## 1 Introduction  
The last decade has seen remarkable Deep Neural Network (DNN) advancements in dealing with large-scale and challenging machine learning problems. Among the commonly used DNNs, the Convolutional Neural Network (CNN) is the most used in the computer vision (CV) field due to its efficiency in image detection [1], segmentation [2, 3], recognition and classification [4, 5]. Their outstanding performance in many fields mainly causes the rise of CNNs. For example, several works adapted them to different tasks, from medical [6], to remote sensing [7], to surveillance [8] and also at different stages of processes that can range from pre-processing [9] to classification [10]. For these reasons and results, CNNs are considered state of the art for many tasks. This can be seen from the number of articles published in recent years that exploit CNNs, either pre-trained or fine-tuned for a specific task. In fact, in the literature, there are more than 17,000 articles (source Scopus, accessed on 13 November 2021) for the keywords \"neural AND networks AND ((fine AND tuning) OR (transfer AND learning))\". As can been from Figure 1, the first articles (less than one per year) starting from the end of the 1960s are related to the classical Artificial Neural Networks(ANNs), which undergo a substantial rise after the advent of CNNs and in particular with the appearance of the most famous architectures: AlexNet [4] and VGG Nets [5]. However, this outstanding success has also led to a \"dangerous\" trend. It is pretty common to choose CNNs to have a more outstanding guarantee of success in terms of performance and publication; manuscripts that exploit CNNs, even those with little novelty, are generally preferred and more cited than manuscripts using traditional methods. In addition, the way of approaching CV tasks has changed radically. In fact, in many cases, authors immediately focus on a deep learning tool without even doing proper preliminary analysis and, worse, without doing a posthoc analysis to understand if the approach used is feasible to the task under consideration. The dangerous tendency mentioned above refers to the superficiality that authors often have when approaching a task. For example, in the medical field, the outcome is crucial, but relying solely and totally on the potential of CNN without a proper analysis of the output results does not guarantee correctness. Conversely, for example, using class activation maps for visual explanation [11; 12] would validate the method's feasibility in clinical practice. In addition, it appears that, when dealing with CNN, a typical preliminary analysis of the input data/images or pros and cons is often neglected, even if different limitations of CNNs have been observed [13; 14; 15; 16]. One of such limitations is mainly related to the use of CNNs for image classification that requires fixed-size input images due to the inclusion of fully-connected layers [17]. This issue has commonly been addressed by simply resizing the images to match the CNN's input size requirement (squared size, typically \(227\times 227\)). This step is often underestimated and instead is very important if the analysis must focus on fine-grained details and should be approached with great caution with large and non-squared images. Indeed, with the resizing process, many details can be lost, and it could compromise the shapes of the objects. This aspect also characterises the use case for peripheral blood smear (PBS) slide analysis we focus on in this work, which is very important for monitoring cell population and potential diseases. In particular, the size and morphology of the leukocytes can indicate the presence of several diseases, including severe ones such as leukaemia. For this reason, losing their detail in the resizing procedure could induce classification errors. Consequently, the primary purpose of this work is to explore the limitations of the leukaemia prediction systems entirely based on CNNs.