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 introduces more computational complexity but enables the model to yield better results than a regular 1DCNN that has the same number of training parameters on various classification and regression problems related to audio signals. The experiments were conducted on three publicly available datasets and demonstrate that the proposed model can achieve a much faster convergence than a 1DCNN on the tackled regression problems.

中文翻译：

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用于音频信号相关问题的一维多项式神经网络

除了极其非线性之外，现代问题还需要数百万甚至数十亿的参数来解决或至少获得解决方案的良好近似值，并且众所周知，神经网络通过加深和扩大其拓扑结构来吸收这种复杂性，以便增加更好的近似所需的非线性水平。然而，紧凑拓扑总是比更深的拓扑更受欢迎，因为它们提供了使用更少计算单元和更少参数的优势。这种紧凑性的代价是非线性度降低，因此解决方案搜索空间有限。我们提出了 1 维多项式神经网络 (1DPNN) 模型，该模型对 1 维卷积神经网络 (1DCNN) 使用自动多项式核估计，并从第一层引入高度非线性，可以补偿深度和/或宽拓扑。我们表明，这种非线性引入了更多的计算复杂性，但使模型能够产生比常规 1DCNN 更好的结果，后者在与音频信号相关的各种分类和回归问题上具有相同数量的训练参数。实验是在三个公开可用的数据集上进行的，并证明所提出的模型在解决的回归问题上可以比 1DCNN 实现更快的收敛。我们表明，这种非线性引入了更多的计算复杂性，但使模型能够产生比常规 1DCNN 更好的结果，后者在与音频信号相关的各种分类和回归问题上具有相同数量的训练参数。实验是在三个公开可用的数据集上进行的，并证明所提出的模型在解决的回归问题上可以比 1DCNN 实现更快的收敛。我们表明，这种非线性引入了更多的计算复杂性，但使模型能够产生比常规 1DCNN 更好的结果，后者在与音频信号相关的各种分类和回归问题上具有相同数量的训练参数。实验是在三个公开可用的数据集上进行的，并证明所提出的模型在解决的回归问题上可以比 1DCNN 实现更快的收敛。