then we compare it with the equivariant $η$-form, modulo exact forms, by a locally computable form. As a consequence, we obtain the singular behavior of the equivariant $η$-form, modulo exact forms, as a function on the acting Lie group. This result…

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

SymPE breaks symmetries in equivariant networks, improving performance across various tasks.

We consider an equivariant analogue of a conjecture of Borcherds. Let $Y$ be a real $K3$ surface without real points. Let $g$ be a Ricci-flat Kaehler metric on $Y$ invariant under the complex conjugation. We shall prove that the equivariant determinant of the Laplacian of $(Y,g)$ with respect to the complex conjugation…

Characterizes group-equivariant neural networks for three groups.

Paper proves equivariant Fried conjecture for specific flows.

The equivariant holomorphic torsion of a compact locally symmetric manifold and an automorphism is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.

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 …

Paper proves non-zero generalization boost for equivariant models.

Study equivariant 4-genus of knots in symmetric 4-manifolds.

New method constructs translationally equivariant hyperbolic affine spheres.

We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is strongly convex and derive convergence of the discrete heat flow to the energy minimizer, with explic…

The paper explores equivariant means on topological spaces.