It has been proposed that random wide neural networks near Gaussian process
are quantum field theories around Gaussian fixed points. In this paper, we
provide a novel map with which a wide class of quantum mechanical systems can
be cast into the form of a neural network with a statistical summation over
network parameters. Our simple idea is to use the universal approximation
theorem of neural networks to generate arbitrary paths in the Feynman's path
integral. The map can be applied to interacting quantum systems / field
theories, even away from the Gaussian limit. Our findings bring machine
learning closer to the quantum world.

通过使用神经网络的通用逼近定理，本文提出了一种新的映射方法，将广义的量子力学系统转化为带有网络参数统计求和的神经网络形式，从而将机器学习与量子世界更加紧密地联系起来。

量子系统的神经网络表示

Neural network representation of quantum systems

Score-based diffusion models have proven effective in image generation and
have gained widespread usage; however, the underlying factors contributing to
the performance disparity between stochastic and deterministic (i.e., the
probability flow ODEs) sampling schemes remain unclear. We introduce a novel
formulation of diffusion models using Feynman's path integral, which is a
formulation originally developed for quantum physics. We find this formulation
providing comprehensive descriptions of score-based generative models, and
demonstrate the derivation of backward stochastic differential equations and
loss functions.The formulation accommodates an interpolating parameter
connecting stochastic and deterministic sampling schemes, and we identify this
parameter as a counterpart of Planck's constant in quantum physics. This
analogy enables us to apply the Wentzel-Kramers-Brillouin (WKB) expansion, a
well-established technique in quantum physics, for evaluating the negative
log-likelihood to assess the performance disparity between stochastic and
deterministic sampling schemes.

利用费曼路径积分的新方法来描述分数评分的扩散模型，推导了反向随机微分方程和损失函数，通过应用量子物理中的 Wentzel-Kramers-Brillouin (WKB) 展开技术来评估随机和确定性采样方案之间的性能差异。