Neuro-Symbolic (NeSy) integration combines symbolic reasoning with Neural Networks (NNs) for tasks requiring perception and reasoning. Most NeSy systems rely on continuous relaxation of logical knowledge, and no discrete decisions are made within the model pipeline. Furthermore, these methods assume that the symbolic rules are given. In this paper, we propose Deep Symbolic Learning (DSL), a NeSy system that learns NeSy-functions, i.e., the composition of a (set of) perception functions which map continuous data to discrete symbols, and a symbolic function over the set of symbols. DSL learns simultaneously the perception and symbolic functions while being trained only on their composition (NeSy-function). The key novelty of DSL is that it can create internal (interpretable) symbolic representations and map them to perception inputs within a differentiable NN learning pipeline. The created symbols are automatically selected to generate symbolic functions that best explain the data. We provide experimental analysis to substantiate the efficacy of DSL in simultaneously learning perception and symbolic functions.
@article{arxiv.2208.11561,
title = {Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions},
author = {Alessandro Daniele and Tommaso Campari and Sagar Malhotra and Luciano Serafini},
journal= {arXiv preprint arXiv:2208.11561},
year = {2024}
}