Neural Networks Enhancement through Prior Logical Knowledge

In the recent past, there has been a growing interest in Neural-Symbolic Integration frameworks, i.e., hybrid systems that integrate connectionist and symbolic approaches: on the one hand, neural networks show remarkable abilities to learn from a large amount of data in presence of noise, on the other, pure symbolic methods can perform reasoning as well as learning from few samples. By combining the two paradigms, it should be possible to obtain a system that can both learn from data and apply inference over some background knowledge. Here we propose KENN (Knowledge Enhanced Neural Networks), a Neural-Symbolic architecture that injects prior knowledge, codified in a set of universally quantified FOL clauses, into a neural network model. In KENN, clauses are used to generate a new final layer of the neural network which modifies the initial predictions based on the knowledge. Among the advantages of this strategy, there is the possibility to include additional learnable parameters, the clause weights, each of which represents the strength of a specific clause. We evaluated KENN on two standard datasets for multi-label classification, showing that the injection of clauses, automatically extracted from the training data, sensibly improves the performances. In a further experiment with manually curated knowledge, KENN outperformed state-of-the-art methods on the VRD Dataset, where the task is to classify relationships between detected objects in images. Finally, to evaluate how KENN deals with relational data, we tested it with different learning configurations on Citeseer, a standard dataset for Collective Classification. The obtained results show that KENN is capable of increasing the performances of the underlying neural network even in the presence of relational data obtaining results in line with other methods that combine learning with logic.