arXiv 2009.040772020-09eess.AScs.LGcs.SDeess.SP

1-用于音频信号相关问题的维数多项式神经网络

1-Dimensional polynomial neural networks for audio signal related problems

University of Winnipeg（温尼伯大学）

Habib Ben Abdallah, Christopher J. Henry, Sheela Ramanna

DOI：: 10.1016/j.knosys.2022.108174

摘要：

除了极端非线性之外，现代问题需要数百万甚至数十亿个参数来解决或至少获得解决方案的良好近似，并且已知神经网络通过深化和扩大其拓扑结构来吸收这种复杂性，以增加更好近似所需的非线性水平。然而，紧凑的拓扑结构总是比更深的拓扑结构更受欢迎，因为它们提供了使用更少计算单元和更少参数的优势。这种紧凑性是以减少非线性为代价的，因此，有限的解决方案搜索空间。我们提出了1维多项式神经网络（1DPNN）模型，该模型使用1维卷积神经网络（1DCNN）的自动多项式核估计，并从第一层引入了高度的非线性，可以补偿对深度和/或宽拓扑结构的需求。我们表明，这种非线性使该模型能够在与音频信号相关的各种分类和回归问题上产生比常规1DCNN更低的计算和空间复杂性更好的结果，尽管它在神经元层面上引入了更多的计算和空间复杂性。实验在三个公开可用的数据集上进行，并证明，在所解决的问题上，所提出的模型可以在更短的时间和更少的内存中从数据中提取比1DCNN更多的相关信息。

英文摘要：

In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by deepening and widening their topology in order to increase the level of non-linearity needed for a better approximation. However, compact topologies are always preferred to deeper ones as they offer the advantage of using less computational units and less parameters. This compacity comes at the price of reduced non-linearity and thus, of limited solution search space. We propose the 1-Dimensional Polynomial Neural Network (1DPNN) model that uses automatic polynomial kernel estimation for 1-Dimensional Convolutional Neural Networks (1DCNNs) and that introduces a high degree of non-linearity from the first layer which can compensate the need for deep and/or wide topologies. We show that this non-linearity enables the model to yield better results with less computational and spatial complexity than a regular 1DCNN on various classification and regression problems related to audio signals, even though it introduces more computational and spatial complexity on a neuronal level. The experiments were conducted on three publicly available datasets and demonstrate that, on the problems that were tackled, the proposed model can extract more relevant information from the data than a 1DCNN in less time and with less memory.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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