Molecular Machine Learning Using Euler Characteristic Transforms

TL;DR

This paper introduces the Euler Characteristic Transform (ECT) as a novel geometric-topological descriptor for molecular shape, demonstrating its effectiveness and complementarity with traditional methods in predicting molecular properties.

Contribution

The study proposes using ECT for molecular shape representation, showing its competitive performance and synergy with existing molecular descriptors and graph neural networks.

Findings

ECT-based representation achieves competitive results on benchmark datasets.

Combining ECT with traditional descriptors improves predictive accuracy.

Hybrid shape-topology representations enhance molecular machine learning models.

Abstract

The shape of a molecule determines its physicochemical and biological properties. However, it is often underrepresented in standard molecular representation learning approaches. Here, we propose using the Euler Characteristic Transform (ECT) as a geometrical-topological descriptor. Computed directly on a molecular graph derived from handcrafted atomic features, the ECT enables the extraction of multiscale structural features, offering a novel way to represent and encode molecular shape in the feature space. We assess the predictive performance of this representation across nine benchmark regression datasets, all centered around predicting the inhibition constant $K_i$. In addition, we compare our proposed ECT-based representation against traditional molecular representations and methods, such as molecular fingerprints/descriptors and graph neural networks (GNNs). Our results show that our ECT-based representation achieves competitive performance, ranking among the best-performing methods on several datasets. More importantly, its combination with traditional representations, particularly with the AVALON fingerprint, significantly \emph{enhances predictive performance}, outperforming other methods on most datasets. These findings highlight the complementary value of multiscale topological information and its potential for being combined with established techniques. Our study suggests that hybrid approaches incorporating explicit shape information can lead to more informative and robust molecular representations, enhancing and opening new avenues in molecular machine learning tasks. To support reproducibility and foster open biomedical research, we provide open access to all experiments and code used in this work.