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.

翻译：等变神经网络利用底层任务对称性来提升泛化能力，但严格的等变约束可能引发更复杂的优化动态，从而阻碍学习。先前的研究通过在训练期间松弛严格等变来解决这些限制，但通常依赖于为每个网络层预设的、显式或隐式的目标松弛水平，这些水平是任务依赖的且调优成本高昂。我们提出了循环等变约束调制（RECM），这是一种逐层约束调制机制，它仅从训练信号以及每层输入-目标分布的对称性属性中学习适当的松弛水平，而无需任何关于任务依赖的目标松弛水平的先验知识。我们证明，在所提出的RECM更新下，每层的松弛水平可证明地收敛到一个值，该值以其对称性间隙为上界，即其输入-目标分布偏离精确对称性的程度。因此，处理对称分布的层恢复完全等变性，而具有近似对称性的层则保留足够的灵活性，以便在数据需要时学习非对称解。实证结果表明，RECM在多种精确和近似等变任务上优于先前的方法，包括在GEOM-Drugs数据集上具有挑战性的分子构象生成任务。