arXiv:2602.02853cs.LG2026-02

让神经网络自动学习每层的对称性松弛程度,提升模型泛化能力。

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

  • 基于训练信号和输入输出对称性,自适应调节每层对称约束强度。
  • 理论证明各层松弛度收敛于对称性偏差上界,保持对称时恢复完整等变性。
  • 适用于分子构象生成等复杂任务,无需人工调参,效果优于现有方法。

等变神经网络利用任务中的对称性提升泛化性能,但严格的等变约束会引发复杂的优化动态,阻碍学习。以往方法虽在训练中放宽等变性,但通常依赖预设的目标松弛水平,且需针对不同任务手动调整,成本高。本文提出递归等变约束调制(RECM),一种逐层约束调制机制,仅根据训练信号和各层输入-目标分布的对称性属性,自动学习合适的松弛程度,无需预先知晓任务相关的最优松弛值。我们证明,在所提的RECM更新规则下,每层的松弛程度可证明收敛至其对称性差距的上界,即输入-目标分布偏离精确对称的程度。因此,处理对称分布的层可恢复完全等变性,而具有近似对称性的层则保留足够灵活性,以在数据需要时学习非对称解。实验表明,RECM在多种精确与近似等变任务中表现超越先前方法,包括在GEOM-Drugs数据集上的分子构象生成这一挑战性任务。

原文摘要 · Abstract (English)

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.

等变网络自适应约束分子生成

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