E Pluribus Unum Ex Machina：同时从许多对撞机事件中学习
E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once
摘要：
最近有一些建议，通过将许多不同的事件组合成一个单一的集合特征，来提高对撞机物理学的机器学习策略的性能。为了评估这些建议的有效性，我们研究了单事件分类器和多事件分类器之间的连接，假设碰撞事件是独立同分布的（IID）。我们展示了如何从单事件分类器构建最佳多事件分类器，我们还展示了如何构建多事件分类器，使其产生最佳单事件分类器。这说明了一个高斯的例子，以及在大型强子对撞机的搜索和测量相关的分类任务。我们将讨论扩展到回归任务，展示它们如何在参数化分类器方面进行措辞。从经验上讲，我们发现训练单事件（每个实例）分类器比训练多事件（每个集成）分类器更有效，至少对于我们研究的情况，我们将这一事实与这两种情况下损失函数梯度的性质联系起来。虽然我们没有确定一个明确的好处，使用多事件分类器在对撞机的情况下，我们推测这些方法的潜在价值的情况下，只涉及近似独立，相关的喷气子结构研究。
英文摘要：
There have been a number of recent proposals to enhance the performance of machine learning strategies for collider physics by combining many distinct events into a single ensemble feature. To evaluate the efficacy of these proposals, we study the connection between single-event classifiers and multi-event classifiers under the assumption that collider events are independent and identically distributed (IID). We show how one can build optimal multi-event classifiers from single-event classifiers, and we also show how to construct multi-event classifiers such that they produce optimal single-event classifiers. This is illustrated for a Gaussian example as well as for classification tasks relevant for searches and measurements at the Large Hadron Collider. We extend our discussion to regression tasks by showing how they can be phrased in terms of parametrized classifiers. Empirically, we find that training a single-event (per-instance) classifier is more effective than training a multi-event (per-ensemble) classifier, as least for the cases we studied, and we relate this fact to properties of the loss function gradient in the two cases. While we did not identify a clear benefit from using multi-event classifiers in the collider context, we speculate on the potential value of these methods in cases involving only approximate independence, as relevant for jet substructure studies.
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