The last decades have seen a drastic improvement of Machine Learning (ML), mainly driven by Deep Learning (DL). However, despite the resounding successes of ML in many domains, the impossibility to provide guarantees of conformity and the fragility of ML systems (faced with distribution shifts, adversarial attacks, etc.) have prevented the design of trustworthy AI systems. Several research paths have been investigated to mitigate this fragility and provide some guarantees regarding the behavior of ML systems, among which are neurosymbolic AI and conformal prediction. Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. One of the objective of this hybridization can be to provide theoritical guarantees that the output of the system will comply with some prior knowledge. Conformal prediction is a set of techniques that enable to take into account the uncertainty of ML systems by transforming the unique prediction into a set of predictions, called a confidence set. Interestingly, this comes with statistical guarantees regarding the presence of the true label inside the confidence set. Both approaches are distribution-free and model-agnostic. In this paper, we see how these two approaches can complement one another. We introduce several neurosymbolic conformal prediction techniques and explore their different characteristics (size of confidence sets, computational complexity, etc.).

Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. Informed multi-label classification is a sub-field of neurosymbolic AI which studies how to leverage prior knowledge to improve neural classification systems. A well known family of neurosymbolic techniques for informed classification use probabilistic reasoning to integrate this knowledge during learning, inference or both. Therefore, the asymptotic complexity of probabilistic reasoning is of cardinal importance to assess the scalability of such techniques. However, this topic is rarely tackled in the neurosymbolic literature, which can lead to a poor understanding of the limits of probabilistic neurosymbolic techniques. In this paper, we introduce a formalism for informed supervised classification tasks and techniques. We then build upon this formalism to define three abstract neurosymbolic techniques based on probabilistic reasoning. Finally, we show computational complexity results on several representation languages for prior knowledge commonly found in the neurosymbolic literature.

Neurosymbolic AI is a growing field of research aiming to combine neural networks learning capabilities with the reasoning abilities of symbolic systems. This hybridization can take many shapes. In this paper, we propose a new formalism for supervised multi-label classification with propositional background knowledge. We introduce a new neurosymbolic technique called semantic conditioning at inference, which only constrains the system during inference while leaving the training unaffected. We discuss its theoritical and practical advantages over two other popular neurosymbolic techniques: semantic conditioning and semantic regularization. We develop a new multi-scale methodology to evaluate how the benefits of a neurosymbolic technique evolve with the scale of the network. We then evaluate experimentally and compare the benefits of all three techniques across model scales on several datasets. Our results demonstrate that semantic conditioning at inference can be used to build more accurate neural-based systems with fewer resources while guaranteeing the semantic consistency of outputs.