A Bridge between Dynamical Systems and Machine Learning: Engineered Ordinary Differential Equations as Classification Algorithm (EODECA)

Abstract

In a world increasingly reliant on machine learning, the interpretability of these models remains a substantial challenge, with many equating their functionality to an enigmatic black box. This study seeks to bridge machine learning and dynamical systems. Recognizing the deep parallels between dense neural networks and dynamical systems, particularly in the light of non-linearities and successive transformations, this manuscript introduces the Engineered Ordinary Differential Equations as Classification Algorithms (EODECAs). Uniquely designed as neural networks underpinned by continuous ordinary differential equations, EODECAs aim to capitalize on the well-established toolkit of dynamical systems. Unlike traditional deep learning models, which often suffer from opacity, EODECAs promise both high classification performance and intrinsic interpretability. They are naturally invertible, granting them an edge in understanding and transparency over their counterparts. By bridging these domains, we hope to usher in a new era of machine learning models where genuine comprehension of data processes complements predictive prowess.

Lorenzo Giambagli

PostDoc Department of Physics, Freie Universität Berlin

My research interests include Spectral analysis of Deep Neural Network (DNN), Structura Pruning, Bayesian Inference in DNN, Simplicial Complexes Dynamics, Theoretical Neuroscience