Stable Attractors for Neural networks classification via Ordinary Differential Equations (SA-nODE)
This work addresses classification tasks for researchers in machine learning and dynamical systems, offering an incremental approach by integrating pre-assigned attractors into neural networks.
The authors tackled the problem of supervised classification by constructing a neural network model with pre-assigned stable attractors, where classification involves steering dynamics toward these attractors. The method, tested on toy models and benchmarks, did not match state-of-the-art deep learning performance but demonstrated that continuous dynamical systems with analytical terms can serve as high-performance classifiers.
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.