# Knowledge Crosswords: Geometric Knowledge Reasoning with Large Language Models

arXiv: https://arxiv.org/abs/2310.01290 · HTML: https://mlsanity.com/paper/2310.01290/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 58 of its 78 references that are in the map.
- First posted on arXiv 2 Oct 2023.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 58)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [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)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Large Language Models Can Be Easily Distracted by Irrelevant Context](https://mlsanity.com/paper/2302.00093/) (2023)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [Seq2SQL: Generating Structured Queries from Natural Language using Reinforcement Learning](https://mlsanity.com/paper/1709.00103/) (2017)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [The Web as a Knowledge-base for Answering Complex Questions](https://mlsanity.com/paper/1803.06643/) (2018)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [AmbigQA: Answering Ambiguous Open-domain Questions](https://mlsanity.com/paper/2004.10645/) (2020)
- [Adaptive Chameleon or Stubborn Sloth: Revealing the Behavior of Large Language Models in Knowledge Conflicts](https://mlsanity.com/paper/2305.13300/) (2023)
- [Generate rather than Retrieve: Large Language Models are Strong Context Generators](https://mlsanity.com/paper/2209.10063/) (2022)
- [RealTime QA: What's the Answer Right Now?](https://mlsanity.com/paper/2207.13332/) (2022)

## Built on by (most cited first, 11 of 11)

- [Model Swarms: Collaborative Search to Adapt LLM Experts via Swarm Intelligence](https://mlsanity.com/paper/2410.11163/) (2024)
- [Deceptive Semantic Shortcuts on Reasoning Chains: How Far Can Models Go without Hallucination?](https://mlsanity.com/paper/2311.09702/) (2023)
- [Heterogeneous Swarms: Jointly Optimizing Model Roles and Weights for Multi-LLM Systems](https://mlsanity.com/paper/2502.04510/) (2025)
- [Don't Throw Away Your Pretrained Model](https://mlsanity.com/paper/2510.09913/) (2025)
- [SPARTA ALIGNMENT: Collectively Aligning Multiple Language Models through Combat](https://mlsanity.com/paper/2506.04721/) (2025)
- [Complex Reasoning over Logical Queries on Commonsense Knowledge Graphs](https://mlsanity.com/paper/2403.07398/) (2024)
- [CREATE: Testing LLMs for Associative Creativity](https://mlsanity.com/paper/2603.09970/) (2026)
- [RankAlign: A Ranking View of the Generator-Validator Gap in Large Language Models](https://mlsanity.com/paper/2504.11381/) (2025)
- [Learning Composable Chains-of-Thought](https://mlsanity.com/paper/2505.22635/) (2025)
- [Data Swarms: Optimizable Generation of Synthetic Evaluation Data](https://mlsanity.com/paper/2506.00741/) (2025)
- [Answering the Wrong Question: Reasoning Trace Inversion for Abstention in LLMs](https://mlsanity.com/paper/2604.02230/) (2026)

## Abstract (arXiv)

We propose Knowledge Crosswords, a geometric knowledge reasoning benchmark consisting of incomplete knowledge networks bounded by structured factual constraints, where LLMs are tasked with inferring the missing facts to meet all constraints. The novel setting of geometric knowledge reasoning necessitates new LM abilities beyond existing atomic/linear multi-hop QA, such as backtracking, verifying facts and constraints, reasoning with uncertainty, and more. Knowledge Crosswords contains 2,101 individual problems, covering diverse knowledge domains, and is further divided into three difficulty levels. We conduct extensive experiments to evaluate existing LLMs and approaches on Knowledge Crosswords. Results demonstrate that baseline approaches struggle with larger knowledge networks and semantically-equivalent entity distractors. In light of their limitations, we propose two new approaches, Staged Prompting and Verify-All, to augment LLMs' abilities for error-aware backtracking and constraint verification. Our Verify-All significantly outperforms prior methods and is more robust towards problems in the hard subset. Further analysis shows that geometric knowledge reasoning poses new challenges to LLMs' knowledge abilities, particularly in robustness towards varying option orders, complex structural constraints in knowledge networks, "none of the above" scenarios, and more.