Molecular Machine Learning Using Euler Characteristic Transforms

2025-07-04

AI Summary

This work addresses the underutilization of molecular shape information in representation learning, which limits the accuracy of inhibition constant (Ki) prediction. To this end, we introduce the Euler Characteristic Transform (ECT) — a multiscale geometric-topological descriptor — into molecular representation for the first time. We propose a complementary fusion strategy integrating ECT with AVALON fingerprints and embed it within a shape-aware framework combining graph neural networks and regression models. Evaluated on nine Ki prediction benchmark datasets, the ECT+AVALON combination achieves state-of-the-art or second-best performance, significantly outperforming methods relying solely on chemical descriptors or graph-structural features. These results empirically validate the indispensable role of topological shape information in bioactivity prediction. Moreover, our analysis reveals strong complementarity between ECT and conventional molecular fingerprints, establishing a novel paradigm for geometric deep learning in drug discovery.

Technology Category

• Knowledge Representation and Reasoning: Other Foundations of Knowledge Representation & Reasoning
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Underrepresentation of molecular shape in standard representation learning
• Predicting inhibition constant Ki using multiscale structural features
• Enhancing predictive performance by combining topological and traditional representations

Innovation

• Euler Characteristic Transform for molecular shape
• Combines topological features with traditional representations
• Enhances predictive performance in molecular learning