Neurosymbolic Conformal Classification

Abstract: 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.).