Learnability and robustness of shallow neural networks learned by a performance-driven BP and a variant of PSO for edge decision-making

In many cases, the computing resources are limited without the benefit from GPU, especially in the edge devices of IoT enabled systems. It may not be easy to implement complex AI models in edge devices. The Universal Approximation Theorem states that a shallow neural network (SNN) can represent any nonlinear function. However, how fat is an SNN enough to solve a nonlinear decision-making problem in edge devices? In this paper, we focus on the learnability and robustness of SNNs, obtained by a greedy tight force heuristic algorithm (performance driven BP) and a loose force meta-heuristic algorithm (a variant of PSO). Two groups of experiments are conducted to examine the learnability and the robustness of SNNs with Sigmoid activation, learned/optimised by KPI-PDBPs and KPI-VPSOs, where, KPIs (key performance indicators: error (ERR), accuracy (ACC) and $F_1$ score) are the objectives, driving the searching process. An incremental approach is applied to examine the impact of hidden neuron numbers on the performance of SNNs, learned/optimised by KPI-PDBPs and KPI-VPSOs. From the engineering prospective, all sensors are well justified for a specific task. Hence, all sensor readings should be strongly correlated to the target. Therefore, the structure of an SNN should depend on the dimensions of a problem space. The experimental results show that the number of hidden neurons up to the dimension number of a problem space is enough; the learnability of SNNs, produced by KPI-PDBP, is better than that of SNNs, optimized by KPI-VPSO, regarding the performance and learning time on the training data sets; the robustness of SNNs learned by KPI-PDBPs and KPI-VPSOs depends on the data sets; and comparing with other classic machine learning models, ACC-PDBPs win for almost all tested data sets.