Efficiently samples and learns densities with symmetries using equivariant methods.
problem Efficiently sampling and learning densities with symmetries.
method Equivariant Stein Variational Gradient Descent (SVGD) and equivariant energy based models.
result Improves and scales up training of energy based models.
Method learns equivariances from data without custom architecture design.
problem Learning equivariances for tasks without manually designed architectures.
method Reparameterization to learn equivariant parameter sharing.
result Can learn equivariances for any finite group of transformations.
The paper develops methods for calculating equivariant homology from Morse functions.
problem Calculating equivariant homology from equivariant Morse functions.
method Alter equivariant Morse functions to stable ones, use generic equivariant metrics, and analyze the Morse spectral sequence.
result Equivariant Morse functions induce a filtration that computes equivariant homology.
New model learns graph neural networks equivariant to various transformations.
problem Learning equivariant graph neural networks for complex transformations.
method E(n)-Equivariant Graph Neural Networks (EGNNs) that are computationally efficient and scalable.
result Achieves competitive or better performance without higher-order representations.
Unified method for CNNs to approximate equivariant maps across various groups.
problem Limited universal approximation theorems for CNNs with specific groups and settings.
method Unified approach to derive universal approximation theorems for equivariant maps by CNNs in diverse settings.
result Ability to handle non-linear equivariant maps between infinite-dimensional spaces for non-compact groups.
Equivariant diffusion model generates 3D molecules efficiently.
problem Generating high-quality 3D molecules efficiently.
method Equivariant Diffusion Model (EDM) that operates on atom coordinates and types.
result Significantly outperforms previous methods in molecule quality and training efficiency.
New method breaks symmetry in neural networks, improving sample efficiency.
problem Symmetry in neural networks limits their ability to learn unique features.
method Introduces 'relaxed equivariance' to overcome symmetry limitations.
result Equivariant multilayer perceptrons (E-MLPs) can now break symmetry at the sample level.
Measures equivariance in vision models using Lie derivative.
problem Understanding the role of equivariance in recent vision models.
method Introducing Lie derivative to measure equivariance with strong mathematical foundations and minimal hyperparameters.
result Many violations of equivariance can be linked to spatial aliasing in network layers, and larger models tend to display more equivariance.
This work introduces a method for almost equivariance in neural networks using Lie algebra convolutions.
problem Real-world data often does not conform to strict group equivariances, leading to underperformance in models.
method Definition and practical implementation of almost equivariance through Lie algebra convolutions.
result Demonstrated the validity of the approach through benchmarking against fully equivariant settings.
The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image d…
New method constructs equivariant neural networks for arbitrary matrix groups.
problem Challenges in constructing equivariant neural networks for complex groups.
method Completely general algorithm for solving equivariant layers of matrix groups.
result Constructs multilayer perceptrons equivariant to multiple groups including O(1,3), O(5), Sp(n), and Rubik's cube group.
Classifies Cp-surfaces using equivariant surgery methods.
problem Classifying closed, connected 2-manifolds with cyclic group actions.
method Equivariant surgery methods
result Provides representatives of each isomorphism class using surgery operations.
A method for making machine learning units-equivariant using dimensional analysis.
problem Ensuring machine learning models respect dimensional consistency.
method Constructing dimensionless inputs and applying equivariant machine learning methods.
result Improved accuracy in tasks requiring dimensional consistency.
Paper uses algebraic methods to prove an equivariant Poincaré-Hopf theorem.
problem Equivariant index theory on manifolds.
method Localization algebras and Witten deformation techniques in K-homology.
result Established an equivariant version of the Poincaré-Hopf theorem.
Study uses equivariant topology to measure distances between G metric spaces.
problem Measuring distances between G metric spaces.
method Equivariant topology methods to derive lower bounds.
result Sharp bounds on Gromov Hausdorff distance between spheres.
Machine learning uses invariant theory to restrict function classes.
problem Creating function classes that respect physical law constraints.
method Using equivariant machine learning and Malgrance's method to parameterize functions.
result Explicitly parameterizes equivariant functions between linear spaces.
GNPE improves inference for astrophysical systems.
problem Efficiently incorporating geometric properties like equivariances in neural density estimation.
method GNPE integrates equivariances into neural posterior estimation, standardizing data pose while estimating parameters.
result GNPE achieves state-of-the-art accuracy in astrophysical binary black hole inference, reducing inference times by 3 orders of magnitude.
EquivCNP learns group symmetries for conditional data.
problem Learning conditional models with data symmetries.
method Group equivariant decomposition and Lie group convolutional layers.
result EquivCNP achieves comparable performance and zero-shot generalization.
We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy-momentum-Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.
A new method uses algebraic insights to create approximately equivariant networks without complex architectures.
problem Designing equivariant neural networks with complex architectures and high computational cost.
method Imposes the group's regular representation as an inductive bias via an auxiliary loss, adding no learnable parameters.
result Matches or outperforms specialized models in several cases, even for infinite groups.
New method finds Lie group representations without explicit groups, enabling new neural network architectures.
problem Building neural networks equivariant to arbitrary Lie groups.
method Algorithm to find Lie group representations from Lie algebra structure constants. Self-contained method for constructing Lie group-equivariant neural networks.
result First object-tracking model equivariant to the Poincaré group.
New minimal discs and annuli found in ellipsoids.
problem Constructing minimal surfaces in ellipsoids.
method Equivariant variational methods.
result At least three distinct embedded free boundary minimal annuli in ellipsoids.
The paper defines new knot genera and finds bounds for stabilization distances.
problem Finding bounds for stabilization distances of symmetric surfaces.
method Defining new knot genera and using them to find bounds.
result Constructs unknotted symmetric 2-spheres without symmetric 3-ball bounds.
New method for Lagrangian Floer homology groups using flow trees.
problem Computing equivariant Lagrangian Floer homology.
method Constructing and exploiting an A-infinity module structure on the Floer complex.
result Established constructions of equivariant Lagrangian Floer homology groups.
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…
RCNPs extend equivariant neural processes to higher dimensions, improving performance on tasks with inherent symmetries.
problem Inherently equivariant tasks in spatio-temporal modeling, Bayesian Optimization, and continuous control.
method Relational Conditional Neural Processes (RCNPs) that extend equivariances to higher dimensions.
result Empirically competitive performance on tasks with equivariances.
SymPE breaks symmetries in equivariant networks, improving performance across various tasks.
problem Equivariant networks cannot break symmetries, leading to poor performance in tasks with symmetrical inputs.
method Novel equivariant conditional distributions and randomized canonicalization.
result SymPE significantly improves performance of group-equivariant and graph neural networks.
Unified classification of equivariant principal bundles using higher homotopy theory.
problem Unified classification of equivariant principal bundles.
method Smooth Oka principle, singular-cohesive homotopy theory, internally describing principal bundles.
result Unified classification results for equivariant principal bundles.
SymDiff uses stochastic symmetrisation for equivariant diffusion models.
problem Constructing equivariant diffusion models for data augmentation.
method Stochastic symmetrisation for lightweight, efficient, and easy-to-implement equivariance.
result SymDiff achieves significant empirical benefit for E(3)-equivariant molecular generation. The paper studies geometric properties of group equivariant operators and their Riemannian structure.
problem Understanding the geometric structure of group equivariant operators.
method Endowing the space of group equivariant non-expansive operators with a Riemannian manifold structure and using gradient descent methods.
result Gradient descent methods can be applied to minimize cost functions on the space of group equivariant non-expansive operators.
We consider a compact connected CR manifold with a transversal CR locally free R-action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish R-equivariant K…
New fusion blocks improve equivariant neural networks for molecular dynamics.
problem Designing equivariant neural networks for tasks with global symmetries.
method Using fusion diagrams from tensor networks to design novel equivariant components.
result Improved performance with fewer parameters on chemical problems.
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…
We give two generalizations of the Atiyah-Bott-Berline-Vergne localization theorem for the equivariant cohomology of a torus action: 1) replacing the torus action by a compact connected Lie group action, 2) replacing the manifold having a torus action by an equivariant map. This provides a systematic method for calcula…
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.
Proposes SE(3) equivariant graph neural networks with local frames for efficient geometric approximation.
problem Equivariance in deep learning for arbitrary transformations, especially in physics.
method Introduces SE(3) equivariant graph neural networks with complete local frames to efficiently approximate geometric quantities.
result Achieves best or competitive performance in Newton mechanics modeling and equilibrium molecule conformation generation.
Unified framework for image restoration using equivariant denoisers.
problem Restoring images with realistic priors and invariant transformations.
method Unified framework named ERED based on equivariant denoisers and stochastic optimization.
result Unified framework ERED converges and improves image restoration.
Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as equivarification. We further show that group convolutional neural networks (G-CNN…
Graphs benefit from unique node identifiers but lose permutation-equivariance. We propose a method to maintain this property.
problem Graph Neural Networks' inherent limitations due to message-passing structure.
method Propose permutation-equivariant UID models and a contrastive loss to regularize them.
result Our method improves generalization and convergence, achieving state-of-the-art performance.
Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper we show that, with the appropriate modifications and assumptions, the…
Develops a framework for designing quantum neural networks that respect symmetries.
problem Trainability and generalization issues in quantum neural networks.
method Equivariant quantum neural networks (EQNN) for any symmetry group.
result Efficient construction of equivariant layers for EQNNs, including QCNNs.
EbC learns equivariant embeddings from unlabeled group actions.
problem Learning equivariant embeddings from unlabeled group actions.
method Equivariance by Contrast (EbC) method to learn equivariant embeddings from observation pairs (y,g⋅y). result High-fidelity equivariance in latent space for diverse groups.
New method constructs translationally equivariant hyperbolic affine spheres.
problem Constructing translationally equivariant hyperbolic affine spheres.
method Noncompact Iwasawa factorization via DPW method and Weierstrass elliptic functions.
result Every translationally equivariant hyperbolic affine sphere is equiaffinely equivalent to one with a circle, hyperbola, or parabola slice curve.
Translationally equivariant neural networks improve performance and generalization in physics problems.
problem Performance and generalization issues in machine learning applied to physics problems.
method Investigation of translationally equivariant convolutional neural networks for complex scalar field theory on a 2D lattice.
result Translationally equivariant neural networks significantly outperform non-equivariant architectures in various regression and classification tasks.
New robustness measure accounts for task-specific symmetries.
problem Traditional robustness measures fail for tasks with inherent symmetries.
method Sound notion of adversarial robustness for equivariant tasks, using randomized smoothing and graph edit distance certificates.
result Provable robustness can be achieved for various tasks with inherent symmetries.
New neural network processes 3D volumes with improved equivariance.
problem Improving neural network performance on 3D volumes with symmetries.
method Equivariant neural network using moving frames approach.
result Trained model outperforms benchmarks in medical volume classification.
A new training method for efficient Boltzmann generators.
problem Training equivariant continuous normalizing flows (CNFs) is computationally expensive.
method Equivariant flow matching, based on optimal transport flow matching.
result Equivariant flow matching yields more efficient flows with shorter integration paths.
E-NFs generate molecules and their positions while preserving Euclidean symmetries.
problem Generating molecules with their positions while preserving Euclidean symmetries.
method Integrating E(n) graph neural networks into a differential equation to create an invertible equivariant function.
result E-NFs significantly outperform baselines and existing methods in log-likelihood for particle systems and molecules.