README.md

---
license: cc-by-4.0
pretty_name: NumerosityVLM
task_categories:
  - visual-question-answering
language:
  - en
size_categories:
  - 10K<n<100K
tags:
  - counting
  - numerosity
  - vision-language-models
  - synthetic
  - cognitive-vision
  - benchmark
---

# NumerosityVLM: A Cognitively Inspired Numerosity Benchmark for Vision-Language Models

NumerosityVLM is a controlled synthetic benchmark for evaluating numerosity perception in vision-language models (VLMs). It disentangles numerosity from correlated visual factors by systematically varying object size, spatial arrangement, and appearance cues.

The benchmark contains **10,800 images** across six controlled conditions, three object categories, and twelve numerosity levels spanning 1 to 100.

This dataset accompanies *A Cognitively Inspired Benchmark for Interpreting Numerosity Representations in Vision-Language Models*, submitted to the [3rd Workshop on Human-inspired Computer Vision (HCV), ECCV 2026](https://sites.google.com/view/hcvworkshop2026). Publication information will be added when available.

## Dataset Examples

The examples below illustrate how the benchmark preserves the target numerosity while controlling or removing non-numerical visual cues. The six conditions progress from naturalistic object images to increasingly abstract representations, making it possible to test whether a model relies on number itself or on correlated properties such as object area, spatial extent, texture, shape, and color.

![Representative samples from the six NumerosityVLM conditions](assets/dataset.png)

*Representative samples from the six controlled conditions. Rows show the three object categories, while columns show the baseline, orthogonal-control, and visual-cue-ablation conditions.*

## Dataset Design

NumerosityVLM comprises two complementary groups of experimental conditions.

### Orthogonal control conditions

| Condition | Purpose |
|---|---|
| **Baseline** | Preserves the natural covariation between numerosity and visual statistics. |
| **Size-Incongruent** | Varies object size while controlling total occupied area, decoupling numerosity from individual object scale. |
| **Space-Incongruent** | Manipulates spatial distribution while controlling spatial extent, decoupling numerosity from spatial coverage. |

### Visual cue ablation conditions

| Condition | Purpose |
|---|---|
| **Texture-Ablated** | Replaces textured objects with abstract, shape-matched colored silhouettes while preserving their spatial layout. |
| **Shape-Ablated** | Replaces objects with solid colored circles. |
| **Color-Ablated** | Converts colored dots to grayscale. |

Together, these conditions form a progression from naturalistic object renderings to minimal visual representations, allowing counting behavior to be examined under controlled changes in non-numerical cues.

## Dataset Summary

| Property | Value |
|---|---:|
| Total images | 10,800 |
| Image resolution | 1024 × 1024 pixels |
| Background | White canvas |
| Conditions | 6 |
| Object categories | 3 |
| Subtypes per category | 5 |
| Numerosity levels | 12 |
| Numerosity range | 1–100 |
| Instances per condition × category × numerosity | 50 |

The total number of images is:

```text
6 conditions × 3 object categories × 12 numerosity levels × 50 instances = 10,800 images
```

The five subtypes are visual variants within each object category and do not constitute an additional factor in the image-count calculation.

The three object categories are:

- apples;
- butterflies;
- human figures.

All objects are non-overlapping and fully contained within the image boundary. The twelve numerosity levels cover both the human **subitizing range** (1–4) and the **Approximate Number System (ANS)** range, with larger values spaced approximately logarithmically up to 100.

## Intended Uses

NumerosityVLM is intended for:

- zero-shot evaluation of counting and numerosity perception in VLMs;
- analysis of sensitivity to object size, spatial arrangement, texture, shape, and color;
- comparison of counting behavior across model architectures;
- research on human-inspired computer vision and computational number perception.

The dataset is primarily a **diagnostic benchmark**, not a training corpus. Training on the evaluation images may compromise the interpretation of benchmark results.

## Dataset Structure

Each image is associated with annotations describing its ground-truth numerosity and controlled visual factors:

```text
image        image file
count        ground-truth numerosity
condition    experimental condition
category     apple, butterfly, or human figure
subtype      within-category visual subtype
instance_id  unique sample identifier
```

### Splits

NumerosityVLM is released as an evaluation benchmark and does not define canonical training, validation, and test partitions.

## Evaluation Framework

The accompanying evaluation framework uses the controlled image conditions to assess VLM counting behavior and analyze numerosity representations across the multimodal pipeline. It connects the dataset design to model-level comparisons, systematic bias analysis, and layer-wise probing, allowing the effects of visual factors and model architecture to be examined separately.

![Overview of the NumerosityVLM benchmark and evaluation framework](assets/main.png)

*Overview of the evaluation framework, connecting the controlled image benchmark with VLM evaluation and representation analysis.*

This Hugging Face repository hosts the **image dataset**. The evaluation code, experimental pipeline, and implementation details are available in the [NumerosityVLM-Benchmark GitHub repository](https://github.com/fuy3/NumerosityVLM-Benchmark).


## Disclaimer

The dataset is provided for research and evaluation; users are responsible for ensuring that their use complies with the applicable terms and rights associated with the repository and its contents.

## Authors

Yiming Fu, Fangjun Li, Xiujin Liu, Ruidong Ma, Hang Yu, Zhichen Lu, Kanwei He, Alessandro Di Nuovo, Angelo Cangelosi, and Zhegong Shangguan*.

This dataset accompanies a paper submitted to the 3rd Workshop on Human-inspired Computer Vision (HCV), ECCV 2026.

For questions about the dataset or paper, contact Yiming Fu at `yimingfu93@gmail.com` or the corresponding author at `zhegong.shangguan@manchester.ac.uk`.