Deep Neural Networks (DNNs) became the standard tool for function approximation with most of the introduced architectures being developed for high-dimensional input data. However, many real-world problems have low-dimensional inputs for which standard Multi-Layer Perceptrons (MLPs) are the default choice. An investigation into specialized architectures is missing. We propose a novel DNN layer called Univariate Radial Basis Function (U-RBF) layer as an alternative. Similar to sensory neurons in the brain, the U-RBF layer processes each individual input dimension with a population of neurons whose activations depend on different preferred input values. We verify its effectiveness compared to MLPs in low-dimensional function regressions and reinforcement learning tasks. The results show that the U-RBF is especially advantageous when the target function becomes complex and difficult to approximate.

翻译：深度神经网络（DNN）已成为函数逼近的标准工具，但现有架构大多针对高维输入数据设计。然而，许多现实问题的输入维度较低，此时标准多层感知器（MLP）是默认选择，而针对此类场景的专用架构研究尚属空白。本文提出一种新型DNN层——单变量径向基函数（U-RBF）层作为替代方案。类似大脑中的感觉神经元，U-RBF层通过一组神经元处理每个独立输入维度，这些神经元的激活依赖于不同的偏好输入值。我们验证了该方法在低维函数回归和强化学习任务中相较MLP的有效性。结果表明，当目标函数变得复杂且难以逼近时，U-RBF层尤其具有优势。