# Interpretable Proof Generation via Iterative Backward Reasoning

arXiv: https://arxiv.org/abs/2205.10714 · HTML: https://mlsanity.com/paper/2205.10714/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 22 of its 33 references that are in the map.
- First posted on arXiv 22 May 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [SpanBERT: Improving Pre-training by Representing and Predicting Spans](https://mlsanity.com/paper/1907.10529/) (2019)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [Retrieve, Program, Repeat: Complex Knowledge Base Question Answering via Alternate Meta-learning](https://mlsanity.com/paper/2010.15875/) (2020)
- [Constructing Datasets for Multi-hop Reading Comprehension Across Documents](https://mlsanity.com/paper/1710.06481/) (2017)
- [MRQA 2019 Shared Task: Evaluating Generalization in Reading Comprehension](https://mlsanity.com/paper/1910.09753/) (2019)
- [QANet: Combining Local Convolution with Global Self-Attention for Reading Comprehension](https://mlsanity.com/paper/1804.09541/) (2018)
- [QuaRTz: An Open-Domain Dataset of Qualitative Relationship Questions](https://mlsanity.com/paper/1909.03553/) (2019)
- [Reasoning Over Paragraph Effects in Situations](https://mlsanity.com/paper/1908.05852/) (2019)
- [PRover: Proof Generation for Interpretable Reasoning over Rules](https://mlsanity.com/paper/2010.02830/) (2020)
- [NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language](https://mlsanity.com/paper/1906.06187/) (2019)
- [Core Semantic First: A Top-down Approach for AMR Parsing](https://mlsanity.com/paper/1909.04303/) (2019)
- [Probabilistic Graph Reasoning for Natural Proof Generation](https://mlsanity.com/paper/2107.02418/) (2021)

## Built on by (most cited first, 9 of 9)

- [Natural Language Reasoning, A Survey](https://mlsanity.com/paper/2303.14725/) (2023)
- [Generating Natural Language Proofs with Verifier-Guided Search](https://mlsanity.com/paper/2205.12443/) (2022)
- [RECKONING: Reasoning through Dynamic Knowledge Encoding](https://mlsanity.com/paper/2305.06349/) (2023)
- [Natural Language Deduction with Incomplete Information](https://mlsanity.com/paper/2211.00614/) (2022)
- [Bag of Tricks for Effective Language Model Pretraining and Downstream Adaptation: A Case Study on GLUE](https://mlsanity.com/paper/2302.09268/) (2023)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [From Hypothesis to Publication: A Comprehensive Survey of AI-Driven Research Support Systems](https://mlsanity.com/paper/2503.01424/) (2025)
- [OmniForce: On Human-Centered, Large Model Empowered and Cloud-Edge Collaborative AutoML System](https://mlsanity.com/paper/2303.00501/) (2023)
- [Explainable Verbal Reasoner Plus (EVR+): A Natural Language Reasoning Framework that Supports Diverse Compositional Reasoning](https://mlsanity.com/paper/2305.00061/) (2023)

## Abstract (arXiv)

We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path and derive the final answer. We handle the limitations of existed works in two folds: 1) enhance the interpretability of reasoning procedures with detailed tracking, by predicting nodes and edges in the proof path iteratively backward from the question; 2) promote the efficiency and accuracy via reasoning on the elaborate representations of nodes and history paths, without any intermediate texts that may introduce external noise during proof generation. There are three main modules in IBR, QA and proof strategy prediction to obtain the answer and offer guidance for the following procedure; parent node prediction to determine a node in the existing proof that a new child node will link to; child node prediction to find out which new node will be added to the proof. Experiments on both synthetic and paraphrased datasets demonstrate that IBR has better in-domain performance as well as cross-domain transferability than several strong baselines. Our code and models are available at https://github.com/find-knowledge/IBR .