Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of the unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. Experimental results show that approximation strategies can be used to find better solutions than the best incomplete solvers in the MaxSAT Evaluation 2017.
Deep neural networks are very successful on many vision tasks, but hard to interpret due to their black box nature. To overcome this, various post-hoc attribution methods have been proposed to identify image regions most influential to the models' decisions. Evaluating such methods is challenging since no ground truth attributions exist. We thus propose three novel evaluation schemes to more reliably measure the faithfulness of those methods, to make comparisons between them more fair, and to make visual inspection more systematic. To address faithfulness, we propose a novel evaluation setting (DiFull) in which we carefully control which parts of the input can influence the output in order to distinguish possible from impossible attributions. To address fairness, we note that different methods are applied at different layers, which skews any comparison, and so evaluate all methods on the same layers (ML-Att) and discuss how this impacts their performance on quantitative metrics. For more systematic visualizations, we propose a scheme (AggAtt) to qualitatively evaluate the methods on complete datasets. We use these evaluation schemes to study strengths and shortcomings of some widely used attribution methods over a wide range of models. Finally, we propose a post-processing smoothing step that significantly improves the performance of some attribution methods, and discuss its applicability.
Incomplete MaxSAT solving aims to quickly find a solution that attempts to minimize the sum of the weights of unsatisfied soft clauses without providing any optimality guarantees. In this paper, we propose two approximation strategies for improving incomplete weighted MaxSAT solving. In one of the strategies, we cluster the weights and approximate them with a representative weight. In another strategy, we break up the problem of minimizing the sum of weights of unsatisfiable clauses into multiple minimization subproblems. We have implemented these strategies in a tool Open-WBO-Inc. Using the subproblem minimization strategy, Open-WBO-Inc placed first and second in the weighted incomplete tracks in the MaxSAT Evaluation 2018 whereas the strategy based on weight approximation was placed fourth. We compare these strategies with the best incomplete MaxSAT solvers on benchmarks taken from MaxSAT Evaluation 2017 and MaxSAT Evaluation 2018 and show that the strategies proposed are competitive with the best of the solvers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.