# Natural Logic-guided Autoregressive Multi-hop Document Retrieval for Fact Verification arXiv: https://arxiv.org/abs/2212.05276 ยท HTML: https://mlsanity.com/paper/2212.05276/ ## Key facts - Cited by 11 papers in the map (data through 14 Oct 2026). - Builds on 24 of its 46 references that are in the map. - First posted on arXiv 10 Dec 2022. ## Builds on (most cited first, 24 of 24) - [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019) - [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019) - [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020) - [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019) - [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017) - [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018) - [KILT: a Benchmark for Knowledge Intensive Language Tasks](https://mlsanity.com/paper/2009.02252/) (2020) - [A Survey on Automated Fact-Checking](https://mlsanity.com/paper/2108.11896/) (2021) - [Autoregressive Entity Retrieval](https://mlsanity.com/paper/2010.00904/) (2020) - [HoVer: A Dataset for Many-Hop Fact Extraction And Claim Verification](https://mlsanity.com/paper/2011.03088/) (2020) - [FEVEROUS: Fact Extraction and VERification Over Unstructured and Structured information](https://mlsanity.com/paper/2106.05707/) (2021) - [Answering Complex Open-Domain Questions with Multi-Hop Dense Retrieval](https://mlsanity.com/paper/2009.12756/) (2020) - [Learning to Retrieve Reasoning Paths over Wikipedia Graph for Question Answering](https://mlsanity.com/paper/1911.10470/) (2019) - [Combining Fact Extraction and Verification with Neural Semantic Matching Networks](https://mlsanity.com/paper/1811.07039/) (2018) - [Fine-grained Fact Verification with Kernel Graph Attention Network](https://mlsanity.com/paper/1910.09796/) (2019) - [A Survey on Stance Detection for Mis- and Disinformation Identification](https://mlsanity.com/paper/2103.00242/) (2021) - [Reasoning Over Semantic-Level Graph for Fact Checking](https://mlsanity.com/paper/1909.03745/) (2019) - [Baleen: Robust Multi-Hop Reasoning at Scale via Condensed Retrieval](https://mlsanity.com/paper/2101.00436/) (2021) - [UKP-Athene: Multi-Sentence Textual Entailment for Claim Verification](https://mlsanity.com/paper/1809.01479/) (2018) - [Pyserini: An Easy-to-Use Python Toolkit to Support Replicable IR Research with Sparse and Dense Representations](https://mlsanity.com/paper/2102.10073/) (2021) - [ProoFVer: Natural Logic Theorem Proving for Fact Verification](https://mlsanity.com/paper/2108.11357/) (2021) - [Answering Open-Domain Questions of Varying Reasoning Steps from Text](https://mlsanity.com/paper/2010.12527/) (2020) - [DeSePtion: Dual Sequence Prediction and Adversarial Examples for Improved Fact-Checking](https://mlsanity.com/paper/2004.12864/) (2020) - [HopRetriever: Retrieve Hops over Wikipedia to Answer Complex Questions](https://mlsanity.com/paper/2012.15534/) (2020) ## Built on by (most cited first, 11 of 11) - [Fact-Checking Complex Claims with Program-Guided Reasoning](https://mlsanity.com/paper/2305.12744/) (2023) - [QACHECK: A Demonstration System for Question-Guided Multi-Hop Fact-Checking](https://mlsanity.com/paper/2310.07609/) (2023) - [Human-in-the-loop Evaluation for Early Misinformation Detection: A Case Study of COVID-19 Treatments](https://mlsanity.com/paper/2212.09683/) (2022) - [QA-NatVer: Question Answering for Natural Logic-based Fact Verification](https://mlsanity.com/paper/2310.14198/) (2023) - [Are Large Language Models Good Fact Checkers: A Preliminary Study](https://mlsanity.com/paper/2311.17355/) (2023) - [M3: A Multi-Task Mixed-Objective Learning Framework for Open-Domain Multi-Hop Dense Sentence Retrieval](https://mlsanity.com/paper/2403.14074/) (2024) - [Multi-Evidence based Fact Verification via A Confidential Graph Neural Network](https://mlsanity.com/paper/2405.10481/) (2024) - [RU22Fact: Optimizing Evidence for Multilingual Explainable Fact-Checking on Russia-Ukraine Conflict](https://mlsanity.com/paper/2403.16662/) (2024) - [Mining the Explainability and Generalization: Fact Verification Based on Self-Instruction](https://mlsanity.com/paper/2405.12579/) (2024) - [SemViQA: A Semantic Question Answering System for Vietnamese Information Fact-Checking](https://mlsanity.com/paper/2503.00955/) (2025) - [Global Consistency Repair for Natural-Language Claim Sets](https://mlsanity.com/paper/2601.13600/) (2026) ## Abstract (arXiv) A key component of fact verification is thevevidence retrieval, often from multiple documents. Recent approaches use dense representations and condition the retrieval of each document on the previously retrieved ones. The latter step is performed over all the documents in the collection, requiring storing their dense representations in an index, thus incurring a high memory footprint. An alternative paradigm is retrieve-and-rerank, where documents are retrieved using methods such as BM25, their sentences are reranked, and further documents are retrieved conditioned on these sentences, reducing the memory requirements. However, such approaches can be brittle as they rely on heuristics and assume hyperlinks between documents. We propose a novel retrieve-and-rerank method for multi-hop retrieval, that consists of a retriever that jointly scores documents in the knowledge source and sentences from previously retrieved documents using an autoregressive formulation and is guided by a proof system based on natural logic that dynamically terminates the retrieval process if the evidence is deemed sufficient. This method is competitive with current state-of-the-art methods on FEVER, HoVer and FEVEROUS-S, while using 5 to 10 times less memory than competing systems. Evaluation on an adversarial dataset indicates improved stability of our approach compared to commonly deployed threshold-based methods. Finally, the proof system helps humans predict model decisions correctly more often than using the evidence alone.