一种量化生成模型求解伊辛模型泛化能力的方法
A method for quantifying the generalization capabilities of generative models for solving Ising models
AI总结：
本文提出在变分自回归网络框架中引入汉明距离正则化器，结合基态求解成功率构成量化指标，用于衡量不同网络架构求解伊辛模型的泛化能力，并可辅助大规模问题下的神经架构搜索。
摘要：
对于具有复杂能量景观的伊辛模型，神经网络能否找到基态在很大程度上取决于训练数据集与基态之间的汉明距离。尽管最近提出的各种生成模型在求解伊辛模型方面表现出良好性能，但关于如何量化其泛化能力仍缺乏充分讨论。本文在变分自回归网络（VAN）这一类生成模型框架中设计了一个汉明距离正则化器，用于量化各种网络架构与VAN结合时的泛化能力。该正则化器可以控制基态与网络生成的训练数据集之间重叠的大小，并与找到基态的成功率一起构成量化泛化能力的定量指标。我们在几种典型网络架构上结合VAN进行了数值实验，包括前馈神经网络、循环神经网络和图神经网络，以量化它们在求解伊辛模型时的泛化能力。此外，考虑到在小规模问题上对网络泛化能力的量化可以用于预测其在大规模问题上的相对性能，我们的方法对于辅助神经架构搜索领域中在求解大规模伊辛模型时寻找最优网络架构具有重要意义。
英文摘要：
For Ising models with complex energy landscapes, whether the ground state can be found by neural networks depends heavily on the Hamming distance between the training datasets and the ground state. Despite the fact that various recently proposed generative models have shown good performance in solving Ising models, there is no adequate discussion on how to quantify their generalization capabilities. Here we design a Hamming distance regularizer in the framework of a class of generative models, variational autoregressive networks (VAN), to quantify the generalization capabilities of various network architectures combined with VAN. The regularizer can control the size of the overlaps between the ground state and the training datasets generated by networks, which, together with the success rates of finding the ground state, form a quantitative metric to quantify their generalization capabilities. We conduct numerical experiments on several prototypical network architectures combined with VAN, including feed-forward neural networks, recurrent neural networks, and graph neural networks, to quantify their generalization capabilities when solving Ising models. Moreover, considering the fact that the quantification of the generalization capabilities of networks on small-scale problems can be used to predict their relative performance on large-scale problems, our method is of great significance for assisting in the Neural Architecture Search field of searching for the optimal network architectures when solving large-scale Ising models.
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