Symmetry is one of the most central concepts in physics, and it is no
surprise that it has also been widely adopted as an inductive bias for
machine-learning models applied to the physical sciences. This is especially
true for models targeting the properties of matter at the atomic scale. Both
established and state-of-the-art approaches, with almost no exceptions, are
built to be exactly equivariant to translations, permutations, and rotations of
the atoms. Incorporating symmetries -- rotations in particular -- constrains
the model design space and implies more complicated architectures that are
often also computationally demanding. There are indications that non-symmetric
models can easily learn symmetries from data, and that doing so can even be
beneficial for the accuracy of the model. We put a model that obeys rotational
invariance only approximately to the test, in realistic scenarios involving
simulations of gas-phase, liquid, and solid water. We focus specifically on
physical observables that are likely to be affected -- directly or indirectly
-- by symmetry breaking, finding negligible consequences when the model is used
in an interpolative, bulk, regime. Even for extrapolative gas-phase
predictions, the model remains very stable, even though symmetry artifacts are
noticeable. We also discuss strategies that can be used to systematically
reduce the magnitude of symmetry breaking when it occurs, and assess their
impact on the convergence of observables.

对于建模原子尺度物质性质的模型，以对称性作为归纳偏差普遍被采用。然而，非对称模型也能从数据中学习对称性，并对模型准确性有益。本研究测试了一个仅近似满足旋转不变性的模型在模拟气相、液态和固态水的实际场景中的性能，发现其在插值、大体积情况下几乎无影响。即使在外推气相预测中，该模型仍然非常稳定，尽管有对称性伪迹存在。我们还讨论了系统减小对称性破缺程度的策略，并评估其对观测量收敛性的影响。

探究机器学习中破坏对称性的影响

Probing the effects of broken symmetries in machine learning

Efficient representation of quantum many-body states on classical computers
is a problem of enormous practical interest. An ideal representation of a
quantum state combines a succinct characterization informed by the system's
structure and symmetries, along with the ability to predict the physical
observables of interest. A number of machine learning approaches have been
recently used to construct such classical representations [1-6] which enable
predictions of observables [7] and account for physical symmetries [8].
However, the structure of a quantum state gets typically lost unless a
specialized ansatz is employed based on prior knowledge of the system [9-12].
Moreover, most such approaches give no information about what states are easier
to learn in comparison to others. Here, we propose a new generative
energy-based representation of quantum many-body states derived from Gibbs
distributions used for modeling the thermal states of classical spin systems.
Based on the prior information on a family of quantum states, the energy
function can be specified by a small number of parameters using an explicit
low-degree polynomial or a generic parametric family such as neural nets, and
can naturally include the known symmetries of the system. Our results show that
such a representation can be efficiently learned from data using exact
algorithms in a form that enables the prediction of expectation values of
physical observables. Importantly, the structure of the learned energy function
provides a natural explanation for the hardness of learning for a given class
of quantum states.

论文提出了一种新的基于能量的生成量子多体状态表示方法，该方法可以在保留系统已知对称性与结构的情况下，使用一个小数量的参数进行学习，并且可以用于预测物理观测量的期望值

学习基于能量的量子多体态表示

Learning Energy-Based Representations of Quantum Many-Body States

The mechanism by which thermodynamics sets the direction of time's arrow has
long fascinated scientists. Here, we show that a machine learning algorithm can
learn to discern the direction of time's arrow when provided with a system's
microscopic trajectory as input. The performance of our algorithm matches
fundamental bounds predicted by nonequilibrium statistical mechanics.
Examination of the algorithm's decision-making process reveals that it
discovers the underlying thermodynamic mechanism and the relevant physical
observables. Our results indicate that machine learning techniques can be used
to study systems out of equilibrium, and ultimately to uncover physical
principles.

机器学习算法可以使用系统的微观轨迹作为输入来辨别时间箭头的方向，其性能符合非平衡态统计力学所预测的基本极限。算法的决策过程解释了发现了潜在的热力学机制和相关物理观测量。结果表明，机器学习技术可以用于研究非平衡态系统，并最终揭示物理原理。