Backpropagating through Markov Logic Networks

We integrate Markov Logic networks with deep learning architectures operating on high-dimensional and noisy feature inputs. Instead of relaxing the discrete components into smooth functions, we propose an approach that allows us to backpropagate through standard statistical relational learning components using perturbation-based differentiation. The resulting hybrid models are shown to outperform models solely relying on deep learning based function fitting. We find that using noise perturbations is required to allow the proposed hybrid models to robustly learn from the training data.