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arXiv 2302.00236cs.LG
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生成对抗对称性发现

Generative Adversarial Symmetry Discovery

University of California San Diego(加州大学圣地亚哥分校);Northeastern University(东北大学);IBM Research(IBM研究院)

Jianke Yang, Robin Walters, Nima Dehmamy, Rose Yu

AI总结:

提出LieGAN框架,通过生成对抗训练自动从数据中发现对称性,表示为可解释的李代数基,并提升现有等变神经网络的准确性和泛化能力。

摘要:

尽管等变神经网络在科学应用中取得了成功,但它们需要事先知道对称群。然而,在实践中可能难以知道哪种对称性适合作为归纳偏置。强制错误的对称性甚至可能损害性能。在本文中,我们提出了一个框架LieGAN,使用类似于生成对抗训练的模式从数据集中自动发现等变性。具体来说,生成器学习应用于数据的一组变换,这些变换保持原始分布并欺骗判别器。LieGAN将对称性表示为可解释的李代数基,并能在轨迹预测和顶夸克标记任务中发现各种对称性,如旋转群SO(n)、受限洛伦兹群SO(1,3)^+。学习到的对称性也可以直接用于几种现有的等变神经网络,以提高预测的准确性和泛化能力。

英文摘要:

Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the wrong symmetry could even hurt the performance. In this paper, we propose a framework, LieGAN, to automatically discover equivariances from a dataset using a paradigm akin to generative adversarial training. Specifically, a generator learns a group of transformations applied to the data, which preserve the original distribution and fool the discriminator. LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries such as the rotation group $\mathrm{SO}(n)$, restricted Lorentz group $\mathrm{SO}(1,3)^+$ in trajectory prediction and top-quark tagging tasks. The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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