In open-domain question-answering (ODQA), most existing questions require single-hop reasoning on commonsense. To further extend this task, we officially introduce open-domain multi-hop reasoning (ODMR) by answering multi-hop questions with explicit reasoning steps in open-domain setting. Recently, large language models (LLMs) have found significant utility in facilitating ODQA without external corpus. Furthermore, chain-of-thought (CoT) prompting boosts the reasoning capability of LLMs to a greater extent with manual or automated paradigms. However, existing automated methods lack of quality assurance, while manual approaches suffer from limited scalability and poor diversity, hindering the capabilities of LLMs. In this paper, we propose Self-prompted Chain-of-Thought (SP-CoT), an automated framework to mass-produce high quality CoTs of LLMs, by LLMs and for LLMs. SP-CoT introduces an automated generation pipeline of high quality ODMR datasets, an adaptive sampler for in-context CoT selection and self-prompted inference via in-context learning. Extensive experiments on four multi-hop question-answering benchmarks show that our proposed SP-CoT not only significantly surpasses the previous SOTA methods on large-scale (175B) LLMs, but also nearly doubles the zero-shot performance of small-scale (13B) LLMs. Further analysis reveals the remarkable capability of SP-CoT to elicit direct and concise intermediate reasoning steps by recalling ~50% of intermediate answers on MuSiQue-Ans dataset.

Training dense passage representations via contrastive learning has been shown effective for Open-Domain Passage Retrieval (ODPR). Existing studies focus on further optimizing by improving negative sampling strategy or extra pretraining. However, these studies keep unknown in capturing passage with internal representation conflicts from improper modeling granularity. Specifically, under our observation that a passage can be organized by multiple semantically different sentences, modeling such a passage as a unified dense vector is not optimal. This work thus presents a refined model on the basis of a smaller granularity, contextual sentences, to alleviate the concerned conflicts. In detail, we introduce an in-passage negative sampling strategy to encourage a diverse generation of sentence representations within the same passage. Experiments on three benchmark datasets verify the efficacy of our method, especially on datasets where conflicts are severe. Extensive experiments further present good transferability of our method across datasets.