From Rules to Vision: Symbolic Knowledge Injection and Rule Extraction under Limited Data

Neurosymbolic learning combines neural representation learning with explicit symbolic knowledge. Among its foundational approaches, rule-based knowledge injection offers a direct way to incorporate structured prior knowledge into a network's topology and initial weights. While this idea has shown value in other domains, its potential for modern image classification remains underexplored, although symbolic rules could provide useful prior structure when labelled data are scarce and support more inspectable models. We therefore adapt the classical knowledge-based artificial neural network (KBANN) framework to image classification and ask whether symbolic knowledge can compensate for very limited labelled data, and whether learned knowledge can later be extracted as readable rules. We implement the full injection-refinement-extraction lifecycle: predicates are grounded as deterministic functions of pixels, rules are translated into neural structure and initial weights, the network is refined through gradient learning, and rules are extracted after training. Controlled experiments separate four factors: rule source, predicate grounding, injection strength, and how the rule pathway is attached to the network. We also compare classical KBANN compilation with a signed projection that maps predicates directly to classes. With one labelled image per class, ten MNIST images in total, supplied digit rules raise balanced accuracy from $0.5022$ for a plain CNN to $0.6183$ with classical compilation and $0.6847$ with the signed projection. Prior benefit tracks standalone rule strength ($r=0.97$), while permuted rules underperform the plain CNN and rules induced from the same ten labels provide no comparable gain. After training, extracted rules preserve the injected structure and reproduce network predictions with fidelity of $0.9814$–$0.9903$, but recover no new antecedents. Knowledge injection can therefore reduce dependence on labelled data and leave inspectable structure behind, while its effectiveness depends strongly on how that knowledge is represented and integrated.