Stochastic Configuration Networks (SCNs) are a class of randomized neural networks that integrate randomized algorithms within an incremental learning framework. A defining feature of SCNs is the supervisory mechanism, which adaptively adjusts the distribution to generate effective random basis functions, thereby enabling error-free learning. In this paper, we present a comprehensive analysis of the impact of the supervisory mechanism on the learning performance of SCNs. Our findings reveal that the current SCN framework evaluates the effectiveness of each random basis function in reducing residual errors using a lower bound on its error reduction potential, which constrains SCNs' overall learning efficiency. Specifically, SCNs may fail to consistently select the most effective random candidate as the new basis function during each training iteration. To overcome this problem, we propose a novel method for evaluating the hidden layer's output matrix, supported by a new supervisory mechanism that accurately assesses the error reduction potential of random basis functions without requiring the computation of the Moore-Penrose inverse of the output matrix. This approach enhances the selection of basis functions, reducing computational complexity and improving the overall scalability and learning capabilities of SCNs. We introduce a Recursive Moore-Penrose Inverse-SCN (RMPI-SCN) training scheme based on the new supervisory mechanism and demonstrate its effectiveness through simulations over some benchmark datasets. Experiments show that RMPI-SCN outperforms the conventional SCN in terms of learning capability, underscoring its potential to advance the SCN framework for large-scale data modeling applications.

翻译：随机配置网络（SCNs）是一类将随机化算法融入增量学习框架的随机化神经网络。SCNs的一个关键特征在于其监督机制，该机制通过自适应调整分布来生成有效的随机基函数，从而实现无误差学习。本文全面分析了监督机制对SCNs学习性能的影响。研究发现，当前SCN框架通过误差缩减潜力的下界来评估各随机基函数在降低残差误差方面的有效性，这限制了SCNs的整体学习效率。具体而言，SCNs在每次训练迭代中可能无法持续选择最有效的随机候选作为新基函数。为解决这一问题，我们提出了一种评估隐藏层输出矩阵的新方法，该方法基于一种新型监督机制，能够在不计算输出矩阵Moore-Penrose逆的情况下精确评估随机基函数的误差缩减潜力。该策略优化了基函数的选择过程，降低了计算复杂度，并提升了SCNs的整体可扩展性与学习能力。基于新监督机制，我们提出了递归Moore-Penrose逆SCN（RMPI-SCN）训练方案，并通过多个基准数据集的仿真实验验证了其有效性。实验表明，RMPI-SCN在学习能力方面优于传统SCN，凸显了其在推动SCN框架应用于大规模数据建模领域的潜力。