Statistical Predictions in String Theory and Deep Generative Models
Statistical Predictions in String Theory and Deep Generative Models
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DOI：
10.1002/prop.202000005
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发表时间：
2020-01
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通讯作者：
James Halverson;Cody Long
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作者：
James Halverson;Cody Long
深度学习中的生成模型允许对近似数据分布的概率分布进行采样。我们建议使用生成模型在弦理论的景观作出近似的统计预测。对于接受拉格朗日描述的真空，这可以被认为是学习耦合的随机张量近似。作为一个具体的原理证明，我们在Calabi-Yau流形的大型集合中证明，在Kähler模空间中的点处评估的Kähler度量可以很好地近似于由深度卷积Wasserstein GAN产生的矩阵集合。精确近似的凯勒度量本征谱实现了远远少于h11高斯绘制。通过条件GAN实现了对训练集之外的h11值的精确外推。总之，这些结果暗示了数据中存在很强的相关性，如果里德的幻想是正确的，这是可以预期的。
Generative models in deep learning allow for sampling probability distributions that approximate data distributions. We propose using generative models for making approximate statistical predictions in the string theory landscape. For vacua admitting a Lagrangian description this can be thought of as learning random tensor approximations of couplings. As a concrete proof‐of‐principle, we demonstrate in a large ensemble of Calabi‐Yau manifolds that Kähler metrics evaluated at points in Kähler moduli space are well‐approximated by ensembles of matrices produced by a deep convolutional Wasserstein GAN. Accurate approximations of the Kähler metric eigenspectra are achieved with far fewer than h11 Gaussian draws. Accurate extrapolation to values of h11 outside the training set are achieved via a conditional GAN. Together, these results implicitly suggest the existence of strong correlations in the data, as might be expected if Reid's fantasy is correct.