Develops approximately equivariant neural processes for better data modeling.
problem Real-world data often breaks exact equivariance; how to model this?
method General approach to creating approximately equivariant architectures, applicable to any model and symmetry group.
result Approximately equivariant neural processes outperform non-equivariant and strictly equivariant models in regression tasks.
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.
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.
New mesh network preserves symmetries in deep learning.
problem No existing mesh processing architecture is equivariant to all symmetries.
method Equivariant attention-based mesh network using relative tangential features.
result The network achieves improved performance and is equivariant to various transformations.
Equivariant neural networks improve performance and generalization in complex scalar field theory tasks.
problem Improving performance and generalization in neural networks for complex scalar field theory tasks.
method Incorporating translational equivariance into neural network architectures.
result Equivariant neural networks significantly outperform non-equivariant networks in various tasks, including those beyond the training set and across different lattice sizes.
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 neural network architecture for auction design exploiting permutation symmetry.
problem Designing incentive-compatible auctions that maximize expected revenue.
method Constructed a permutation-equivariant neural network architecture.
result Permutation-equivariant architectures can perfectly recover optimal mechanisms.
Improves U-Net for scale equivariance in semantic segmentation.
problem Improving generalization in semantic segmentation tasks with varying scales.
method Introduces Scale Equivariant U-Net (SEU-Net) with carefully applied subsampling and upsampling layers and scale-equivariant layers.
result Significantly improved generalization to different scales compared to U-Net and scale-equivariant architecture without upsampling.
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.
Equivariant neural network simplifies particle physics models.
problem Complexity and interpretability in particle physics classification.
method Lorentz group equivariant neural network architecture.
result Simplified, interpretable models with fewer parameters.
ESAN improves graph neural networks by processing subgraphs.
problem Limitations of MPNNs in graph isomorphism.
method ESAN represents graphs as sets of subgraphs and processes them with equivariant architectures.
result ESAN increases the expressive power of GNNs and more expressive architectures.
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…
Equivariant neural networks improve performance and generalization in lattice field theory tasks.
problem Improving neural network performance and generalization in lattice field theory.
method Investigation of translationally equivariant neural networks in a two-dimensional scalar field model.
result Equivariant neural networks significantly outperform non-equivariant ones in various tasks, including physical parameters and lattice sizes.
LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.
problem Limitations of specialized layers in Lorentz-equivariant neural networks.
method LLoCa framework using local reference frames and geometric message passing.
result Models achieve competitive and state-of-the-art accuracy on particle physics tasks.
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…
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.
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.
Develops neural networks for reductive Lie groups, enhancing symmetry respect.
problem Symmetry respect in neural networks for reductive Lie groups.
method General equivariant neural network architecture for any reductive Lie Group G.
result Demonstrates generality and performance in top quark decay tagging and shape recognition.
Frame Averaging makes neural networks invariant or equivariant to new symmetries.
problem Designing neural networks that respect symmetries while being expressive and efficient.
method Introduces Frame Averaging (FA) as a systematic framework to adapt architectures to become invariant or equivariant to new symmetries.
result Frame Averaging guarantees exact invariance or equivariance while being simpler to compute than full group averaging.
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.
SpeqNets improve graph neural networks by scaling and adapting to graph sparsity.
problem Graph neural networks struggle with permutation-equivariant functions and scalability to large graphs.
method Introducing sparsity-aware, permutation-equivariant graph networks with heuristics for graph isomorphism.
result Significantly improved predictive performance and reduced computation times compared to existing methods.
Bayesian convolutional deep sets improve ambiguity in stationary process modeling.
problem Ambiguity in translation equivariant functional representations due to insufficient data points.
method Introduce Bayesian convolutional deep sets with task-dependent stationary prior.
result Improves representation quality compared to kernel smoother and non-parametric models.
SE-RRMs solve structured problems like Sudoku and ARC-AGI by enforcing symbol equivariance.
problem Structured reasoning problems like Sudoku and ARC-AGI.
method Symbol-equivariant recurrent reasoning models enforcing permutation equivariance.
result SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize to larger and smaller instances.
L-CNNs preserve gauge symmetry in lattice simulations.
problem Breaking gauge symmetry in neural network models.
method Lattice gauge equivariant convolutional neural networks (L-CNNs).
result L-CNNs represent gauge invariant functions on the lattice.
L-CNNs preserve gauge symmetry in neural networks.
problem Applying machine learning to lattice gauge theory while preserving gauge symmetry.
method L-CNNs use gauge equivariance to construct a gauge equivariant convolutional layer and bilinear layer.
result L-CNNs achieve higher accuracy in non-linear regression tasks compared to non-equivariant CNNs.
Generalizes CNNs for Lie group equivariance across various data types.
problem Equivariance to transformations like rotations for non-image data.
method Constructs equivariant convolutional layers for Lie groups.
result Models conserve linear and angular momentum in Hamiltonian systems.
GNNs generalize CNNs for graph data, showing equivariance and stability.
problem Processing signals on graphs.
method Graph convolutional filters, nonlinearities, stacked layers.
result GNNs converge to graphon neural networks under graph convergence.
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.
Equivariant CNNs improve RL performance in symmetric environments.
problem Learning equivariant representations for RL in symmetric environments.
method Proposed and studied equivariant CNNs for RL.
result Equivariant CNNs enhance RL performance and sample efficiency.
Sign equivariant networks improve model expressiveness for spectral geometric learning.
problem Limited expressiveness of sign invariant models for tasks like graph link prediction.
method Developed sign equivariant neural network architectures based on new analytic sign equivariant polynomials.
result Sign equivariant models achieve theoretical benefits in spectral geometric learning tasks.
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.
Unified framework for machine learning interatomic potentials.
problem Designing and optimizing machine learning models for interatomic potentials.
method Unified mathematical framework unifying ACE and NequIP, providing a systematic design space.
result Demonstrated through ablation studies, critical design choices for high accuracy.
Weisfeiler and Leman enhance graph learning for machine learning tasks.
problem Learning from graph data in machine learning.
method Weisfeiler and Leman algorithm applied to graph and node representation learning.
result The algorithm improves graph and node representation learning in machine learning.
This paper explores how enforcing equivariance constraints limits neural network expressivity and proposes compensatory model size increases.
problem The impact of enforcing equivariance constraints on the expressive power of neural networks.
method Examined 2-layer ReLU networks, analyzed boundary hyperplanes and channel vectors, and constructed upper bounds on model size required for compensation.
result Enforcing equivariance constraints reduces the expressive power of neural networks, but this can be compensated by increasing model size.
MFNs parameterize non-local interactions through matrix equivariant functions, improving graph neural network performance.
problem Challenges in modeling non-local interactions in graphs, such as oversmoothing and oversquashing.
method Matrix Function Neural Networks (MFNs) using resolvent expansions for non-local interactions.
result Achieves state-of-the-art performance in graph benchmarks and captures intricate non-local interactions.
Graph Metanetworks process diverse neural architectures efficiently.
problem Processing diverse neural architectures efficiently.
method Builds metanetworks using graph neural networks to process graphs representing input neural networks.
result Proves GMNs are expressive and equivariant to parameter permutation symmetries.
Paper presents a novel neural network for MIMO symbol detection.
problem Handling a variable number of users in MIMO systems.
method Recurrent and permutation equivariant neural network architecture with iterative decoding.
result The neural detector outperforms existing methods in accuracy and efficiency.
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. 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.
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.
Derives formulae for general permutation equivariant layers and presents a second order graph variational encoder.
problem Tackles the limitation of previous equivariant neural networks by considering permutations of matrices.
method Derives formulae for general permutation equivariant layers, including matrix permutations. Presents a second order graph variational encoder.
result Latent distribution of equivariant generative models must be exchangeable.
LieTransformer extends self-attention to Lie groups for improved deep learning tasks.
problem Improving deep learning performance through group equivariant self-attention.
method LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups.
result Competitive experimental results on various tasks.
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.
Paper compares expressive power of GNNs, proving approximation guarantees for practical architectures.
problem Understanding the expressive power of Graph Neural Networks (GNNs).
method Theoretical framework comparing invariant and equivariant GNNs, proving approximation guarantees for practical architectures.
result Folklore Graph Neural Networks (FGNN) are the most expressive architectures for a given tensor order.
The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.
problem Equivariant neural networks on homogeneous spaces.
method Deriving generalized steerability constraints for non-linear equivariant layers.
result The universality of the derived construction for non-linear equivariant layers.
L-GATr transforms high-energy physics data using geometric algebra and Lorentz symmetry.
problem Extracting scientific understanding from particle-physics experiments with high precision and efficiency.
method L-GATr, a geometric algebra Transformer, representing data in 4D space-time and being equivariant under Lorentz transformations.
result L-GATr achieves performance comparable to or better than domain-specific baselines on regression, classification, and generative tasks.
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…
In this work we propose a new neural network architecture that efficiently implements and learns general purpose set-equivariant functions. Such a function f maps a set of entities x = {x1, . . . , xn} from one domain to a set of same cardinality y = f (x) = {y1, . . . , yn} in another domain regardless of the ordering…