原子机器学习的最优不变基
Optimal Invariant Bases for Atomistic Machine Learning
AI总结：
本文通过移除冗余的函数依赖描述符，构建了满足完整性的最小原子环境描述符集，并基于此改进了原子团簇展开和标量神经网络，提出了一种能在每个神经元识别多达5体模式的新消息传递网络架构，在保持低计算成本的同时实现了高精度。
摘要：
原子构型的表示为机器学习模型催生了众多描述符，通常用于描述原子的局部环境。然而，许多此类表示是不完整和/或存在函数依赖的。不完整的描述符集无法表示原子环境中所有有意义的变化。另一方面，原子环境描述符的完整构造通常存在高度的函数依赖，即某些描述符可以写成其他描述符的函数。这些冗余描述符不能提供区分不同原子环境的额外能力，反而增加了计算负担。通过将模式识别文献中的技术应用于现有的原子表示，我们移除了作为其他描述符函数的描述符，从而产生满足完整性的最小可能集合。我们以两种方式应用此方法：首先，我们改进了现有描述——原子团簇展开（Atomistic Cluster Expansion）。我们证明这产生了一个更高效的描述符子集。其次，我们增强了一个基于标量神经网络的非完整构造，产生了一种新的消息传递网络架构，该架构通过利用笛卡尔张量不变量的最优集，能够在每个神经元中识别多达5体模式。该架构在保持低计算成本的同时，在最新基准测试中表现出强大的准确性。我们的结果不仅产生了改进的模型，而且为在众多应用中最小化成本同时最大化表达力的不变基类别指明了方向。
英文摘要：
The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or functionally dependent. Incomplete descriptor sets are unable to represent all meaningful changes in the atomic environment. Complete constructions of atomic environment descriptors, on the other hand, often suffer from a high degree of functional dependence, where some descriptors can be written as functions of the others. These redundant descriptors do not provide additional power to discriminate between different atomic environments and increase the computational burden. By employing techniques from the pattern recognition literature to existing atomistic representations, we remove descriptors that are functions of other descriptors to produce the smallest possible set that satisfies completeness. We apply this in two ways: first we refine an existing description, the Atomistic Cluster Expansion. We show that this yields a more efficient subset of descriptors. Second, we augment an incomplete construction based on a scalar neural network, yielding a new message-passing network architecture that can recognize up to 5-body patterns in each neuron by taking advantage of an optimal set of Cartesian tensor invariants. This architecture shows strong accuracy on state-of-the-art benchmarks while retaining low computational cost. Our results not only yield improved models, but point the way to classes of invariant bases that minimize cost while maximizing expressivity for a host of applications.
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。
