The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry
The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry
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DOI：
10.48550/arxiv.2211.09231
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Dian Wang;Jung Yeon Park;Neel Sortur;Lawson L. S. Wong;R. Walters;Robert W. Platt
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作者：
Dian Wang;Jung Yeon Park;Neel Sortur;Lawson L. S. Wong;R. Walters;Robert W. Platt
大量的工作已经证明，等变神经网络可以通过在网络架构中强制执行归纳偏差来显着提高样本效率和泛化能力。这些应用通常假设域对称性完全由模型输入和输出的显式变换来描述。然而，许多现实生活中的应用程序只包含潜在的或部分的对称性，这不能很容易地通过简单的输入变换来描述。在这些情况下，有必要在环境中学习对称性，而不是将其数学地强加于网络架构。我们发现，令人惊讶的是，施加不完全匹配的域对称性的等方差约束是非常有帮助的学习真正的对称性的环境。我们区分外在和不正确的对称性约束，并表明，虽然施加不正确的对称性会阻碍模型的性能，施加外在的对称性实际上可以提高性能。我们证明了，在机器人操作和控制问题的监督学习和强化学习中，等变模型在具有潜在对称性的域上的性能明显优于非等变方法。
Extensive work has demonstrated that equivariant neural networks can significantly improve sample efficiency and generalization by enforcing an inductive bias in the network architecture. These applications typically assume that the domain symmetry is fully described by explicit transformations of the model inputs and outputs. However, many real-life applications contain only latent or partial symmetries which cannot be easily described by simple transformations of the input. In these cases, it is necessary to learn symmetry in the environment instead of imposing it mathematically on the network architecture. We discover, surprisingly, that imposing equivariance constraints that do not exactly match the domain symmetry is very helpful in learning the true symmetry in the environment. We differentiate between extrinsic and incorrect symmetry constraints and show that while imposing incorrect symmetry can impede the model's performance, imposing extrinsic symmetry can actually improve performance. We demonstrate that an equivariant model can significantly outperform non-equivariant methods on domains with latent symmetries both in supervised learning and in reinforcement learning for robotic manipulation and control problems.