用张量网络形式主义统一 O(3) 等变神经网络设计

IF 6.3 2区 物理与天体物理 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Zimu Li, Zihan Pengmei, Han Zheng, Erik Thiede, Junyu Liu and Risi Kondor
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引用次数: 0

摘要

许多学习任务,包括从原子动力学计算中学习势能面,都涉及原子或一般粒子之间的全局空间对称性和排列对称性。等变图神经网络是解决此类问题的标准方法,其中最成功的方法之一是利用在空间群下变换的各种张量之间的张量乘积。然而,随着不同张量的数量和它们之间关系的复杂性的增加,保持解析性和等差性变得越来越具有挑战性。在本文中,我们建议使用融合图(一种广泛应用于模拟 SU(2)-symmetric 量子多体问题的技术)为神经网络设计新的空间等差数元件。这就产生了一种构建新型神经网络架构的图解方法。当应用于给定局部邻域内的粒子时,由此产生的组件(我们称之为 "融合块")可作为邻域上定义的任何连续等变函数的通用近似值。我们在已有的等变架构(Cormorant 和 MACE)中加入了融合块,从而在一系列具有挑战性的化学问题上以更少的参数提高了性能。此外,我们还将群等变神经网络用于研究二苯乙烯顺反异构的非绝热分子动力学。我们的方法将张量网络与等变神经网络相结合,为设计更具表现力的等变神经网络提供了一个潜在的富有成效的方向。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unifying O(3) equivariant neural networks design with tensor-network formalism
Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard approach to such problems, with one of the most successful methods employing tensor products between various tensors that transform under the spatial group. However, as the number of different tensors and the complexity of relationships between them increase, maintaining parsimony and equivariance becomes increasingly challenging. In this paper, we propose using fusion diagrams, a technique widely employed in simulating SU(2)-symmetric quantum many-body problems, to design new spatial equivariant components for neural networks. This results in a diagrammatic approach to constructing novel neural network architectures. When applied to particles within a given local neighborhood, the resulting components, which we term ‘fusion blocks,’ serve as universal approximators of any continuous equivariant function defined on the neighborhood. We incorporate a fusion block into pre-existing equivariant architectures (Cormorant and MACE), leading to improved performance with fewer parameters on a range of challenging chemical problems. Furthermore, we apply group-equivariant neural networks to study non-adiabatic molecular dynamics of stilbene cis-trans isomerization. Our approach, which combines tensor networks with equivariant neural networks, suggests a potentially fruitful direction for designing more expressive equivariant neural networks.
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来源期刊
Machine Learning Science and Technology
Machine Learning Science and Technology Computer Science-Artificial Intelligence
CiteScore
9.10
自引率
4.40%
发文量
86
审稿时长
5 weeks
期刊介绍: Machine Learning Science and Technology is a multidisciplinary open access journal that bridges the application of machine learning across the sciences with advances in machine learning methods and theory as motivated by physical insights. Specifically, articles must fall into one of the following categories: advance the state of machine learning-driven applications in the sciences or make conceptual, methodological or theoretical advances in machine learning with applications to, inspiration from, or motivated by scientific problems.
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