GENEOnet: Statistical analysis supporting explainability and trustworthiness

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.

A novel approach to graph distinction through GENEOs and permutants

The theory of Group Equivariant Non-Expansive Operators (GENEOs) was initially developed in Topological Data Analysis for the geometric approximation of data observers, including their invariances and symmetries. This paper departs from that line of research and explores the use of GENEOs for distinguishing $r$-regular graphs up to isomorphisms. In doing so, we aim to test the capabilities and flexibility of these operators. Our experiments show that GENEOs offer a good compromise between efficiency and computational cost in comparing $r$-regular graphs, while their actions on data are easily interpretable. This supports the idea that GENEOs could be a general-purpose approach to discriminative problems in Machine Learning when some structural information about data and observers is explicitly given.

Low-Resource White-Box Semantic Segmentation of Supporting Towers on 3D Point Clouds via Signature Shape Identification

Research in 3D semantic segmentation has been increasing performance metrics, like the IoU, by scaling model complexity and computational resources, leaving behind researchers and practitioners that (1) cannot access the necessary resources and (2) do need transparency on the model decision mechanisms. In this paper, we propose SCENE-Net, a low-resource white-box model for 3D point cloud semantic segmentation. SCENE-Net identifies signature shapes on the point cloud via group equivariant non-expansive operators (GENEOs), providing intrinsic geometric interpretability. Our training time on a laptop is 85~min, and our inference time is 20~ms. SCENE-Net has 11 trainable geometrical parameters and requires fewer data than black-box models. SCENE--Net offers robustness to noisy labeling and data imbalance and has comparable IoU to state-of-the-art methods. With this paper, we release a 40~000 Km labeled dataset of rural terrain point clouds and our code implementation.

GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection

Nowadays there is a big spotlight cast on the development of techniques of explainable machine learning. Here we introduce a new computational paradigm based on Group Equivariant Non-Expansive Operators, that can be regarded as the product of a rising mathematical theory of information-processing observers. This approach, that can be adjusted to different situations, may have many advantages over other common tools, like Neural Networks, such as: knowledge injection and information engineering, selection of relevant features, small number of parameters and higher transparency. We chose to test our method, called GENEOnet, on a key problem in drug design: detecting pockets on the surface of proteins that can host ligands. Experimental results confirmed that our method works well even with a quite small training set, providing thus a great computational advantage, while the final comparison with other state-of-the-art methods shows that GENEOnet provides better or comparable results in terms of accuracy.