arXiv research

New neural network learns relevant transformations in data, improving object recognition.

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.

New mesh network preserves symmetries in deep learning.

Equivariant CNNs improve RL performance in symmetric environments.

Measures equivariance in vision models using Lie derivative.

Method learns equivariances from data without custom architecture design.

IsoGCNs learn invariant and equivariant graph features for efficient simulations.

Equivariant diffusion model generates 3D molecules efficiently.

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.

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

Generalizes CNNs for Lie group equivariance across various data types.

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

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…

The paper introduces REQNNs for robust 3D point cloud processing.

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.

New framework for conformal equivariant cycles in KK-theory.

Let $G$ be a linear connected complex reductive Lie group. The purpose of this paper is to give explicit symplectic isomorphisms from twisted cotangent bundles of the complex generalized flag varieties, whose transition functions are given by affine transformations instead of linear transformations, onto the complex co…

Capsule networks are constrained by the parameter-expensive nature of their layers, and the general lack of provable equivariance guarantees. We present a variation of capsule networks that aims to remedy this. We identify that learning all pair-wise part-whole relationships between capsules of successive layers is ine…

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…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

New framework for equivariant neural networks using Lie group decompositions.

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.

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

STAR improves equivariant and invariant representation learning by routing projection heads.

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…

NFT learns group actions without knowing the data's structure.

A neural scene representation framework enforcing 3D transformations.

Geometric Algebra Transformer (GATr) handles various geometric data types efficiently.

Equivariant T-duality connects bundles with twists.

The characteristic forms in the bundle of connections of a principal bundle P over M determine the characteristic classes of P for degree less or equal to the dimension of M, and differential forms on the space of connections for higher degree. The equivariant characteristic classes provide canonical equivariant extens…

Proposes a topological model for partial equivariance in neural networks.

Solve Painleve VI to relate instanton bundles.

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

Maps asymptotically embed conic transforms from circle bundles.

New model improves field learning with improved equivariance.

In the previous paper, the author defined equivariant Floer cohomology for a complete intersection in a toric variety and showed that it is isomorphic to the small quantum D-module after a mirror transformation when the first Chern class c_1(M) of the tangent bundle is nef. In this paper, even when c_1(M) is not nef, w…

EquivCNP learns group symmetries for conditional data.

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of s…

Paper defines mathematical framework for neural network explainability.