Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions

• URL: http://arxiv.org/abs/2510.21706v1
• Date: Fri, 24 Oct 2025 17:59:46 GMT
• Title: Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actions
• Authors: Tobias Schmidt, Steffen Schneider, Matthias Bethge,
• Abstract summary: We learn equivariant embeddings from observation pairs $(mathbfy, g cdot mathbfy)$, where $g$ is drawn from a finite group acting on the data.<n>Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps.
• Score: 18.11344454990819
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

Related papers

• Lie Group Decompositions for Equivariant Neural Networks [12.139222986297261]
  We show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the benchmark affine-invariant classification task.
  arXiv  Detail & Related papers  (2023-10-17T16:04:33Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Equivariant Representation Learning in the Presence of Stabilizers [13.11108596589607]
  EquIN is suitable for group actions that are not free, i.e., that stabilize data via nontrivial symmetries. EquIN is theoretically grounded in the orbit-stabilizer theorem from group theory.
  arXiv  Detail & Related papers  (2023-01-12T11:43:26Z)
• Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views? [21.06669693699965]
  We find that the fraction of separable dichotomies is determined by the dimension of the space that is fixed by the group action. We show how this relation extends to operations such as convolutions, element-wise nonlinearities, and global and local pooling.
  arXiv  Detail & Related papers  (2021-10-14T15:46:53Z)
• Group Equivariant Subsampling [60.53371517247382]
  Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions. We first introduce translation equivariant subsampling/upsampling layers that can be used to construct exact translation equivariant CNNs. We then generalise these layers beyond translations to general groups, thus proposing group equivariant subsampling/upsampling.
  arXiv  Detail & Related papers  (2021-06-10T16:14:00Z)
• Commutative Lie Group VAE for Disentanglement Learning [96.32813624341833]
  We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. A simple model named Commutative Lie Group VAE is introduced to realize the group-based disentanglement learning. Experiments show that our model can effectively learn disentangled representations without supervision, and can achieve state-of-the-art performance without extra constraints.
  arXiv  Detail & Related papers  (2021-06-07T07:03:14Z)
• A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups [115.58550697886987]
  We provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before. Our approach outperforms non-equivariant baselines, with applications to particle physics and dynamical systems.
  arXiv  Detail & Related papers  (2021-04-19T17:21:54Z)
• On the geometric and Riemannian structure of the spaces of group equivariant non-expansive operators [0.0]
  Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning. We show how a space $mathcalF$ of group equivariant non-expansive operators can be endowed with the structure of a Riemannian manifold. We also describe a procedure to select a finite set of representative group equivariant non-expansive operators in the considered manifold.
  arXiv  Detail & Related papers  (2021-03-03T17:29:25Z)
• GroupifyVAE: from Group-based Definition to VAE-based Unsupervised Representation Disentanglement [91.9003001845855]
  VAE-based unsupervised disentanglement can not be achieved without introducing other inductive bias. We address VAE-based unsupervised disentanglement by leveraging the constraints derived from the Group Theory based definition as the non-probabilistic inductive bias. We train 1800 models covering the most prominent VAE-based models on five datasets to verify the effectiveness of our method.
  arXiv  Detail & Related papers  (2021-02-20T09:49:51Z)
• Group Equivariant Conditional Neural Processes [30.134634059773703]
  We present the group equivariant conditional neural process (EquivCNP) We show that EquivCNP achieves comparable performance to conventional conditional neural processes in a 1D regression task.
  arXiv  Detail & Related papers  (2021-02-17T13:50:07Z)
• LieTransformer: Equivariant self-attention for Lie Groups [49.9625160479096]
  Group equivariant neural networks are used as building blocks of group invariant neural networks. We extend the scope of the literature to self-attention, that is emerging as a prominent building block of deep learning models. We propose the LieTransformer, an architecture composed of LieSelfAttention layers that are equivariant to arbitrary Lie groups and their discrete subgroups.
  arXiv  Detail & Related papers  (2020-12-20T11:02:49Z)
• Stochastic Flows and Geometric Optimization on the Orthogonal Group [52.50121190744979]
  We present a new class of geometrically-driven optimization algorithms on the orthogonal group $O(d)$. We show that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, flows and metric learning.
  arXiv  Detail & Related papers  (2020-03-30T15:37:50Z)

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.