Publications
Papers
- G. Bocchi, S. Botteghi, M. Brasini, P. Frosini, and N. Quercioli, "On the finite representation of linear group equivariant operators via permutant measures." Annals of Mathematics and Artificial Intelligence. Vol. 91, pp. 465–487, Feb. 2023. https://doi.org/10.1007/s10472-022-09830-1 Available: https://rdcu.be/c5Obw
Abstract Recent advances in machine learning have highlighted the importance of using group equivariant non-expansive operators for building neural networks in a more transparent and interpretable way. An operator is called equivariant with respect to a group if the action of the group commutes with the operator. Group equivariant non-expansive operators can be seen as multi-level components that can be joined and connected in order to form neural networks by applying the operations of chaining, convex combination and direct product. In this paper we prove that each linear G-equivariant non-expansive operator (GENEO) can be produced by a weighted summation associated with a suitable permutant measure, provided that the group G transitively acts on a finite signal domain. This result is based on the Birkhoff–von Neumann decomposition of doubly stochastic matrices and some well known facts in group theory. Our theorem makes available a new method to build all linear GENEOs with respect to a transitively acting group in the finite setting. This work is part of the research devoted to develop a good mathematical theory of GENEOs, seen as relevant components in machine learning.
Preprints
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G. Bocchi, P. Frosini, A. Micheletti, A. Pedretti, C. Gratteri, F. Lunghini, A.R. Beccari and C. Talarico, “GENEOnet: A new machine learning paradigm based on Group Equivariant Non-Expansive Operators. An application to protein pocket detection” 2022. arXiv: 2202.00451.
Abstract 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.
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D. Lavado, C. Soares, A. Micheletti, G. Bocchi, A. Coronati, M. Silva and P. Frosini, “Low-Resource White-Box Semantic Segmentation of Supporting Towers on 3D Point Clouds via Signature Shape Identification” 2023. arXiv: 2306.07809.
Abstract 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.