Michelangelo Diligenti

Mateo Espinosa Zarlenga, Pietro Barbiero, Gabriele Ciravegna et al. · cambridge

Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an intermediate level of human-like concepts. This enables human interventions which can correct mispredicted concepts to improve the model's performance. However, existing concept bottleneck models are unable to find optimal compromises between high task accuracy, robust concept-based explanations, and effective interventions on concepts -- particularly in real-world conditions where complete and accurate concept supervisions are scarce. To address this, we propose Concept Embedding Models, a novel family of concept bottleneck models which goes beyond the current accuracy-vs-interpretability trade-off by learning interpretable high-dimensional concept representations. Our experiments demonstrate that Concept Embedding Models (1) attain better or competitive task accuracy w.r.t. standard neural models without concepts, (2) provide concept representations capturing meaningful semantics including and beyond their ground truth labels, (3) support test-time concept interventions whose effect in test accuracy surpasses that in standard concept bottleneck models, and (4) scale to real-world conditions where complete concept supervisions are scarce.

Ying Jiao, Rodrigo Castellano Ontiveros, Luc De Raedt et al.

Neurosymbolic (NeSy) AI aims to combine the strengths of neural architectures and symbolic reasoning to improve the accuracy, interpretability, and generalization capability of AI models. While logic inference on top of subsymbolic modules has been shown to effectively guarantee these properties, this often comes at the cost of reduced scalability, which can severely limit the usability of NeSy models. This paper introduces DeepProofLog (DPrL), a novel NeSy system based on stochastic logic programs, which addresses the scalability limitations of previous methods. DPrL parameterizes all derivation steps with neural networks, allowing efficient neural guidance over the proving system. Additionally, we establish a formal mapping between the resolution process of our deep stochastic logic programs and Markov Decision Processes, enabling the application of dynamic programming and reinforcement learning techniques for efficient inference and learning. This theoretical connection improves scalability for complex proof spaces and large knowledge bases. Our experiments on standard NeSy benchmarks and knowledge graph reasoning tasks demonstrate that DPrL outperforms existing state-of-the-art NeSy systems, advancing scalability to larger and more complex settings than previously possible.

Michelangelo Diligenti, Francesco Giannini, Stefano Fioravanti et al.

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.

Rodrigo Castellano Ontiveros, Francesco Giannini, Marco Gori et al.

A large class of Neural-Symbolic (NeSy) methods employs a machine learner to process the input entities, while relying on a reasoner based on First-Order Logic to represent and process more complex relationships among the entities. A fundamental role for these methods is played by the process of logic grounding, which determines the relevant substitutions for the logic rules using a (sub)set of entities. Some NeSy methods use an exhaustive derivation of all possible substitutions, preserving the full expressive power of the logic knowledge. This leads to a combinatorial explosion in the number of ground formulas to consider and, therefore, strongly limits their scalability. Other methods rely on heuristic-based selective derivations, which are generally more computationally efficient, but lack a justification and provide no guarantees of preserving the information provided to and returned by the reasoner. Taking inspiration from multi-hop symbolic reasoning, this paper proposes a parametrized family of grounding methods generalizing classic Backward Chaining. Different selections within this family allow us to obtain commonly employed grounding methods as special cases, and to control the trade-off between expressiveness and scalability of the reasoner. The experimental results show that the selection of the grounding criterion is often as important as the NeSy method itself.

Francesco De Santis, Gabriele Ciravegna, Giovanni De Felice et al.

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically fix their task predictor to a single linear or Boolean expression, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of experts and the functional form of each expert, exposing an underexplored region of the design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data under user-specified operator vocabularies. Empirical evaluation demonstrates that varying the mixture size and functional form provides a robust framework for navigating the accuracy-interpretability trade-off, adapting to different user and task needs.

Giuseppe Marra, Francesco Giannini, Michelangelo Diligenti et al.

In the last few years the systematic adoption of deep learning to visual generation has produced impressive results that, amongst others, definitely benefit from the massive exploration of convolutional architectures. In this paper, we propose a general approach to visual generation that combines learning capabilities with logic descriptions of the target to be generated. The process of generation is regarded as a constrained satisfaction problem, where the constraints describe a set of properties that characterize the target. Interestingly, the constraints can also involve logic variables, while all of them are converted into real-valued functions by means of the t-norm theory. We use deep architectures to model the involved variables, and propose a computational scheme where the learning process carries out a satisfaction of the constraints. We propose some examples in which the theory can naturally be used, including the modeling of GAN and auto-encoders, and report promising results in problems with the generation of handwritten characters and face transformations.