Self-Consistency samples diverse reasoning chains with answers and chooses the final answer by majority voting. It is based on forward reasoning and cannot further improve performance by sampling more reasoning chains when saturated. To further boost performance, we introduce backward reasoning to verify candidate answers. Specifically, for mathematical tasks, we mask a number in the question and ask the LLM to answer a backward question created by a simple template, i.e., to predict the masked number when a candidate answer is provided. Instead of using forward or backward reasoning alone, we propose **FOBAR** to combine **FO**rward and **BA**ckward **R**easoning for verification. Extensive experiments on six standard mathematical data sets and three LLMs show that FOBAR achieves state-of-the-art performance. In particular, FOBAR outperforms Self-Consistency, which uses forward reasoning alone, demonstrating that combining forward and backward reasoning is more accurate in verification. In addition, FOBAR achieves higher accuracy than existing verification methods, showing the effectiveness of the simple template used in backward reasoning and the proposed combination.

Knowledge Graph Completion (KGC) is crucial for addressing knowledge graph incompleteness and supporting downstream applications. Many models have been proposed for KGC and they can be categorized into two main classes, including triple-based and test-based approaches. Triple-based methods struggle with long-tail entities due to limited structural information and imbalanced distributions of entities. Text-based methods alleviate this issue but require costly training for language models and specific finetuning for knowledge graphs, which limits their efficiency. To alleviate the limitations in the two approaches, in this paper, we propose KICGPT, a framework that integrates a large language model (LLM) and a triple-based KGC retriever, to alleviate the long-tail problem without incurring additional training overhead. In the proposed KICGPT model, we propose an in-context learning strategy called Knowledge Prompt, which encodes structural knowledge into demonstrations to guide LLM. Empirical results on benchmark datasets demonstrate the effectiveness of the proposed KICGPT model with lighter training overhead and no finetuning.