Learning logic rules for knowledge graph reasoning is essential as such rules provide interpretable explanations for reasoning and can be generalized to different domains. However, existing methods often face challenges such as searching in a vast search space (e.g., enumeration of relational paths or multiplication of high-dimensional matrices) and inefficient optimization (e.g., techniques based on reinforcement learning or EM algorithm). To address these limitations, this paper proposes a novel framework called LatentLogic to efficiently mine logic rules by controllable generation in the latent space. Specifically, to map the discrete relational paths into the latent space, we leverage a pre-trained VAE and employ a discriminator to establish an energy-based distribution. Additionally, we incorporate a sampler based on ordinary differential equations, enabling the efficient generation of logic rules in our approach. Extensive experiments on benchmark datasets demonstrate the effectiveness and efficiency of our proposed method.

Labeling large amounts of extractive summarization data is often prohibitive expensive due to time, financial, and expertise constraints, which poses great challenges to incorporating summarization system in practical applications. This limitation can be overcome by semi-supervised approaches: consistency-training and pseudo-labeling to make full use of unlabeled data. Researches on the two, however, are conducted independently, and very few works try to connect them. In this paper, we first use the noise-injected consistency training paradigm to regularize model predictions. Subsequently, we propose a novel entropy-constrained pseudo labeling strategy to obtain high-confidence labels from unlabeled predictions, which can obtain high-confidence labels from unlabeled predictions by comparing the entropy of supervised and unsupervised predictions. By combining consistency training and pseudo-labeling, this framework enforce a low-density separation between classes, which decently improves the performance of supervised learning over an insufficient labeled extractive summarization dataset.