NumerosityVLM: A Cognitively Inspired Benchmark for Interpreting Numerosity Representations in Vision-Language Models
Authors: Yiming Fu, Fangjun Li, Xiujin Liu, Ruidong Ma, Hang Yu, Zhichen Lu, Kanwei He, Alessandro Di Nuovo, +2 more
Organizations: Cognitive Robotics Lab, Department of Computer Science, The University of Manchester, Manchester M13 9PL, UK · University of Michigan, MI 48109, USA · Sheffield Hallam University, Sheffield S1 1WB, UK · Tufts University, MA 02155, USA · ENSTA, Institut Polytechnique de Paris, Palaiseau 91120, France
Vision-language models (VLMs) achieve strong performance on high-level multimodal tasks, yet numerosity perception, a cognitive ability that emerges in human infants before language acquisition, remains poorly understood in current models, as existing counting benchmarks entangle numerosity with correlated visual factors. We introduce a cognitively inspired diagnostic benchmark, NumerosityVLM, comprising 10,800 synthetic images across six controlled conditions. The benchmark orthogonally manipulates object size, spatial arrangement, and numerosity, while progressively ablating texture, shape, and color. Evaluating seven VLMs in a zero-shot setting, multi-factor analysis reveals that model architecture explains the largest proportion of performance variance (partial ω2=0.325), far exceeding visual conditions. Layer-wise probing further shows that linearly separable numerosity signals consistently emerge at early stages of the vision encoder, while performance differences across evaluated models are primarily associated with the language model component. Code and data are publicly available at https://github.com/fuy3/NumerosityVLM-Benchmark, and https://huggingface.co/datasets/fuy3/NumerosityVLM.
Figures & tables
Figure 1: Overview of the proposed NumerosityVLM benchmark framework. Left: The diagnostic benchmark comprises three object categories, six controlled conditions, and 12 numerosity levels. Right: Layer-wise probing is conducted across the full VLM pipeline to localize the source of numerosity perception failures.
Figure 2: Representative dataset stimuli under the six controlled conditions. Columns show the designed controlled conditions. Rows illustrate numerosities of 1, 11, and 100 using examples from the apple, butterfly, and human-figure categories.
Model
Version
Year
Input Size
Vision Model
Language Model
CLIP
CLIP-ViT-B/32
2021
224 × 224
ViT-B/32
Transformer
LLaVA
LLaVA-1.5-7B-hf
2023
336 × 336
ViT-L/14
Vicuna-7B
LLaVA-OneVision- Qwen2-7B-ov-hf
2024
384 × 384
SigLIP
Qwen2-7B
InternVL
InternVL3-1B-hf
2025
448 × 448
InternViT
Qwen2.5-0.5B
InternVL3-8B-hf
2025
448 × 448
InternViT
Qwen2.5-7B
QwenVL
Qwen3VL-4B-Instruct
2025
Dynamic
Qwen3-ViT
Qwen3-4B
Table 1: Overview of the seven evaluated open-source vision-language models, including the backbone architectures of their vision and language components.
Model
Accuracy (%) ↑
MAE error ↓
NAE error ↓
InternVL3-1B
15.56
21.40
2.24
CLIP-ViT-B/32
20.39
24.06
2.97
LLaVA-1.5-7B
27.24
32.23
1.95
LLaVA-OneVision-Qwen2-7B
71.28
18.14
0.35
InternVL3-8B
77.21
18.47
0.35
Qwen3VL-4B-Instruct
77.73
24.97
0.36
Table 2: Overall performance comparison across different VLMs.
Figure 3: Comprehensive evaluation of numerosity understanding in VLMs. (a–b) Accuracy across conditions and mean residuals indicating underestimation at higher numerosity. (c–d) Output-layer and linear-probe confusion matrices for selected models.
Group
Comparison
Raw p -value
Corrected p -value
Sig.
Tier-1
Baseline vs Size-incongruent
1.96×10−3
2.75×10−3
∗∗
Tier-1
Baseline vs Space-incongruent
8.31×10−1
8.49×10−1
−
Tier-1
Baseline vs Texture-ablated
1.63×10−29
5.72×10−29
∗∗∗
Tier-1
Texture-ablated vs Shape-ablated
3.87×10−40
2.71×10−39
∗∗∗
Tier-1
Shape-ablated vs Color-ablated
1.79×10−14
4.17×10−14
∗∗∗
Tier-2
Baseline vs Size-incongruent
2.53×10−52
1.77×10−51
∗∗∗
Table 4: Pairwise statistical comparisons across experimental conditions. Reported p -values are shown before and after multiple-comparison correction. Significance levels: ∗p<0.05 , ∗∗p<0.01 , ∗∗∗p<0.001 ; − indicates no significant difference.
Figure 4: Layer-wise probing results. Numerosity signals emerge early in the vision encoder, while performance differences primarily arise during language modeling.
Figure 5: PC1 projections across evaluated models. Tier-1 models (a–d) show clear monotonic organization, whereas Tier-2 models (e–g) exhibit weaker or inconsistent scaling.
Recent vision-language models (VLMs) excel at multimodal understanding and reasoning, yet their fine-grained visual perception remains underexplored. A natural extension of ``How many r are there in Strawberry?'' asks: how small a visual pattern can a VLM reliably perceive? As such, we introduce FineSightBench, a new benchmark that systematically probes this limit by separating perception tasks (pixel-level recognition of letters, shapes, objects) from reasoning tasks (spatial reasoning, counting, ordering over small targets) across controlled scales of 4--48px. Through comprehensive experiments and detailed failure mode analysis on state-of-the-art models, we reveal a sharp dissociation: perception saturates around 12px, while reasoning remains limited even at larger scales, with persistent numeracy and sequence errors. These findings expose fundamental deficiencies in VLMs' fine-scale visual reasoning that demand more rigorous evaluation.
Lujun Li, Lama Sleem, Niccolo Gentile +4
University of Luxembourg · Foyer S.A. · Université Paris-Saclay
Vision-Language Models (VLMs) have advanced across multimodal benchmarks but still show clear gaps in ordinal number understanding, i.e., the ability to track relative positions and generalize to large indices. We present OrdinalBench, a diagnostic benchmark that standardizes ordinal number understanding as an evaluation task for VLMs. The core task is N-th object identification, defined by a starting reference and traversal rule. Task difficulty is controlled along three axes: (i) ordinal magnitude, from small numbers to extreme cases up to 300; (ii) arrangement complexity, from single loops to maze-like paths; and (iii) object count. The benchmark provides 39,000 question-answer pairs, each annotated with a ground-truth reasoning trajectory and balanced across difficulty levels for controlled large-scale testing. Beyond answer-only evaluation, our framework requires models to generate structured stepwise traces of the counting process and provides an open evaluation toolkit that measures both final accuracy and step-level path consistency. Zero-shot evaluations of GPT-5, Gemini 2.5 Flash Lite, Qwen2.5-VL, InternVL3.5, and Molmo reveal sharp degradation under large-ordinal and complex-path conditions, highlighting weak generalization despite strong scores on standard multimodal tasks. By framing ordinal number understanding as a core target, OrdinalBench provides a reproducible benchmark and diagnostic framework for developing VLMs with stronger sequential reasoning. All data and code are available at https://ordinalbench.github.io/
Yusuke Tozaki, Hisashi Miyamori
Division of Frontier Informatics, Kyoto Sangyo University, Kyoto, Japan
Vision--language models (VLMs) have achieved impressive performance on complex multimodal reasoning tasks, yet they still fail on simple grounding skills such as object counting. Existing evaluations mostly assess only final outputs, offering limited insight into where these failures arise inside the model. In this work, we present an empirical study of VLM counting behavior through both behavioral and mechanistic analysis. We introduce COUNTINGTRICKS, a controlled evaluation suite of simple shape-based counting cases designed to expose vulnerabilities under different patchification layouts and adversarial prompting conditions. Using attention analysis and component-wise probing, we show that count-relevant visual evidence is strongest in the modality projection stage but degrades substantially in later language layers, where models become more susceptible to text priors. Motivated by this finding, we further evaluate Modality Attention Share (MAS), a lightweight intervention that encourages a minimum budget of visual attention during answer generation. Our results suggest that counting failures in VLMs stem not only from visual perception limits, but also from the underuse of visual evidence during language-stage reasoning. Code and dataset will be released at https://github.com/leduy99/-CVPRW26-Modality-Attention-Share.
Duy Le Dinh Anh, Patrick Amadeus Irawan, Tuan Van Vo