用机器学习分析6维超引力模型,发现复杂结构与罕见异常模型。
Machine Learning the 6d Supergravity Landscape
- 用自编码器压缩异常系数矩阵,实现模型聚类与降维。
- 识别出难以消除曲率四次项异常的稀有异常模型。
- 构建分类器预测模型一致性,精度达0.91,适用于百万级模型。
本文将监督与无监督机器学习应用于6维$/mathcal{N} = (1,0)$超引力理论的弦景观与沼泽地研究。数据为几乎无反常的模型,以反常系数的格拉姆矩阵表征。通过自编码器进行无监督学习,将格拉姆矩阵压缩至二维,相似模型聚类显现,并揭示显著特征。该方法识别出难以重构的异常模型,其中一例在组合时极难使$ ext{tr}R^{4}$反常消失,表明其在景观中极为罕见。进一步利用监督学习构建两类分类器:(1)探测弦插入下模型一致性,精度0.78,可预测214,837个模型;(2)反常流入下的不一致性,精度0.91,可预测1,909,359个模型。将预测结果投影至自编码器的二维隐空间,一致模型呈现聚集,表明模型已学习到深层复杂特征,可能为6维超引力景观与沼泽地提供新映射路径。
原文摘要 · Abstract (English)
In this paper, we apply both supervised and unsupervised machine learning algorithms to the study of the string landscape and swampland in 6-dimensions. Our data are the (almost) anomaly-free 6-dimensional $\mathcal{N} = (1,0)$ supergravity models, characterised by the Gram matrix of anomaly coefficients. Our work demonstrates the ability of machine learning algorithms to efficiently learn highly complex features of the landscape and swampland. Employing an autoencoder for unsupervised learning, we provide an auto-classification of these models by compressing the Gram matrix data to 2-dimensions. Through compression, similar models cluster together, and we identify prominent features of these clusters. The autoencoder also identifies outlier models which are difficult to reconstruct. One of these outliers proves to be incredibly difficult to combine with other models such that the $\text{tr}R^{4}$ anomaly vanishes, making its presence in the landscape extremely rare. Further, we utilise supervised learning to build two classifiers predicting (1) model consistency under probe string insertion (precision: 0.78, predicting consistency for 214,837 models with reasonable certainty) and (2) inconsistency under anomaly inflow (precision: 0.91, predicting inconsistency for 1,909,359 models). Notably, projecting these predictions onto the autoencoder's 2-dimensional latent layer shows consistent models clustering together, further indicating that the autoencoder has learnt interesting and complex features of the set of models and potentially offers a novel approach to mapping the landscape and swampland of 6-dimensional supergravity theories.
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