In this work, we present a neural approach to reconstructing rooted tree graphs describing hierarchical interactions, using a novel representation we term the Lowest Common Ancestor Generations (LCAG) matrix. This compact formulation is equivalent to the adjacency matrix, but enables learning a tree's structure from its leaves alone without the prior assumptions required if using the adjacency matrix directly. Employing the LCAG therefore enables the first end-to-end trainable solution which learns the hierarchical structure of varying tree sizes directly, using only the terminal tree leaves to do so. In the case of high-energy particle physics, a particle decay forms a hierarchical tree structure of which only the final products can be observed experimentally, and the large combinatorial space of possible trees makes an analytic solution intractable. We demonstrate the use of the LCAG as a target in the task of predicting simulated particle physics decay structures using both a Transformer encoder and a Neural Relational Inference encoder Graph Neural Network. With this approach, we are able to correctly predict the LCAG purely from leaf features for a maximum tree-depth of $8$ in $92.5\%$ of cases for trees up to $6$ leaves (including) and $59.7\%$ for trees up to $10$ in our simulated dataset.
翻译:在这项工作中,我们展示了一种神经学方法来重建植树图,说明等级互动,我们用一种新型的表述方式,我们称之为低能粒子物理学,粒子衰变形成一种等级树结构,其中只有最后产品可以实验地观察,而可能树木的庞大组合空间使得分析性解决办法难以解决。我们用LCG来证明使用模拟粒子物理腐烂结构作为任务的目标,同时使用变压器和神经反应反应器,直接了解不同树大小的等级结构,只使用终端树叶来这样做。在高能粒子物理学中,粒子衰变形形成一种等级树结构,只有最后产品可以实验地观察,而可能树木的庞大组合空间使得分析性解决办法难以解决。我们用LCG作为预测模拟粒子物理腐坏结构的目标,同时使用变压器和神经反应反应器,只使用终端树叶状图。通过这种方法,我们可以准确地预测LCG纯值$,从叶色特性到最高值的美元,从每棵树的9-2.5美元到最深的8美元。