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In adversarial training, a set of models learn together by pursuing competinggoals, usually defined on single data instances. However, in relationallearning and other non-i.i.d domains, goals can also be defined over sets ofinstances. For example, a link predictor for the is-a relation needs to beconsistent with the transitivity property: if is-a(x_1, x_2) and is-a(x_2, x_3)hold, is-a(x_1, x_3) needs to hold as well. Here we use such assumptions forderiving an inconsistency loss, measuring the degree to which the modelviolates the assumptions on an adversarially-generated set of examples. Thetraining objective is defined as a minimax problem, where an adversary findsthe most offending adversarial examples by maximising the inconsistency loss,and the model is trained by jointly minimising a supervised loss and theinconsistency loss on the adversarial examples. This yields the first methodthat can use function-free Horn clauses (as in Datalog) to regularise anyneural link predictor, with complexity independent of the domain size. We showthat for several link prediction models, the optimisation problem faced by theadversary has efficient closed-form solutions. Experiments on link predictionbenchmarks indicate that given suitable prior knowledge, our method cansignificantly improve neural link predictors on all relevant metrics.

Adversarial Sets for Regularising Neural Link Predictors