循环等变约束调节：从数据中学习每层对称性放松
Recurrent Equivariant Constraint Modulation: Learning Per-Layer Symmetry Relaxation from Data
AI总结：
RECM通过从数据中学习每层对称性放松水平，提高等变神经网络的泛化能力与学习效率。
摘要：
等变神经网络利用底层任务对称性来提高泛化能力，但严格的等变约束可能导致更复杂的优化动态，从而阻碍学习。先前的工作通过在训练过程中放松严格的等变性来解决这些限制，但通常依赖于预设的、显式或隐式的放松水平，这些水平是任务依赖性的且调优成本高。我们提出了循环等变约束调节（RECM），这是一种逐层约束调节机制，该机制仅从训练信号和每层输入-目标分布的对称性属性中学习适当的放松水平，而不需要任何关于任务依赖性目标放松水平的先验知识。我们证明，在所提出的RECM更新下，每层的放松水平可以证明收敛到一个上界，即其对称性缺口，也就是其输入-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的等变性，而那些具有近似对称性的层保留足够的灵活性，以在数据需要时学习非对称解。实验上，RECM在多样化的精确和近似等变任务中均优于先前方法，包括在GEOM-Drugs数据集上的挑战性分子构象生成。
英文摘要：
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.
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