Although data preprocessing is a universal technique that can be widely used in neural networks, most research in this area is focused on designing new neural network architectures. In our work, we propose a preprocessing technique that enriches the original image data using local intensity information; this technique is motivated by human perception. To encode this information into an image, we introduce a new image structure named Image Represented by a Fuzzy Function. When using this structure, a crisp intensity value of each pixel is replaced by a fuzzy set given by a membership function constructed with the usage of extremal values from the particular neighborhood of that pixel. We describe this structure and its properties and propose a way in which it can be used as an input into existing neural networks without any modifications. Based on our benchmark consisting of three well-known datasets and five neural network architectures, we show that the proposed preprocessing can, in most cases, decrease classification error compared with a baseline and two other preprocessing methods. To support our claim, we have also selected several publicly available projects and tested the impact of the preprocessing with a positive result.

This paper delves into the interpretability of Graph Neural Networks in the context of Boolean Satisfiability. The goal is to demystify the internal workings of these models and provide insightful perspectives into their decision-making processes. This is done by uncovering connections to two approximation algorithms studied in the domain of Boolean Satisfiability: Belief Propagation and Semidefinite Programming Relaxations. Revealing these connections has empowered us to introduce a suite of impactful enhancements. The first significant enhancement is a curriculum training procedure, which incrementally increases the problem complexity in the training set, together with increasing the number of message passing iterations of the Graph Neural Network. We show that the curriculum, together with several other optimizations, reduces the training time by more than an order of magnitude compared to the baseline without the curriculum. Furthermore, we apply decimation and sampling of initial embeddings, which significantly increase the percentage of solved problems.