论文标题
神经网络中的新量子
Emergent Quantumness in Neural Networks
论文作者
论文摘要
最近显示，Madelung方程，即Schrödinger方程的流体动力形式，可以从神经网络的规范集合中得出，在该集合中，用隐藏变量的自由能鉴定了量子相。相反，我们认为神经网络的宏伟典型合奏是通过允许与辅助子系统的神经元交换，以表明自由能也必须是多相关的。通过在自由能中施加多价条件，我们通过隐藏变量的化学潜力确定了“普朗克的常数”来得出Schrödinger方程。这表明量子力学对学习均衡的神经网络的大规范集合的动力学提供了正确的统计描述。我们还讨论了结果对机器学习，基本物理学以及更具推测性的进化生物学的影响。
It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schrödinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden variables. We consider instead a grand canonical ensemble of neural networks, by allowing an exchange of neurons with an auxiliary subsystem, to show that the free energy must also be multivalued. By imposing the multivaluedness condition on the free energy we derive the Schrödinger equation with "Planck's constant" determined by the chemical potential of hidden variables. This shows that quantum mechanics provides a correct statistical description of the dynamics of the grand canonical ensemble of neural networks at the learning equilibrium. We also discuss implications of the results for machine learning, fundamental physics and, in a more speculative way, evolutionary biology.
