# Why Vision Language Models Struggle with Visual Arithmetic? Towards Enhanced Chart and Geometry Understanding

arXiv: https://arxiv.org/abs/2502.11492 · HTML: https://mlsanity.com/paper/2502.11492/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 29 of 29)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [InternVL: Scaling up Vision Foundation Models and Aligning for Generic Visual-Linguistic Tasks](https://mlsanity.com/paper/2312.14238/) (2023)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs](https://mlsanity.com/paper/2401.06209/) (2024)
- [DataComp: In search of the next generation of multimodal datasets](https://mlsanity.com/paper/2304.14108/) (2023)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [LLaVA-CoT: Let Vision Language Models Reason Step-by-Step](https://mlsanity.com/paper/2411.10440/) (2024)
- [Prismatic VLMs: Investigating the Design Space of Visually-Conditioned Language Models](https://mlsanity.com/paper/2402.07865/) (2024)
- [Enhancing the Reasoning Ability of Multimodal Large Language Models via Mixed Preference Optimization](https://mlsanity.com/paper/2411.10442/) (2024)
- [MM1: Methods, Analysis & Insights from Multimodal LLM Pre-training](https://mlsanity.com/paper/2403.09611/) (2024)
- [ShowUI: One Vision-Language-Action Model for GUI Visual Agent](https://mlsanity.com/paper/2411.17465/) (2024)
- [Improve Vision Language Model Chain-of-thought Reasoning](https://mlsanity.com/paper/2410.16198/) (2024)
- [Why are Visually-Grounded Language Models Bad at Image Classification?](https://mlsanity.com/paper/2405.18415/) (2024)
- [No "Zero-Shot" Without Exponential Data: Pretraining Concept Frequency Determines Multimodal Model Performance](https://mlsanity.com/paper/2404.04125/) (2024)
- [CRMArena: Understanding the Capacity of LLM Agents to Perform Professional CRM Tasks in Realistic Environments](https://mlsanity.com/paper/2411.02305/) (2024)
- [When Do We Not Need Larger Vision Models?](https://mlsanity.com/paper/2403.13043/) (2024)
- [From Pixels to Insights: A Survey on Automatic Chart Understanding in the Era of Large Foundation Models](https://mlsanity.com/paper/2403.12027/) (2024)
- [Do LVLMs Understand Charts? Analyzing and Correcting Factual Errors in Chart Captioning](https://mlsanity.com/paper/2312.10160/) (2023)
- [VisOnlyQA: Large Vision Language Models Still Struggle with Visual Perception of Geometric Information](https://mlsanity.com/paper/2412.00947/) (2024)
- [Slow Perception: Let's Perceive Geometric Figures Step-by-step](https://mlsanity.com/paper/2412.20631/) (2024)
- [Visually Descriptive Language Model for Vector Graphics Reasoning](https://mlsanity.com/paper/2404.06479/) (2024)
- [The Illusion-Illusion: Vision Language Models See Illusions Where There Are None](https://mlsanity.com/paper/2412.18613/) (2024)

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

- [Recitation over Reasoning: How Cutting-Edge Language Models Can Fail on Elementary School-Level Reasoning Problems?](https://mlsanity.com/paper/2504.00509/) (2025)
- [ReCAD: Reinforcement Learning Enhanced Parametric CAD Model Generation with Vision-Language Models](https://mlsanity.com/paper/2512.06328/) (2025)
- [Multimodal Cultural Safety: Evaluation Framework and Alignment Strategies](https://mlsanity.com/paper/2505.14972/) (2025)
- [VLMs have Tunnel Vision: Evaluating Nonlocal Visual Reasoning in Leading VLMs](https://mlsanity.com/paper/2507.13361/) (2025)
- [Watch Before You Answer: Learning from Visually Grounded Post-Training](https://mlsanity.com/paper/2604.05117/) (2026)
- [A Survey of Deep Learning for Geometry Problem Solving](https://mlsanity.com/paper/2507.11936/) (2025)
- [Visual serial processing deficits explain divergences in human and VLM reasoning](https://mlsanity.com/paper/2509.25142/) (2025)
- [Visual Language Models show widespread visual deficits on neuropsychological tests](https://mlsanity.com/paper/2504.10786/) (2025)
- [MEENA (PersianMMMU): Multimodal-Multilingual Educational Exams for N-level Assessment](https://mlsanity.com/paper/2508.17290/) (2025)
- [TangramSR: Can Vision-Language Models Reason in Continuous Geometric Space?](https://mlsanity.com/paper/2602.05570/) (2026)
- [Egocentric Co-Pilot: Web-Native Smart-Glasses Agents for Assistive Egocentric AI](https://mlsanity.com/paper/2603.01104/) (2026)
- [Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey](https://mlsanity.com/paper/2505.14340/) (2025)
- [M3Kang: Evaluating Multilingual Multimodal Mathematical Reasoning in Vision-Language Models](https://mlsanity.com/paper/2601.16218/) (2026)
- [GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solving](https://mlsanity.com/paper/2602.08524/) (2026)
- [Multimodal Information Fusion for Chart Understanding: A Survey of MLLMs -- Evolution, Limitations, and Cognitive Enhancement](https://mlsanity.com/paper/2602.10138/) (2026)
- [Almieyar-Oryx-BloomBench: A Bilingual Multimodal Benchmark for Cognitively Informed Evaluation of Vision-Language Models](https://mlsanity.com/paper/2606.05531/) (2026)
- [What's in Common? Multimodal Models Hallucinate When Reasoning Across Scenes](https://mlsanity.com/paper/2511.03768/) (2025)
- [Left-Right Symmetry Breaking in CLIP-style Vision-Language Models Trained on Synthetic Spatial-Relation Data](https://mlsanity.com/paper/2601.12809/) (2026)
- [CoTZero: Annotation-Free Human-Like Vision Reasoning via Hierarchical Synthetic CoT](https://mlsanity.com/paper/2602.08339/) (2026)
- [VLMs Trace Without Tracking: Diagnosing Failures in Visual Path Following](https://mlsanity.com/paper/2605.15672/) (2026)
- [Anchored, Not Graded: Vision-Language Models Fail at Slant-from-Texture Perception](https://mlsanity.com/paper/2606.06714/) (2026)
- [A Dataset for Dynamic Human Preferences for Vision Language Models](https://mlsanity.com/paper/2606.07653/) (2026)
- [Math2Visual-X: A Modular Framework for Pedagogically Aligned Lower-Primary Math Visuals Generation](https://mlsanity.com/paper/2609.22647/) (2026)
- [When to Rethink: Learning Multi-Perspective Self-Verification for Vision-Language Models](https://mlsanity.com/paper/2610.07018/) (2026)

## Abstract (arXiv)

Vision Language Models (VLMs) have achieved remarkable progress in multimodal tasks, yet they often struggle with visual arithmetic, seemingly simple capabilities like object counting or length comparison, which are essential for relevant complex tasks like chart understanding and geometric reasoning. In this work, we first investigate the root causes of this deficiency through a suite of probing tasks focusing on basic visual arithmetic. Our analysis reveals that while pre-trained vision encoders typically capture sufficient information, the text decoder often fails to decode it correctly for arithmetic reasoning. To address this, we propose CogAlign, a novel post-training strategy inspired by Piaget's theory of cognitive development. CogAlign trains VLMs to recognize invariant properties under visual transformations. We demonstrate that this approach significantly improves the performance of three diverse VLMs on our proposed probing tasks. Furthermore, CogAlign enhances performance by an average of 4.6% on CHOCOLATE and 2.9% on MATH-VISION, outperforming or matching supervised fine-tuning methods while requiring only 60% less training data. These results highlight the effectiveness and generalizability of CogAlign in improving fundamental visual arithmetic capabilities and their transfer to downstream tasks.