# LANS: A Layout-Aware Neural Solver for Plane Geometry Problem

arXiv: https://arxiv.org/abs/2311.16476 · HTML: https://mlsanity.com/paper/2311.16476/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 54 references that are in the map.
- First posted on arXiv 25 Nov 2023.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Bottom-Up and Top-Down Attention for Image Captioning and Visual Question Answering](https://mlsanity.com/paper/1707.07998/) (2017)
- [ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision](https://mlsanity.com/paper/2102.03334/) (2021)
- [LayoutLM: Pre-training of Text and Layout for Document Image Understanding](https://mlsanity.com/paper/1912.13318/) (2019)
- [Unicoder-VL: A Universal Encoder for Vision and Language by Cross-modal Pre-training](https://mlsanity.com/paper/1908.06066/) (2019)
- [Unifying Vision-and-Language Tasks via Text Generation](https://mlsanity.com/paper/2102.02779/) (2021)
- [LayoutLMv2: Multi-modal Pre-training for Visually-Rich Document Understanding](https://mlsanity.com/paper/2012.14740/) (2020)
- [TAT-QA: A Question Answering Benchmark on a Hybrid of Tabular and Textual Content in Finance](https://mlsanity.com/paper/2105.07624/) (2021)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [Deep Modular Co-Attention Networks for Visual Question Answering](https://mlsanity.com/paper/1906.10770/) (2019)
- [IconQA: A New Benchmark for Abstract Diagram Understanding and Visual Language Reasoning](https://mlsanity.com/paper/2110.13214/) (2021)
- [DocFormer: End-to-End Transformer for Document Understanding](https://mlsanity.com/paper/2106.11539/) (2021)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [LayoutTransformer: Layout Generation and Completion with Self-attention](https://mlsanity.com/paper/2006.14615/) (2020)
- [BROS: A Pre-trained Language Model Focusing on Text and Layout for Better Key Information Extraction from Documents](https://mlsanity.com/paper/2108.04539/) (2021)
- [LayoutReader: Pre-training of Text and Layout for Reading Order Detection](https://mlsanity.com/paper/2108.11591/) (2021)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Document Collection Visual Question Answering](https://mlsanity.com/paper/2104.14336/) (2021)

## Built on by (most cited first, 24 of 24)

- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [MM-LLMs: Recent Advances in MultiModal Large Language Models](https://mlsanity.com/paper/2401.13601/) (2024)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solving](https://mlsanity.com/paper/2402.10104/) (2024)
- ["Not Aligned" is Not "Malicious": Being Careful about Hallucinations of Large Language Models' Jailbreak](https://mlsanity.com/paper/2406.11668/) (2024)
- [GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training](https://mlsanity.com/paper/2412.11863/) (2024)
- [SLANG: New Concept Comprehension of Large Language Models](https://mlsanity.com/paper/2401.12585/) (2024)
- [Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration](https://mlsanity.com/paper/2504.12773/) (2025)
- [HiddenGuard: Fine-Grained Safe Generation with Specialized Representation Router](https://mlsanity.com/paper/2410.02684/) (2024)
- [a1: Steep Test-time Scaling Law via Environment Augmented Generation](https://mlsanity.com/paper/2504.14597/) (2025)
- [Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information](https://mlsanity.com/paper/2503.05543/) (2025)
- [FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Network](https://mlsanity.com/paper/2402.11461/) (2024)
- [GeoDANO: Geometric VLM with Domain Agnostic Vision Encoder](https://mlsanity.com/paper/2502.11360/) (2025)
- [Large Language Models as Computable Approximations to Solomonoff Induction](https://mlsanity.com/paper/2505.15784/) (2025)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving](https://mlsanity.com/paper/2602.08524/) (2026)
- [Enhancing Geometric Perception in VLMs via Translator-Guided Reinforcement Learning](https://mlsanity.com/paper/2602.22703/) (2026)
- [Non-Parametric Structural Priors for Geometry Theorem Prediction](https://mlsanity.com/paper/2603.04852/) (2026)
- [BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction](https://mlsanity.com/paper/2606.04648/) (2026)
- [Verifiable Geometry Problem Solving: Solver-Driven Autoformalization and Theorem Proposing](https://mlsanity.com/paper/2606.27926/) (2026)
- [Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry](https://mlsanity.com/paper/2608.14585/) (2026)
- [From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning](https://mlsanity.com/paper/2609.10335/) (2026)
- [Dense Neuro-Symbolic Reasoning in a Unified Geometry State](https://mlsanity.com/paper/2610.04280/) (2026)

## Abstract (arXiv)

Geometry problem solving (GPS) is a challenging mathematical reasoning task requiring multi-modal understanding, fusion, and reasoning. Existing neural solvers take GPS as a vision-language task but are short in the representation of geometry diagrams that carry rich and complex layout information. In this paper, we propose a layout-aware neural solver named LANS, integrated with two new modules: multimodal layout-aware pre-trained language module (MLA-PLM) and layout-aware fusion attention (LA-FA). MLA-PLM adopts structural-semantic pre-training (SSP) to implement global relationship modeling, and point-match pre-training (PMP) to achieve alignment between visual points and textual points. LA-FA employs a layout-aware attention mask to realize point-guided cross-modal fusion for further boosting layout awareness of LANS. Extensive experiments on datasets Geometry3K and PGPS9K validate the effectiveness of the layout-aware modules and superior problem-solving performance of our LANS solver, over existing symbolic and neural solvers. The code will be made public available soon.