Gravitational wave science is a pioneering field with rapidly evolving data analysis methodology currently assimilating and inventing deep learning techniques. The bulk of the sophisticated flagship searches of the field rely on the time-tested matched filtering principle within their core. In this paper, we make a key observation on the relationship between the emerging deep learning and the traditional techniques: matched filtering is formally equivalent to a particular neural network. This means that a neural network can be constructed analytically to exactly implement matched filtering, and can be further trained on data or boosted with additional complexity for improved performance. Moreover, we show that the proposed neural network architecture can outperform matched filtering, both with or without knowledge of a prior on the parameter distribution. When a prior is given, the proposed neural network can approach the statistically optimal performance. We also propose and investigate two different neural network architectures MNet-Shallow and MNet-Deep, both of which implement matched filtering at initialization and can be trained on data. MNet-Shallow has simpler structure, while MNet-Deep is more flexible and can deal with a wider range of distributions. Our theoretical findings are corroborated by experiments using real LIGO data and synthetic injections, where our proposed methods significantly outperform matched filtering at false positive rates above $5\times 10^{-3}\%$. The fundamental equivalence between matched filtering and neural networks allows us to define a "complexity standard candle" to characterize the relative complexity of the different approaches to gravitational wave signal searches in a common framework. Finally, our results suggest new perspectives on the role of deep learning in gravitational wave detection.
翻译:重力波科学是一个开创性领域,其数据分析方法正在迅速演变,目前正在同化,并发明深层学习技术。 实地的精密旗舰搜索主要依靠其核心中经过时间测试的匹配过滤原则。 在本文中,我们对新兴深层学习和传统技术之间的关系进行关键观察: 匹配过滤在形式上相当于特定的神经网络。 这意味着神经网络可以分析构建, 以精确地实施匹配过滤, 并且可以进一步接受数据分析培训, 或提高数据复杂性, 改进性能。 此外, 我们显示, 拟议的神经网络结构可以超越过滤系统, 不论是否了解参数分布的先前知识。 在提供之前, 拟议的神经网络可以接近统计上的最佳性业绩。 我们还提议并调查两种不同的神经网络结构 MNet- Shallow 和 MNet- Deepeep, 两者在初始化时执行匹配过滤, 并且可以进行数据培训。 MNet- Shallow有更简单的结构, 而MNet- Develrial- develrial comnial rogration le la la labilal lactional laftal labal laction labal labal labal labal labal lavecial laveal laction ladal laction labal labal labal labildal laveal lads lads 在10 abal laveopmental 10 abal rodal roupdal ladal roupdal roupdmental rodmental roupdmental rodmentddddddmentalds subal subal subal subal subal 中, 我们, 我们我们提出理论方法, 在10 10 a 和在使用10 10 10 和在模拟方法中, 我们 和在模拟分析中建议中建议中建议中建议方法中建议进进进进制的理论方法,我们的理论方法,我们的理论方法中建议的理论方法,我们的理论方法可以大大比比比比比比比比比比比比比比比比比比比比