Related papers: Almost Equivariance via Lie Algebra Convolutions

Metanetworks are neural architectures designed to operate directly on pretrained weights to perform downstream tasks. However, the parameter space serves only as a proxy for the underlying function class, and the parameter-function mapping…

We introduce the concept of a non-associative (i.e. non-necessarily associtive) inverse semialgebra over a field, the Lie version of which is inspired by the set of all partially defined derivations of a non-associative algebra, whereas the…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…

We consider associative algebras over a field. An algebra variety is said to be {\em Lie nilpotent} if it satisfies a polynomial identity of the kind $[x_1, x_2, ..., x_n] = 0$ where $[x_1,x_2] = x_1x_2 - x_2x_1$ and $[x_1, x_2, ..., x_n]$…

A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…

Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established…

An almost Abelian group is a non-Abelian Lie group with a codimension 1 Abelian subgroup. This paper investigates invariant Hermitian and K\"{a}hler structures on connected complex almost Abelian groups. We find explicit formulas for the…

For G an almost-connected Lie group, we study G-equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of G-invariant Riemannian metrics of positive scalar curvature. We…

We prove an impossibility result, which in the context of function learning says the following: under certain conditions, it is impossible to simultaneously learn symmetries and functions equivariant under them using an ansatz consisting of…

Although provably robust to translational perturbations, convolutional neural networks (CNNs) are known to suffer from extreme performance degradation when presented at test time with more general geometric transformations of inputs.…

Many scientific and geometric problems exhibit general linear symmetries, yet most equivariant neural networks are built for compact groups or simple vector features, limiting their reuse on matrix-valued data such as covariances, inertias,…

Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…

Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries,…

The weight-sharing mechanism of convolutional kernels ensures translation-equivariance of convolution neural networks (CNNs). Recently, rotation-equivariance has been investigated. However, research on scale-equivariance or simultaneous…

We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semi-bounded if the corresponding operators $i\dd\pi(x)$ from the derived representations are uniformly bounded from above on some non-empty open subset…

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…