Refining neural network predictions using background knowledge
This work addresses the issue of integrating logical constraints into neural networks for researchers and practitioners in machine learning, though it is incremental as it builds on existing methods for using background knowledge.
The paper tackles the problem of neural network predictions not satisfying logical background knowledge at test time by introducing differentiable refinement functions and an algorithm called Iterative Local Refinement (ILR) to correct predictions, resulting in significantly fewer iterations for complex SAT formulas and competitive performance on the MNIST addition task.
Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is discarded after training, even if it is still useful at test time. Instead, we ensure neural network predictions satisfy the knowledge by refining the predictions with an extra computation step. We introduce differentiable refinement functions that find a corrected prediction close to the original prediction. We study how to effectively and efficiently compute these refinement functions. Using a new algorithm called Iterative Local Refinement (ILR), we combine refinement functions to find refined predictions for logical formulas of any complexity. ILR finds refinements on complex SAT formulas in significantly fewer iterations and frequently finds solutions where gradient descent can not. Finally, ILR produces competitive results in the MNIST addition task.