Loss functions with symbolic constraints in deep learning

For this talk, I will choose to focus on some of our recent inquiries regarding loss functions using logical formulas. This all began with the so-called multiplexnet paper with Nicholas Hoernle from AAAI 2022, which is related to approaches such as the semantic loss from UCLA and DeepProbLog from KU Leuven. From there, the work we’ve been doing recently goes along two directions. In some work that I’m carrying out with Nijesh Uperti, we’re looking at the foundations of weak supervision from a logical standpoint. The idea is to provide an idealized characterization of what kind of hypotheses are learned in the weak signal experimental evaluations in these papers. The second piece of related work is looking at the idea of a loss function using logical formulas from a geometric point of view, mainly in work with Miguel Mendez (ICAART 2025). The idea is that if you see the loss function as a kind of constrained distribution and the baseline neural network as the input distribution, we are trying to minimize the distance between these two distributions. This talk was given at the new Research Theme dedicated to Safe and Secure AI for Robotics, by Ekaterina Komendantskaya, Marta Romeo, among others.