Recurrent Equivariant Constraint Modulation: Learning Per-Layer Symmetry Relaxation from Data

• URL: http://arxiv.org/abs/2602.02853v1
• Date: Mon, 02 Feb 2026 21:59:35 GMT
• Title: Recurrent Equivariant Constraint Modulation: Learning Per-Layer Symmetry Relaxation from Data
• Authors: Stefanos Pertigkiozoglou, Mircea Petrache, Shubhendu Trivedi, Kostas Daniilidis,
• Abstract summary: Equivariant neural networks exploit underlying task symmetries to improve generalization.<n>We propose Recurrent Equivariant Constraint Modulation (RECM), a layer-wise constraint modulation mechanism.<n>RECM learns appropriate relaxation levels solely from the training signal and the symmetry properties of each layer's input-target distribution.
• Score: 36.287199718605
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Equivariant neural networks exploit underlying task symmetries to improve generalization, but strict equivariance constraints can induce more complex optimization dynamics that can hinder learning. Prior work addresses these limitations by relaxing strict equivariance during training, but typically relies on prespecified, explicit, or implicit target levels of relaxation for each network layer, which are task-dependent and costly to tune. We propose Recurrent Equivariant Constraint Modulation (RECM), a layer-wise constraint modulation mechanism that learns appropriate relaxation levels solely from the training signal and the symmetry properties of each layer's input-target distribution, without requiring any prior knowledge about the task-dependent target relaxation level. We demonstrate that under the proposed RECM update, the relaxation level of each layer provably converges to a value upper-bounded by its symmetry gap, namely the degree to which its input-target distribution deviates from exact symmetry. Consequently, layers processing symmetric distributions recover full equivariance, while those with approximate symmetries retain sufficient flexibility to learn non-symmetric solutions when warranted by the data. Empirically, RECM outperforms prior methods across diverse exact and approximate equivariant tasks, including the challenging molecular conformer generation on the GEOM-Drugs dataset.

Related papers

• Stability and Generalization of Push-Sum Based Decentralized Optimization over Directed Graphs [55.77845440440496]
  Push-based decentralized communication enables optimization over communication networks, where information exchange may be asymmetric.<n>We develop a unified uniform-stability framework for the Gradient Push (SGP) algorithm.<n>A key technical ingredient is an imbalance-aware generalization bound through two quantities.
  arXiv  Detail & Related papers  (2026-02-24T05:32:03Z)
• Scale redundancy and soft gauge fixing in positively homogeneous neural networks [0.0]
  Neural networks with positively homogeneous activations exhibit an exact continuous reparametrization symmetry.<n>We introduce gauge-adapted coordinates that separate invariant and scale-imbalance directions.<n>Inspired by gauge fixing in field theory, we introduce a soft orbit-selection functional acting only on redundant scale coordinates.
  arXiv  Detail & Related papers  (2026-02-16T13:21:49Z)
• Equivariant Evidential Deep Learning for Interatomic Potentials [55.6997213490859]
  Uncertainty quantification is critical for assessing the reliability of machine learning interatomic potentials in molecular dynamics simulations.<n>Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance.<n>We propose textitEquivariant Evidential Deep Learning for Interatomic Potentials ($texte2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly.
  arXiv  Detail & Related papers  (2026-02-11T02:00:25Z)
• Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environments [10.122552307413711]
  Group symmetries provide a powerful inductive bias for reinforcement learning (RL)<n>Group symmetries provide a powerful inductive bias for reinforcement learning (RL)
  arXiv  Detail & Related papers  (2025-11-30T14:41:08Z)
• Controlled Data Rebalancing in Multi-Task Learning for Real-World Image Super-Resolution [51.79973519845773]
  Real-world image super-resolution (Real-SR) is a challenging problem due to the complex degradation patterns in low-resolution images.<n>We propose an improved paradigm that frames Real-SR as a data-heterogeneous multi-task learning problem.
  arXiv  Detail & Related papers  (2025-06-05T21:40:21Z)
• A Regularization-Guided Equivariant Approach for Image Restoration [46.44312175792672]
  Equivariant and invariant deep learning models have been developed to exploit intrinsic symmetries in data.<n>These methods often suffer from limited representation accuracy and rely on strict symmetry assumptions that may not hold in practice.<n>We propose a rotation-equivariant regularization strategy that adaptively enforces the appropriate symmetry constraints on the data while preserving the network's representational accuracy.
  arXiv  Detail & Related papers  (2025-05-26T10:30:26Z)
• 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)
• Improving Equivariant Model Training via Constraint Relaxation [31.507956579770088]
  We propose a novel framework for improving the optimization of such models by relaxing the hard equivariance constraint during training.<n>We provide experimental results on different state-of-the-art network architectures, demonstrating how this training framework can result in equivariant models with improved generalization performance.
  arXiv  Detail & Related papers  (2024-08-23T17:35:08Z)
• Learning Layer-wise Equivariances Automatically using Gradients [66.81218780702125]
  Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and can not be adapted. Our goal is to allow flexible symmetry constraints that can automatically be learned from data using gradients.
  arXiv  Detail & Related papers  (2023-10-09T20:22:43Z)
• Compressed Regression over Adaptive Networks [58.79251288443156]
  We derive the performance achievable by a network of distributed agents that solve, adaptively and in the presence of communication constraints, a regression problem. We devise an optimized allocation strategy where the parameters necessary for the optimization can be learned online by the agents.
  arXiv  Detail & Related papers  (2023-04-07T13:41:08Z)
• Reinforcement Learning for Adaptive Mesh Refinement [63.7867809197671]
  We propose a novel formulation of AMR as a Markov decision process and apply deep reinforcement learning to train refinement policies directly from simulation. The model sizes of these policy architectures are independent of the mesh size and hence scale to arbitrarily large and complex simulations.
  arXiv  Detail & Related papers  (2021-03-01T22:55:48Z)

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.