Incorporating equivariance as an inductive bias into deep learning architectures to take advantage of the data symmetry has been successful in multiple applications, such as chemistry and dynamical systems. In particular, roto-translations are crucial for effectively modeling geometric graphs and molecules, where understanding the 3D structures enhances generalization. However, strictly equivariant models often pose challenges due to their higher computational complexity. In this paper, we introduce REMUL, a training procedure that learns \emph{approximate} equivariance for unconstrained networks via multitask learning. By formulating equivariance as a tunable objective alongside the primary task loss, REMUL offers a principled way to control the degree of approximate symmetry, relaxing the rigid constraints of traditional equivariant architectures. We show that unconstrained models (which do not build equivariance into the architecture) can learn approximate symmetries by minimizing an additional simple equivariance loss. This enables quantitative control over the trade-off between enforcing equivariance constraints and optimizing for task-specific performance. Our method achieves competitive performance compared to equivariant baselines while being significantly faster (up to 10$\times$ at inference and 2.5$\times$ at training), offering a practical and adaptable approach to leveraging symmetry in unconstrained architectures.

翻译：将等变性作为归纳偏置融入深度学习架构以利用数据对称性，已在化学和动力学系统等多个应用领域取得成功。特别是，旋转平移对于有效建模几何图与分子至关重要，其中理解三维结构能提升泛化能力。然而，严格等变模型常因其较高的计算复杂度而带来挑战。本文提出REMUL，一种通过多任务学习为无约束网络学习近似等变性的训练方法。通过将等变性构建为与主任务损失并列的可调目标，REMUL提供了一种控制近似对称程度的原理性方法，从而松弛了传统等变架构的刚性约束。我们证明，无约束模型（未在架构中内置等变性）可通过最小化额外的简单等变损失来学习近似对称性。这使得在强制等变约束与优化任务特定性能之间的权衡得以量化控制。与等变基线模型相比，我们的方法实现了具有竞争力的性能，同时显著提升了速度（推理阶段最高达10倍，训练阶段达2.5倍），为在无约束架构中利用对称性提供了一种实用且适应性强的方法。