Post-hoc methods in Explainable AI (XAI) elucidate black-box models by identifying input features critical to the model's decision-making. Recent advancements in these methods have facilitated the generation of logic-based explanations that capture interactions among input features. However, these techniques often encounter critical limitations, notably the inability to ensure logical consistency and fidelity between generated explanations and the model's actual decision-making processes. Such inconsistencies jeopardize the reliability of explanations particularly in high-risk domains. To address this gap, we introduce a novel, theoretically rigorous approach rooted in category theory. Specifically, we propose the concept of an explaining functor, which preserves logical entailment structurally between the explanations and the decisions of black-box models. By establishing a categorical framework, our method guarantees the coherence and accuracy of extracted explanations, thus overcoming the common pitfalls associated with heuristic-based explanation methods. We demonstrate the practical efficacy of our theoretical contributions through two synthetic benchmarks that highlight significant reductions in contradictory and unfaithful explanations. Our experiments show how our framework can provide mathematically grounded, compositional, and coherent explanations.

Knowledge Graph Embeddings (KGE) have become a quite popular class of models specifically devised to deal with ontologies and graph structure data, as they can implicitly encode statistical dependencies between entities and relations in a latent space. KGE techniques are particularly effective for the biomedical domain, where it is quite common to deal with large knowledge graphs underlying complex interactions between biological and chemical objects. Recently in the literature, the PharmKG dataset has been proposed as one of the most challenging knowledge graph biomedical benchmark, with hundreds of thousands of relational facts between genes, diseases and chemicals. Despite KGEs can scale to very large relational domains, they generally fail at representing more complex relational dependencies between facts, like logic rules, which may be fundamental in complex experimental settings. In this paper, we exploit logic rules to enhance the embedding representations of KGEs on the PharmKG dataset. To this end, we adopt Relational Reasoning Network (R2N), a recently proposed neural-symbolic approach showing promising results on knowledge graph completion tasks. An R2N uses the available logic rules to build a neural architecture that reasons over KGE latent representations. In the experiments, we show that our approach is able to significantly improve the current state-of-the-art on the PharmKG dataset. Finally, we provide an ablation study to experimentally compare the effect of alternative sets of rules according to different selection criteria and varying the number of considered rules.

Transformers have been established as one of the most effective neural approach in performing various Natural Language Processing tasks. However, following common trend in modern deep architectures, their scale has quickly grown to an extent that reduces the concrete possibility for several enterprises to train such models from scratch. Indeed, despite their high-level performances, Transformers have the general drawback of requiring a huge amount of training data, computational resources and energy consumption to be successfully optimized. For this reason, more recent architectures like Bidirectional Encoder Representations from Transformers rely on unlabeled data to pre-train the model, which is later fine-tuned for a specific downstream task using a relatively smaller amount of training data. In a similar fashion, this paper considers a plug-and-play framework that can be used to inject multiple syntactic features, like Part-of-Speech Tagging or Dependency Parsing, into any kind of pre-trained Transformer. This novel approach allows to perform sequence-to-sequence labeling tasks by exploiting: (i) the (more abundant) available training data that is also used to learn the syntactic features, (ii) the language data that is used to pre-train the transformer model. The experimental results show that our approach improves over the baseline performances of the underlying model in different datasets, thus proving the effectiveness of employing syntactic language information for semantic regularization. In addition, we show that our architecture has a huge efficiency advantage over pure large language models. Indeed, by using a model with limited size, but whose input data are enriched with syntactic information, we show that it is possible to obtain a significant reduction of CO2 emissions without decreasing the prediction performances.

The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA)---one of the fields laying the foundations of modern mathematics---is still completely unexplored. This work proposes the first use of AI to investigate UA's conjectures with an equivalent equational and topological characterization. While topological representations would enable the analysis of such properties using graph neural networks, the limited transparency and brittle explainability of these models hinder their straightforward use to empirically validate existing conjectures or to formulate new ones. To bridge these gaps, we propose a general algorithm generating AI-ready datasets based on UA's conjectures, and introduce a novel neural layer to build fully interpretable graph networks. The results of our experiments demonstrate that interpretable graph networks: (i) enhance interpretability without sacrificing task accuracy, (ii) strongly generalize when predicting universal algebra's properties, (iii) generate simple explanations that empirically validate existing conjectures, and (iv) identify subgraphs suggesting the formulation of novel conjectures.

This paper presents a novel predictive coding scheme for image-data compression by vector quantization (VQ). On the basis of a prediction, further compression is achieved by using a dynamic codebook-reordering strategy that allows a more efficient Huffman encoding of vector addresses. The proposed method is lossless, for it increases the compression performances of a baseline vector quantization scheme, without causing any further image degradation. Results are presented and a comparison with Cache-VQ is made.

The paper addresses the problem of a real time approach for thin structures identification. The proposed method make use of adaptive morphological operators in which the normal textural properties are brought to bear on the filter design in order to enhance the output related to anomalous structures. The authors discuss how the introduction of adaptivity criteria is useful to reduce the sensitivity of morphological filtering to local variations typical of textures and to noise. In addition, theoretical investigations related to the problem of the optimization algorithm are presented and discussed. Experimental results have been carried out both on classical natural textures and on ceramic tile images and prove the efficiency of the proposed approach in many practical applications.

The paper addresses the analysis of singular distributions defined on a fractal support, called fractal measures. In general, a fractal measure has an infinite number of singularities of infinitely many types. The term multifractals expresses the fact that points, corresponding to a given type of singularity, typically form a fractal subset whose dimensions depend on the type of singularity. The theory of the q-th order generalized fractal dimensions supplies a tool for the characterization of such multifractal measures. This theory results from an extension of the fractal dimension to different-order statistics. The paper exploits such concepts in order to face the problem of texture recognition. In particular the fractal measure taken into account is the 2D distribution of the optical mass of an image; some theoretical aspects related to this problem are addressed. Results on real images are presented and discussed.

This paper presents a novel multiresolution wavelet-based algorithm for filtering SAR images in order to remove speckle noise. The basic idea is to apply to the wavelet coefficients a size-decreasing half-interpolated median filter. The size of the median filter is adapted to the noise energy reduction between the image pyramid levels and different filter shapes are used in each wavelet subbands according to the dominant frequencies. Experimental results showed, that the proposed algorithm results in significant noise removal while the edges are preserved in the images.

A novel predictive coding scheme for VQ is presented, called dynamic codebook reordering VQ (DCRVQ). Residual correlations between neighboring codevectors are exploited by a nonlinear prediction, that is a neural one. As a matter of fact, on the basis of the previously decoded codevectors, a multilayer neural network makes a prediction, and this result is used to reorganize the codebook in a dynamic way. This allows for efficient Huffman compression of codevector addresses after reordering.>

The paper deals with the theory of qth-order fractal dimensions and its application to texture analysis. In particular, a novel algorithm for estimating such dimensions is proposed and its use in digital-image processing is described. Results on classical Brodatz textures are reported.>

A data compression technique based on neural networks is presented. The schema consists of multiple multilayer perceptron networks, which produce a transformation of the original image with a reduced redundancy. A perceptron with a hidden layer is used; the input and output layers have the same number of nodes, while in the middle the number is reduced, thus producing a data compression of the original information. The transformation is carried out by the neural networks in an adaptive way. A split segmentation, based on spatial activities of regions, is applied to the original image in order to locate uniform blocks. A higher ratio between the input and the hidden nodes is used with large blocks and a lower one with smaller blocks; details are then retained in a good way. Major advantages of the proposed approach lie in its good performance, even with images outside the training set.>

A system for the processing and interpretation of underwater images acquired with an acoustic sensor is presented. As a first objective, the system aims to recognize simple objects with known characteristics located at different positions so as to create a scenario. The proposed recognition system exhibits the features of a knowledge-based system, as it is based on ideal models (provided by an expert) of the possible objects present in the scene, and the matching of such models with the real objects detected by processing data coming from the acquisition system. The numerical data provided by different types of sensors are first processed by some low-level modules. The high-level modules operate a matching of the objects detected with the models, according to criteria of maximum fuzzy reliability. Results are presented and discussed.>

An approach to natural surface analysis and characterization that is based on multifractals is presented. Such an approach presents many interesting peculiarities in the extraction of textural features from an image. A new method to compute such features is suggested, together with their use in the image segmentation process. Comparative results on SAR (synthetic aperture radar) images, by applying a data-fusion segmentation module, are presented and discussed.>