# Nodes Are Early, Edges Are Late: Probing Diagram Representations in Large Vision-Language Models

arXiv: https://arxiv.org/abs/2603.02865 · HTML: https://mlsanity.com/paper/2603.02865/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Placed in

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

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

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [A Diagram Is Worth A Dozen Images](https://mlsanity.com/paper/1603.07396/) (2016)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Annotation Artifacts in Natural Language Inference Data](https://mlsanity.com/paper/1803.02324/) (2018)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [What do you learn from context? Probing for sentence structure in contextualized word representations](https://mlsanity.com/paper/1905.06316/) (2019)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Towards Best Practices of Activation Patching in Language Models: Metrics and Methods](https://mlsanity.com/paper/2309.16042/) (2023)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Interpreting CLIP's Image Representation via Text-Based Decomposition](https://mlsanity.com/paper/2310.05916/) (2023)
- [An Analysis of Visual Question Answering Algorithms](https://mlsanity.com/paper/1703.09684/) (2017)
- [SciCap: Generating Captions for Scientific Figures](https://mlsanity.com/paper/2110.11624/) (2021)
- [DeepStack: Deeply Stacking Visual Tokens is Surprisingly Simple and Effective for LMMs](https://mlsanity.com/paper/2406.04334/) (2024)
- [Beyond Question-Based Biases: Assessing Multimodal Shortcut Learning in Visual Question Answering](https://mlsanity.com/paper/2104.03149/) (2021)
- [Cognitive Dissonance: Why Do Language Model Outputs Disagree with Internal Representations of Truthfulness?](https://mlsanity.com/paper/2312.03729/) (2023)
- [Do Vision-Language Models Really Understand Visual Language?](https://mlsanity.com/paper/2410.00193/) (2024)
- [FlowLearn: Evaluating Large Vision-Language Models on Flowchart Understanding](https://mlsanity.com/paper/2407.05183/) (2024)
- [Localizing Lying in Llama: Understanding Instructed Dishonesty on True-False Questions Through Prompting, Probing, and Patching](https://mlsanity.com/paper/2311.15131/) (2023)
- [Benchmarking and Improving Large Vision-Language Models for Fundamental Visual Graph Understanding and Reasoning](https://mlsanity.com/paper/2412.13540/) (2024)
- [Summaries as Captions: Generating Figure Captions for Scientific Documents with Automated Text Summarization](https://mlsanity.com/paper/2302.12324/) (2023)
- [Evaluating Nuanced Bias in Large Language Model Free Response Answers](https://mlsanity.com/paper/2407.08842/) (2024)
- [Shape It Up: An Empirically Grounded Approach for Designing Shape Palettes](https://mlsanity.com/paper/2408.16079/) (2024)
- [Perception of Line Attributes for Visualization](https://mlsanity.com/paper/2308.04150/) (2023)

## Built on by (most cited first, 1 of 1)

- [Diagram-MMU: A Multi-Modal Benchmark for Scientific Diagrams](https://mlsanity.com/paper/2608.12262/) (2026)

## Abstract (arXiv)

Large vision-language models (LVLMs) demonstrate strong performance on diagram understanding benchmarks, yet they still struggle with understanding relationships between elements, particularly those represented by nodes and directed edges (e.g., arrows and lines). To investigate the underlying causes of this limitation, we probe the internal representation of LVLMs using a carefully constructed synthetic diagram dataset based on directed graphs. Our probing experiments reveal that edge information is not linearly separable in the vision encoder and becomes linearly encoded only in the text tokens in the language model. In contrast, node information and global structural features are already linearly encoded in individual hidden states of the vision encoder. These findings suggest that the stage at which linearly separable representations are formed varies depending on the type of visual information. In particular, the delayed emergence of edge representations may help explain why LVLMs struggle with relational understanding, such as interpreting edge directions, which require more abstract, compositionally integrated processes.