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GENEOnet: Statistical analysis supporting explainability and trustworthiness

Giovanni Bocchi, Patrizio Frosini, Alessandra Micheletti, Alessandro Pedretti, Carmen Gratteri, Filippo Lunghini, Andrea Rosario Beccari, Carmine Talarico

TL;DR

The paper investigates the explainability, trustworthiness, and robustness of GENEO-based networks for protein pocket detection, centered on GENEOnet. It formalizes GENEOs (group-equivariant and non-expansive) and argues that their mathematical structure supports interpretability via global feature importances ($\alpha$ coefficients) and stable predictions under geometric perturbations. Empirically, GENEOnet shows a high degree of equivariance compared to competing methods and robustness to perturbations in both rigid and non-rigid transformations, as demonstrated through rotations and MD simulations. Together, these results advocate for GENEOs as a principled foundation for trustworthy AI in structural biology, with clear paths for extending rotation analyses and longer MD studies in future work.

Abstract

Group Equivariant Non-Expansive Operators (GENEOs) have emerged as mathematical tools for constructing networks for Machine Learning and Artificial Intelligence. Recent findings suggest that such models can be inserted within the domain of eXplainable Artificial Intelligence (XAI) due to their inherent interpretability. In this study, we aim to verify this claim with respect to GENEOnet, a GENEO network developed for an application in computational biochemistry by employing various statistical analyses and experiments. Such experiments first allow us to perform a sensitivity analysis on GENEOnet's parameters to test their significance. Subsequently, we show that GENEOnet exhibits a significantly higher proportion of equivariance compared to other methods. Lastly, we demonstrate that GENEOnet is on average robust to perturbations arising from molecular dynamics. These results collectively serve as proof of the explainability, trustworthiness, and robustness of GENEOnet and confirm the beneficial use of GENEOs in the context of Trustworthy Artificial Intelligence.

GENEOnet: Statistical analysis supporting explainability and trustworthiness

TL;DR

The paper investigates the explainability, trustworthiness, and robustness of GENEO-based networks for protein pocket detection, centered on GENEOnet. It formalizes GENEOs (group-equivariant and non-expansive) and argues that their mathematical structure supports interpretability via global feature importances ( coefficients) and stable predictions under geometric perturbations. Empirically, GENEOnet shows a high degree of equivariance compared to competing methods and robustness to perturbations in both rigid and non-rigid transformations, as demonstrated through rotations and MD simulations. Together, these results advocate for GENEOs as a principled foundation for trustworthy AI in structural biology, with clear paths for extending rotation analyses and longer MD studies in future work.

Abstract

Group Equivariant Non-Expansive Operators (GENEOs) have emerged as mathematical tools for constructing networks for Machine Learning and Artificial Intelligence. Recent findings suggest that such models can be inserted within the domain of eXplainable Artificial Intelligence (XAI) due to their inherent interpretability. In this study, we aim to verify this claim with respect to GENEOnet, a GENEO network developed for an application in computational biochemistry by employing various statistical analyses and experiments. Such experiments first allow us to perform a sensitivity analysis on GENEOnet's parameters to test their significance. Subsequently, we show that GENEOnet exhibits a significantly higher proportion of equivariance compared to other methods. Lastly, we demonstrate that GENEOnet is on average robust to perturbations arising from molecular dynamics. These results collectively serve as proof of the explainability, trustworthiness, and robustness of GENEOnet and confirm the beneficial use of GENEOs in the context of Trustworthy Artificial Intelligence.

Paper Structure

This paper contains 10 sections, 3 theorems, 1 equation, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Group Equivariant Non-Expansive Operators
  3. GENEOnet
  4. Data sources
  5. Sensitivity analysis
  6. Equivariance analysis
  7. Robustness analysis
  8. Concluding remarks
  9. Appendix on equivariance analysis
  10. Appendix on perturbation analysis

Key Result

Theorem 2.2

If $\Phi$ and $\Psi$ are compact, then $F_{all}$ is compact with respect to the topology induced by $D_{GENEO}$.

Figures (4)

  • Figure 1: Model architecture and optimal parameters obtained after training the model.
  • Figure 2: Empirical distributions of the estimated parameters of GENEOnet, obtained by randomly varying the training set
  • Figure 3: Mean values and confidence intervals, obtained from different protein samples, of the proportions $\hat{p}_j^{\mathcal{M};\tau}$ computed for GENEOnet and other three methods for pocket detection, obtained for different values of the threshold $\tau$.
  • Figure 4: Robustness analysis

Theorems & Definitions (4)

  • Definition 2.1
  • Theorem 2.2
  • Corollary 2.3
  • Theorem 2.4