# Probabilistic Graph Reasoning for Natural Proof Generation

arXiv: https://arxiv.org/abs/2107.02418 · HTML: https://mlsanity.com/paper/2107.02418/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 6 Jul 2021.

## Builds on (most cited first, 14 of 14)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [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)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Neural Programmer-Interpreters](https://mlsanity.com/paper/1511.06279/) (2015)
- [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)
- [Neural Programmer: Inducing Latent Programs with Gradient Descent](https://mlsanity.com/paper/1511.04834/) (2015)
- [Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting](https://mlsanity.com/paper/1904.02688/) (2019)
- [An Experimental Study of Formula Embeddings for Automated Theorem Proving in First-Order Logic](https://mlsanity.com/paper/2002.00423/) (2020)

## Built on by (most cited first, 3 of 3)

- [Generating Natural Language Proofs with Verifier-Guided Search](https://mlsanity.com/paper/2205.12443/) (2022)
- [Learning Deductive Reasoning from Synthetic Corpus based on Formal Logic](https://mlsanity.com/paper/2308.07336/) (2023)
- [Interpretable Proof Generation via Iterative Backward Reasoning](https://mlsanity.com/paper/2205.10714/) (2022)

## Abstract (arXiv)

In this paper, we investigate the problem of reasoning over natural language statements. Prior neural based approaches do not explicitly consider the inter-dependency among answers and their proofs. In this paper, we propose PRobr, a novel approach for joint answer prediction and proof generation. PRobr defines a joint probabilistic distribution over all possible proof graphs and answers via an induced graphical model. We then optimize the model using variational approximation on top of neural textual representation. Experiments on multiple datasets under diverse settings (fully supervised, few-shot and zero-shot evaluation) verify the effectiveness of PRobr, e.g., achieving 10%-30% improvement on QA accuracy in few/zero-shot evaluation. Our codes and models can be found at https://github.com/changzhisun/PRobr/.