神经网络的纠缠能力
Entangling power of neural networks
AI总结：
该研究针对编码器-解码器神经网络，定义了其纠缠能力并结合多项式解码器精确计算，证实适度资源的神经网络具备指数级纠缠能力，还为机器学习关联分析提供了推广施密特秩的框架。
AI中文摘要：
表征子系统间关联的复杂性是信息论、机器学习及诸多科学领域的基础任务。在量子物理中，神经网络已被越来越多地应用于学习波函数。本文引入编码器-解码器神经网络的纠缠能力，该能力量化其生成子系统间纠缠的本领，取决于潜在空间维度$K$与解码器的复杂度类别。我们针对作用于$K$维潜在空间的$p$次多项式解码器，精确计算了该量。结果表明，拥有适度资源的神经网络具备指数级纠缠能力，更广泛而言，本工作为分析机器学习中的关联提供了一个框架，该框架推广了纠缠理论中的施密特秩概念。
英文摘要：
Characterizing the complexity of correlations between subsystems is a fundamental task across information theory, machine learning, and science. In quantum physics, neural networks have found increasing application in learning wavefunctions. Here we introduce the entangling power of an encoder-decoder neural network, which quantifies its ability to generate entanglement between subsystems, dependent on a latent space dimension $K$ and the complexity class of the decoder. We exactly calculate this quantity for polynomial decoders of degree $p$ acting on a $K$-dimensional latent space. Our results establish the exponential entangling power of neural networks with modest resources. More broadly, our work provides a framework for analyzing correlations in machine learning that generalizes the notion of the Schmidt rank in entanglement theory.
