Adversarial Sets for Regularising Neural Link Predictors

TL;DR

This paper introduces a novel adversarial training method that uses set-based assumptions like transitivity to regularize neural link predictors, improving their performance by enforcing logical consistency.

Contribution

It presents the first approach to incorporate function-free Horn clauses as regularizers for neural link predictors with domain-size-independent complexity.

Findings

Significant performance improvements on link prediction benchmarks.

Efficient closed-form solutions for adversarial example generation.

Effective use of prior logical knowledge for regularization.

Abstract

In adversarial training, a set of models learn together by pursuing competing goals, usually defined on single data instances. However, in relational learning and other non-i.i.d domains, goals can also be defined over sets of instances. For example, a link predictor for the is-a relation needs to be consistent 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 for deriving an inconsistency loss, measuring the degree to which the model violates the assumptions on an adversarially-generated set of examples. The training objective is defined as a minimax problem, where an adversary finds the most offending adversarial examples by maximising the inconsistency loss, and the model is trained by jointly minimising a supervised loss and the inconsistency loss on the adversarial examples. This yields the first method that can use function-free Horn clauses (as in Datalog) to regularise any neural link predictor, with complexity independent of the domain size. We show that for several link prediction models, the optimisation problem faced by the adversary has efficient closed-form solutions. Experiments on link prediction benchmarks indicate that given suitable prior knowledge, our method can significantly improve neural link predictors on all relevant metrics.