Approximate equivariance via projection-based regularisation

• URL: http://arxiv.org/abs/2601.05028v1
• Date: Thu, 08 Jan 2026 15:35:42 GMT
• Title: Approximate equivariance via projection-based regularisation
• Authors: Torben Berndt, Jan Stühmer,
• Abstract summary: Non-equivariant models have regained attention, due to their better runtime performance and imperfect symmetries.<n>This has motivated the development of approximately equivariant models that strike a middle ground between respecting symmetries and fitting the data distribution.<n>We present a mathematical framework for computing the non-equivariance penalty exactly and efficiently in both the spatial and spectral domain.
• Score: 1.5755923640031846
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Equivariance is a powerful inductive bias in neural networks, improving generalisation and physical consistency. Recently, however, non-equivariant models have regained attention, due to their better runtime performance and imperfect symmetries that might arise in real-world applications. This has motivated the development of approximately equivariant models that strike a middle ground between respecting symmetries and fitting the data distribution. Existing approaches in this field usually apply sample-based regularisers which depend on data augmentation at training time, incurring a high sample complexity, in particular for continuous groups such as $SO(3)$. This work instead approaches approximate equivariance via a projection-based regulariser which leverages the orthogonal decomposition of linear layers into equivariant and non-equivariant components. In contrast to existing methods, this penalises non-equivariance at an operator level across the full group orbit, rather than point-wise. We present a mathematical framework for computing the non-equivariance penalty exactly and efficiently in both the spatial and spectral domain. In our experiments, our method consistently outperforms prior approximate equivariance approaches in both model performance and efficiency, achieving substantial runtime gains over sample-based regularisers.

Related papers

• Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation [56.361076943802594]
  CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
  arXiv  Detail & Related papers  (2026-02-16T18:58:55Z)
• Unconditional flow-based time series generation with equivariance-regularised latent spaces [0.0]
  Flow-based models have proven successful for time-series generation.<n>However, how to design latent representations with desirable equivariance properties for time-series generative modelling remains underexplored.<n>We propose a latent flow-matching framework in which equivariance is explicitly encouraged through a simple regularisation of a pre-trained autoencoder.
  arXiv  Detail & Related papers  (2026-01-30T11:19:33Z)
• Learning (Approximately) Equivariant Networks via Constrained Optimization [25.51476313302483]
  Equivariant neural networks are designed to respect symmetries through their architecture.<n>Real-world data often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects.<n>We introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model.
  arXiv  Detail & Related papers  (2025-05-19T18:08:09Z)
• Rao-Blackwell Gradient Estimators for Equivariant Denoising Diffusion [55.95767828747407]
  In domains such as molecular and protein generation, physical systems exhibit inherent symmetries that are critical to model.<n>We present a framework that reduces training variance and provides a provably lower-variance gradient estimator.<n>We also present a practical implementation of this estimator incorporating the loss and sampling procedure through a method we call Orbit Diffusion.
  arXiv  Detail & Related papers  (2025-02-14T03:26:57Z)
• Symmetry and Generalisation in Machine Learning [0.0]
  We show that for any predictor that is not equivariant, there is an equivariant predictor with strictly lower test risk on all regression problems.<n>We adopt an alternative perspective and formalise the common intuition that learning with invariant models reduces to a problem in terms of orbit representatives.
  arXiv  Detail & Related papers  (2025-01-07T15:14:58Z)
• Equivariant score-based generative models provably learn distributions with symmetries efficiently [7.90752151686317]
  Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization and sampling efficiency. We provide the first theoretical analysis and guarantees of score-based generative models (SGMs) for learning distributions that are invariant with respect to some group symmetry.
  arXiv  Detail & Related papers  (2024-10-02T05:14:28Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Supervised Contrastive Learning with Heterogeneous Similarity for Distribution Shifts [3.7819322027528113]
  We propose a new regularization using the supervised contrastive learning to prevent such overfitting and to train models that do not degrade their performance under the distribution shifts. Experiments on benchmark datasets that emulate distribution shifts, including subpopulation shift and domain generalization, demonstrate the advantage of the proposed method.
  arXiv  Detail & Related papers  (2023-04-07T01:45:09Z)
• Equivariant Disentangled Transformation for Domain Generalization under Combination Shift [91.38796390449504]
  Combinations of domains and labels are not observed during training but appear in the test environment. We provide a unique formulation of the combination shift problem based on the concepts of homomorphism, equivariance, and a refined definition of disentanglement.
  arXiv  Detail & Related papers  (2022-08-03T12:31:31Z)
• Predicting Out-of-Domain Generalization with Neighborhood Invariance [59.05399533508682]
  We propose a measure of a classifier's output invariance in a local transformation neighborhood. Our measure is simple to calculate, does not depend on the test point's true label, and can be applied even in out-of-domain (OOD) settings. In experiments on benchmarks in image classification, sentiment analysis, and natural language inference, we demonstrate a strong and robust correlation between our measure and actual OOD generalization.
  arXiv  Detail & Related papers  (2022-07-05T14:55:16Z)
• Equivariance Discovery by Learned Parameter-Sharing [153.41877129746223]
  We study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. Also, we theoretically analyze the method for Gaussian data and provide a bound on the mean squared gap between the studied discovery scheme and the oracle scheme.
  arXiv  Detail & Related papers  (2022-04-07T17:59:19Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Decentralized Local Stochastic Extra-Gradient for Variational Inequalities [125.62877849447729]
  We consider distributed variational inequalities (VIs) on domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that covers the settings of fully decentralized calculations. We theoretically analyze its convergence rate in the strongly-monotone, monotone, and non-monotone settings.
  arXiv  Detail & Related papers  (2021-06-15T17:45:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.