Entity resolution (ER) aims at matching records that refer to the same real-world entity. Although widely studied for the last 50 years, ER still represents a challenging data management problem, and several recent works have started to investigate the opportunity of applying deep learning (DL) techniques to solve this problem. In this paper, we study the fundamental problem of explainability of the DL solution for ER. Understanding the matching predictions of an ER solution is indeed crucial to assess the trustworthiness of the DL model and to discover its biases. We treat the DL model as a black box classifier and -while previous approaches to provide explanations for DL predictions are agnostic to the classification task -we propose the CERTA approach that is aware of the semantics of the ER problem. Our approach produces both saliency explanations, which associate each attribute with a saliency score, and counterfactual explanations, which provide examples of values that can flip the prediction. CERTA builds on a probabilistic framework that aims at computing the explanations evaluating the outcomes produced by using perturbed copies of the input records. We experimentally evaluate CERTA's explanations of state-of-the-art ER solutions based on DL models using publicly available datasets, and demonstrate the effectiveness of CERTA over recently proposed methods for this problem.

Entity resolution (ER) aims at matching records that refer to the same real-world entity. Although widely studied for the last 50 years, ER still represents a challenging data management problem, and several recent works have started to investigate the opportunity of applying deep learning (DL) techniques to solve this problem. In this paper, we study the fundamental problem of explainability of the DL solution for ER. Understanding the matching predictions of an ER solution is indeed crucial to assess the trustworthiness of the DL model and to discover its biases. We treat the DL model as a black box classifier and -while previous approaches to provide explanations for DL predictions are agnostic to the classification task -we propose the certa approach that is aware of the semantics of the ER problem. Our approach produces both saliency explanations, which associate each attribute with a saliency score, and counterfactual explanations, which provide examples of values that can flip the prediction. certa builds on a probabilistic framework that aims at computing the explanations evaluating the outcomes produced by using perturbed copies of the input records.We experimentally evaluate certa's explanations of state-of-the-art ER solutions based on DL models using publicly available datasets, and demonstrate the effectiveness of certa over recently proposed methods for this problem.

Let W ⊂ P 13 be the image of the rational map defined by the linear system of the sextic surfaces of P 3 having double points along the edges of a tetrahedron. Let L be the linear system of the hyperplane sections of W . It is known that a general S ∈ L is an Enriques surface. The aim of this paper is to study the sublinear system L• ⊂ L of the hyperplane sections of W having a triple point at a general point w ∈ W . We will show that a general element of L• is birational to an elliptic ruled surface and that the image of W via the rational map defined by L• is a cubic Del Pezzo surface ∆ ⊂ P 3 with 4 nodes. Interestingly, this fact appears to be related to a conjecture of Castelnuovo.

In order to find useful information to complete the classification of Enriques-Fano threefolds, we will computationally study the singularities of some known Enriques-Fano threefolds of genus 6, 7, 8, 9, 10, 13 and 17. We will also deduce the projective normality of these threefolds.

In this paper, we describe the simple isotropic decompositions of the curve sections of the known Enriques-Fano threefolds. The simple isotropic decompositions allow us to identify the irreducible components of the moduli space of the polarized Enriques surfaces. Thus, our analysis will enable us to show to which families of polarized Enriques surfaces the hyperplane sections of the Enriques-Fano threefolds belong.