Engineered Ordinary Differential Equations as Classification Algorithm
  (EODECA): thorough characterization and testing
Raffaele Marino Lorenzo Buffoni Lorenzo Chicchi Lorenzo Giambagli Duccio Fanelli
EODECA (Engineered Ordinary Differential Equations as Classification
Algorithm) is a novel approach at the intersection of machine learning and
dynamical systems theory, presenting a unique framework for classification
tasks [1]. This method stands out with its dynamical system structure,
utilizing ordinary differential equations (ODEs) to efficiently handle complex
classification challenges. The paper delves into EODECA's dynamical properties,
emphasizing its resilience against random perturbations and robust performance
across various classification scenarios. Notably, EODECA's design incorporates
the ability to embed stable attractors in the phase space, enhancing
reliability and allowing for reversible dynamics. In this paper, we carry out a
comprehensive analysis by expanding on the work [1], and employing a Euler
discretization scheme. In particular, we evaluate EODECA's performance across
five distinct classification problems, examining its adaptability and
efficiency. Significantly, we demonstrate EODECA's effectiveness on the MNIST
and Fashion MNIST datasets, achieving impressive accuracies of $98.06\%$ and
$88.21\%$, respectively. These results are comparable to those of a multi-layer
perceptron (MLP), underscoring EODECA's potential in complex data processing
tasks. We further explore the model's learning journey, assessing its evolution
in both pre and post training environments and highlighting its ability to
navigate towards stable attractors. The study also investigates the
invertibility of EODECA, shedding light on its decision-making processes and
internal workings. This paper presents a significant step towards a more
transparent and robust machine learning paradigm, bridging the gap between
machine learning algorithms and dynamical systems methodologies.