Learning Constraints for Structured Prediction Using Rectifier Networks
Table 5: Effectiveness of learned constraints for the synthetic ILP experiments.
['[EMPTY]', 'Number of ReLUs 2', 'Number of ReLUs 3', 'Number of ReLUs 4', 'Number of ReLUs 5', 'Number of ReLUs 6', 'Number of ReLUs 7', 'Number of ReLUs 8', 'Number of ReLUs 9', 'Number of ReLUs 10']
First, we want to know whether the learned rectifier network can correctly predict the synthetically generated positive and negative examples. The binary classification accuracies are listed in the first row. The second row lists the bitwise accuracies of the predicted solutions based on learned constraints, compared with the gold solutions. We see that the accuracy values of the solutions based on learned constraints are in the range from 80.2–83.5%. As a comparison, without using any constraints, the accuracy of the baseline is 56.8%. Therefore the learned constraints can substantially improve the prediction accuracy in the down stream inference tasks. The third row lists the percentage of the predicted solutions satisfying the original constraints. Solutions based on learned constraints satisfy 69.8–74.4% of the original constraints. In contrast, the baseline solutions satisfy 55.3% of the original constraints. The last row lists the percentage of the gold solutions satisfying the learned constraints. We see that the gold solutions almost always satisfy the learned constraints.