ChartDensity-Bench: Benchmarking MLLMs for Numerical Data Reconstruction under Visual Density

Xinhe Wu; Yadong Jin

cs.LGSep 30, 2026

ChartDensity-Bench: Benchmarking MLLMs for Numerical Data Reconstruction under Visual Density

Authors: Xinhe Wu, Yadong Jin

Organizations: iSoftStone AI Research Lab (ISSAIR) iSoftStone Beijing, China

Abstract

Multimodal large language models (MLLMs) offer a promising approach for recovering numerical data from scientific charts, but their ability to reconstruct chart data from visually dense figures remains poorly understood. Existing chart understanding benchmarks primarily evaluate question answering or chart-level reasoning and provide limited support for evaluating structured numerical reconstruction from scientific figures. We introduce \textbf{ChartDensity-Bench}, a benchmark for evaluating MLLMs on structured numerical data reconstruction from compound chart figures under controlled visual density. Built from charts paired with source-level ground-truth data, ChartDensity-Bench systematically varies the number of simultaneously presented charts ( $k\in{1,3,6,9}$ ), enabling controlled evaluation of density-induced degradation. We further propose a multi-dimensional evaluation framework covering structural reliability, reconstruction completeness, parseability, and numerical fidelity. Experiments on five recent MLLMs show that numerical reconstruction generally degrades as visual density increases, while the magnitude of degradation varies substantially across models. Chart-level paired comparisons further show that the same source chart can incur higher reconstruction error when embedded in denser visual contexts. These findings highlight visual density as an important and previously underexplored factor in MLLM chart data reconstruction and provide a systematic benchmark for evaluating model robustness in this setting.

Figures & tables

Figure 1 : Overview of ChartDensity-Bench. Source charts are systematically composed into increasingly dense compound figures with

k\in\{1,3,6,9\}

charts. MLLMs must identify each constituent chart and reconstruct its underlying numerical data. The benchmark separately measures structural reliability, reconstruction completeness, and numerical fidelity, enabling controlled analysis of performance degradation under increasing visual density.

Panel of Figure 2 — Figure 2 : Numerical reconstruction error under increasing chart density. The x-axis denotes the number of simultaneously presented subplots. Lower values indicate better reconstruction fidelity.

Model	$\Delta$ MAE $\uparrow$	Rel. $\Delta$ MAE $\uparrow$	$\Delta$ RMSE $\uparrow$	Rel. $\Delta$ RMSE $\uparrow$
Doubao	4.4009	51.82%	5.6338	47.30%
Gemini	3.0017	54.46%	3.8754	47.57%
GLM	7.3937	84.81%	8.5409	67.31%
Kimi	1.5191	19.18%	2.2397	19.89%
Qwen	5.7183	81.01%	7.4899	73.30%

Table 1: Density-induced degradation in numerical reconstruction from 1 to 9 subplots.

\Delta

denotes the absolute increase in error, while Relative

\Delta

measures the increase relative to the single-chart baseline.

Panel of Figure 3 — Figure 3 : Relationship between point coverage and numerical reconstruction error under increasing chart density. Better reconstruction lies toward the upper-right region, corresponding to higher point coverage and lower numerical error.

Panel of Figure 4 — Figure 4 : Paired chart-level comparison between the 1- and 9-chart conditions. Each point corresponds to the same source chart; values above the diagonal indicate higher error under density 9. The right panel shows the distribution of per-chart error changes.

Model	$\beta$	Std. Error	95% CI	$p$	$R^{2}$
Doubao	0.582	0.117	[0.354, 0.811]	$<.001$	.013
Gemini	0.296	0.099	[0.103, 0.490]	.003	.004
GLM	0.940	0.138	[0.671, 1.210]	$<.001$	.027
Kimi	0.181	0.096	[-0.008, 0.369]	.060	.002
Qwen	0.627	0.109	[0.413, 0.841]	$<.001$	.018

Table 2: Per-model sensitivity of chart reconstruction error to visual density.

\beta

is the slope from

MAE=\alpha+\beta\cdot Density+\epsilon

. Positive slopes indicate increasing numerical error as more charts are presented simultaneously.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Subplots	RFV	EC	PR	Point Coverage	MAE	RMSE
doubao	1	1.0000	0.8366	0.7629	0.5331	8.4932	11.9111
	3	0.9914	0.7817	0.7652	0.4844	9.1226	13.1354
	6	0.9310	0.6887	0.7500	0.4411	11.4940	16.2040
	9	0.8182	0.5754	0.7213	0.3896	12.8941	17.5449
gemini	1	1.0000	0.8731	0.8428	0.6052	5.5119	8.1466
	3	0.9310	0.7771	0.8889	0.5559	8.2033	11.6073

Appendix

Table S1 : Overall reconstruction performance comparison across different models and subplot counts.

Panel of Figure 8 — Figure S1 : Paired chart-level comparison between the 1- and 9-chart conditions. Each point corresponds to the same source chart; values above the diagonal indicate higher error under density 9. The right panel shows the distribution of per-chart error changes.

Model (ref. = kimi)
Term	Coef.	Std. Error	$z$	$p$ -value	CI Low	CI High
Intercept	8.7545	0.6280	13.9398	$<$ 0.0001	7.5235	9.9854
doubao	0.4171	0.6438	0.6479	0.5171	-0.8448	1.6789
gemini	-2.4025	0.6306	-3.8097	0.0001	-3.6385	-1.1664
glm	0.3972	0.6235	0.6370	0.5241	-0.8249	1.6193
qwen	-1.0514	0.6309	-1.6665	0.0956	-2.2879	0.1852

Appendix

Table S2 : Regression results for the linear mixed-effects model. The reference categories are kimi for model and 1 for density.

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Chart-FR1: Visual Focus-Driven Fine-Grained Reasoning on Dense Charts

Hongkun Pan, Yuwei Wu, Wanyi Hong, Shenghui Hu+7

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Chart Multimodal Reasoning Multimodal Large Language Models Large Reasoning Models Fine-Grained Perception Dense

Open paper AskPDF arXiv

Multimodal large language models (MLLMs) have shown considerable potential in chart understanding and reasoning tasks. However, they still struggle with high information density (HID) charts characterized by multiple subplots, legends, and dense annotations due to three major challenges: (1) limited fine-grained perception results in the omission of critical visual cues; (2) redundant or noisy visual information undermines the performance of multimodal reasoning; (3) lack of adaptive deep reasoning relative to the amount of visual information. To tackle these challenges, we present a novel focus-driven fine-grained chart reasoning model, Chart-FR1, to improve perception, focusing efficiency, and adaptive deep reasoning on HID charts. Specifically, we propose Focus-CoT, a visual focusing chain-of-thought that enhances fine-grained perception by explicitly linking reasoning steps to key visual cues, such as local image regions and OCR signals. Building on this, we introduce Focus-GRPO, a focus-driven reinforcement learning algorithm with an information-efficiency reward that compresses redundant visual information for efficient focusing, and an adaptive KL penalty mechanism that enables flexible control over reasoning depth as more visual cues are discovered. Furthermore, to fill the gap in benchmarks for HID charts, we build HID-Chart, a challenging benchmark with an information-density metric designed to evaluate fine-grained chart reasoning capabilities. Extensive experiments on multiple chart benchmarks demonstrate that Chart-FR1 outperforms state-of-the-art MLLMs in chart understanding and reasoning. Code is available at https://github.com/phkhub/Chart-FR1.

Abstract

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