Neural Disjunctive Normal Form (DNF) based models are powerful and interpretable approaches to neuro-symbolic learning and have shown promising results in classification and reinforcement learning settings without prior knowledge of the tasks. However, their performance is degraded by the thresholding of the post-training symbolic translation process. We show here that part of the performance degradation during translation is due to its failure to disentangle the learned knowledge represented in the form of the networks' weights. We address this issue by proposing a new disentanglement method; by splitting nodes that encode nested rules into smaller independent nodes, we are able to better preserve the models' performance. Through experiments on binary, multiclass, and multilabel classification tasks (including those requiring predicate invention), we demonstrate that our disentanglement method provides compact and interpretable logical representations for the neural DNF-based models, with performance closer to that of their pre-translation counterparts.

The unification of low-level perception and high-level reasoning is a long-standing problem in artificial intelligence, which has the potential to not only bring the areas of logic and learning closer together but also demonstrate how abstract concepts might emerge from sensory data. Precisely because deep learning methods dominate perception-based learning, including vision, speech, and linguistic grammar, there is fast-growing literature on how to integrate symbolic reasoning and deep learning. Broadly, efforts seem to fall into three camps: those focused on defining a logic whose formulas capture deep learning, ones that integrate symbolic constraints in deep learning, and others that allow neural computations and symbolic reasoning to co-exist separately, to enjoy the strengths of both worlds. In this paper, we identify another dimension to this inquiry: what do the hidden layers really capture, and how can we reason about that logically? In particular, we consider autoencoders that are widely used for dimensionality reduction and inject a symbolic generative framework onto the feature layer.