The study of machine learning-based logical query-answering enables reasoning with large-scale and incomplete knowledge graphs. This paper further advances this line of research by considering the uncertainty in the knowledge. The uncertain nature of knowledge is widely observed in the real world, but does not align seamlessly with the first-order logic underpinning existing studies. To bridge this gap, we study the setting of soft queries on uncertain knowledge, which is motivated by the establishment of soft constraint programming. We further propose an ML-based approach with both forward inference and backward calibration to answer soft queries on large-scale, incomplete, and uncertain knowledge graphs. Theoretical discussions reveal that our method ensures there are no catastrophic cascading errors in our forward inference algorithm while maintaining the same complexity as state-of-the-art inference algorithms for first-order queries. Empirical results justify the superior performance of our approach against previous ML-based methods with number embedding extensions.

Transformer based Large Language Models (LLMs) often impose limitations on the length of the text input to ensure the generation of fluent and relevant responses due to the quadratic complexity. These constraints restrict their applicability in long text scenarios. In this paper, we propose a novel semantic compression method that enables generalization to texts that are 6-8 times longer without incurring significant computational costs or requiring fine-tuning. Our proposed framework draws inspiration from source coding in information theory and employs a pre-trained model to reduce the semantic redundancy of long inputs before passing them to the LLMs for downstream tasks. Experimental results demonstrate that our method effectively extends the context window of LLMs across a range of tasks including question answering, summarization, few-shot learning, and information retrieval. Furthermore, the proposed semantic compression method exhibits consistent fluency in text generation while reducing the associated computational overhead.

Answering complex queries on knowledge graphs is important but particularly challenging because of the data incompleteness. Query embedding methods address this issue by learningbased models and simulating logical reasoning with set operators. Previous works focus on specific forms of embeddings, but scoring functions between embeddings are underexplored. In contrast to existing scorning functions motivated by local comparison or global transport, this work investigates the local and global trade-off with unbalanced optimal transport theory. Specifically, we embed sets as bounded measures in R endowed with a scoring function motivated by the Wasserstein-Fisher-Rao metric. Such a design also facilitates closed-form set operators in the embedding space. Moreover, we introduce a convolution-based algorithm for linear time computation and a block diagonal kernel to enforce the trade-off. Results show that WFRE is capable of outperforming existing query embedding methods on standard datasets, evaluation sets with combinatorially complex queries, and hierarchical knowledge graphs. Ablation study shows that finding a better local and global trade-off is essential for performance improvement.