A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification purposes, the untrained model is a priori constructed to accommodate for a set of pre-assigned stationary stable attractors. Classifying amounts to steer the dynamics towards one of the planted attractors, depending on the specificity of the processed item supplied as an input. Asymptotically the system will hence converge on a specific point of the explored multi-dimensional space, flagging the category of the object to be eventually classified. Working in this context, the inherent ability to perform classification, as acquired ex post by the trained model, is ultimately reflected in the shaped basin of attractions associated to each of the target stable attractors. The performance of the proposed method is here challenged against simple toy models crafted for the purpose, as well as by resorting to well established reference standards. Although this method does not reach the performance of state-of-the-art deep learning algorithms, it illustrates that continuous dynamical systems with closed analytical interaction terms can serve as high-performance classifiers.

翻译：一种介于机器学习与动力系统理论交叉领域的有监督分类新方法被提出。与其它采用常微分方程进行分类的方法不同，该未训练模型预先构建以容纳一组预设的固定稳定吸引子。分类过程通过根据输入处理项的特定性，将动力学导向其中一个预设吸引子来实现。系统将渐近收敛于所探索多维空间中的特定点，标示待分类对象的类别。在此框架下，训练后模型事后获得的分类能力最终体现为与每个目标稳定吸引子相关的塑造吸引域。通过针对目的设计的简单玩具模型以及采用公认参考标准，对所提方法的性能进行了验证。尽管该方法未达到最先进深度学习算法水平，但论证了具有封闭解析相互作用项的连续动力系统可作为高性能分类器。