## 1 Introduction  
Biometric technologies are gaining popularity owing to their reliability and ease. Faces, fingerprints, and other biometric traits can identify individuals with a high degree of accuracy. Among these, the fingerprint is the most widespread due to its uniqueness and ease of use. However, artificial fingerprint replicas, also called spoofs or presentation attacks (PAs), can circumvent fingerprint-based personal recognition. Both consensual and non-consensual procedures may be used to replicate a fingerprint. Consensual techniques need the awareness and cooperation of the intended person, whereas nonconsensual approaches are more dangerous and covert and are based on the acquisition of latent fingerprints left unknowingly on reflective or partially reflective surfaces. Given that automated fingerprint identification systems (AFIS) frequently secure sensitive and critical data, it is crucial to equip them with presentation attack detectors (PADs) that help determining whether the fingerprint acquired by the sensor is genuine (live) or a replica (fake). Although PADs are nowadays very accurate, their development and use still present open problems. One of these is the so-called lack of interoperability. A PAD trained on data from one sensor works precisely on images of that sensor. However, it can lead to much lower results when used on images of different sensors. This is a frequent problem when a manufacturer or user needs to replace the sensor of an authentication system with a more current and high-performing device. In this case, in fact, it is not possible to use the previous PAD; the system must be retrained, fine-tuned, or updated on new images. Obtaining these new images may not be easy, as it requires multiple acquisitions of real users and fake fingerprints made with different materials and techniques. Although some recently proposed works aim to mitigate the problem of interoperability [1], they require a subset of the target sensor samples. This makes interoperability an open and critical issue for AFIS systems, especially when obtaining target samples at the design stage is difficult or even infeasible. Another open problem is the lack of ability of modern PADs to recognize PAs obtained with acquisition techniques and/or materials not used during the training phase. Even in this case, to make the PAD robust and able to recognize the greatest number of types of PAs, a designer must predict, obtain, and use them in the training phase. Obtaining PAs made with all known state-of-the-art techniques and materials can be very expensive. As the organizers of the Fingerprint Liveness Detection Competition (LivDet) ([[https://livdet.diee.unica.it/](https://livdet.diee.unica.it/)]([https://livdet.diee.unica.it/](https://livdet.diee.unica.it/)), accessed on 19 September 2022) we were able to observe some different PAD training techniques among researchers. In fact, most of the LivDet competitors trained their PADs on single-sensor data. This training procedure is recommended and rewarded for the purposes of the competition because it allows a precise reading of the results and associates cause and effect in the proposed challenges. However, other competitors used all the data of the training sets from different acquisition sensors simultaneously, and others on additional data compared to the training sets provided. These procedures proved successful in the latest edition of the competition, LivDet 2021, obtaining the best results in terms of presentation attack detection, even on the \"advanced\" never-seen-before attacks perpetrated by a new semi-consensual acquisition technique called ScreenSpoof [2]. Moreover, these large-trained algorithms have been shown to be particularly robust across the sensors of the competition. Based on this evidence, we wondered to which extent training on data acquired with multiple sensors helps detect artificial replicas. Is this procedure truly beneficial in solving the interoperability and/or generalization problem?