Datasets:

lulidong
/

PhysCount

---
pretty_name: PhysCount
language:
  - en
task_categories:
  - visual-question-answering
size_categories:
  - 1K<n<10K
tags:
  - visual-counting
  - multimodal
  - physical-reasoning
  - reflection
  - transparency
configs:
  - config_name: questions
    data_files:
      - split: test
        path: data/questions.jsonl
  - config_name: annotations
    data_files:
      - split: test
        path: data/annotations.jsonl
---
# PhysCount

**PhysCount: Do MLLMs Count Visual Appearances or Physical Entities?**

![PhysCount overview](assets/teaser.png)

## Summary

**PhysCount** evaluates whether multimodal large language models distinguish visible appearances from the physical objects they depict. Mirrors and glass can make one entity appear several times, while some objects are visible only through reflection or transmission. Counting these scenes requires identifying appearances, recognizing how they are observed, and determining which appearances belong to the same physical entity.

The benchmark contains **4,595 human-written counting questions** from **546 real-world images**, organized into **651 target-specific annotation groups**. Each group pairs questions with appearance locations, image-formation labels, and same-entity assignments. Four question families examine complementary quantities derived from the same annotated scene:

- **Appearance:** enumerate every visible occurrence of the target.
- **Entity:** count physical objects, merging appearances of the same entity when required.
- **Image formation:** count reflected appearances or appearances seen through glass.
- **Correspondence:** count shared identities, intersections, exclusive sets, and reflection multiplicities.

Experiments with 40 MLLMs show a substantial gap between enumerating appearances and answering counts defined by physical identity. Even the strongest evaluated model answers every question correctly in only **13.36%** of groups.

![PhysCount statistics](assets/benchmark_statistics.png)

## Dataset Statistics

| Property | Value |
|---|---:|
| Images | 546 |
| Annotation groups | 651 |
| Counting questions | 4,595 |
| Annotated appearances | 7,086 |
| Counting targets | 137 |
| Groups covering all four question families | 599 |
| Appearance questions | 651 |
| Entity questions | 1,150 |
| Image-formation questions | 711 |
| Correspondence questions | 2,083 |

Each group includes one appearance question. The appearance annotations comprise 2,416 direct appearances, 3,996 reflected appearances, and 674 appearances seen through glass. PhysCount provides a test split with factual counting questions.

## Results

All 40 evaluated models are reported below. **Score** is the primary ranking metric; **Group-Acc** measures complete-group correctness, and **Phys-Gnd** measures physical reasoning after an exact appearance count.

| Model | A-MAE ↓ | A-NAE ↓ | E-MAE ↓ | E-NAE ↓ | I-MAE ↓ | I-NAE ↓ | C-MAE ↓ | C-NAE ↓ | Score ↑ | Group-Acc ↑ | Phys-Gnd ↑ |
|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| Gemini 3.7 Flash | 2.724 | 20.08 | 2.046 | 27.36 | 2.467 | 30.62 | 1.396 | 33.88 | 36.45 | 13.36 | 73.00 |
| Muse-Glimmer-30B | 2.943 | 20.31 | 2.478 | 32.10 | 2.405 | 28.69 | 1.608 | 43.04 | 29.61 | 7.83 | 65.51 |
| Qwen3.8-27B | 3.149 | 19.89 | 2.511 | 32.42 | 2.702 | 29.66 | 1.685 | 44.68 | 28.84 | 7.37 | 65.96 |
| Qwen3.5-397B-A17B | 2.836 | 18.99 | 2.442 | 33.28 | 2.386 | 26.88 | 1.859 | 46.73 | 27.95 | 5.84 | 62.16 |
| Qwen3.5-27B | 4.103 | 20.64 | 3.216 | 34.58 | 3.017 | 26.78 | 2.942 | 48.56 | 26.32 | 6.30 | 60.83 |
| Gemma 4-31B | 3.307 | 21.83 | 2.700 | 36.88 | 2.814 | 33.71 | 1.879 | 41.86 | 26.32 | 6.61 | 60.07 |
| Qwen3.5-122B-A10B | 4.192 | 17.96 | 2.527 | 34.40 | 2.603 | 27.80 | 2.068 | 49.00 | 26.03 | 5.99 | 57.13 |
| Qwen3.5-35B-A3B | 3.143 | 18.81 | 2.425 | 33.44 | 2.621 | 28.49 | 2.011 | 51.51 | 25.70 | 5.99 | 58.76 |
| Gemma 4-26B-A4B | 3.257 | 22.70 | 2.852 | 39.22 | 2.936 | 36.53 | 1.888 | 44.02 | 23.79 | 5.53 | 57.17 |
| Qwen3.5-9B | 2.845 | 20.04 | 3.708 | 36.09 | 3.805 | 30.05 | 4.816 | 53.38 | 23.54 | 5.07 | 55.41 |
| GPT-5.6 Sol | 3.028 | 22.82 | 2.808 | 36.58 | 2.544 | 31.94 | 2.113 | 52.11 | 21.73 | 3.84 | 55.65 |
| InternVL3.5-241B-A28B | 4.135 | 30.21 | 2.825 | 36.24 | 4.597 | 36.63 | 1.983 | 48.11 | 21.04 | 4.92 | 60.27 |
| GPT-6 Astra | 3.049 | 24.87 | 2.673 | 37.72 | 2.517 | 30.99 | 1.905 | 47.83 | 20.77 | 3.38 | 51.89 |
| DeepSeek-V4-Flash-Vision | 4.321 | 30.52 | 2.814 | 36.12 | 3.406 | 37.19 | 1.864 | 48.56 | 20.74 | 5.22 | 61.61 |
| GPT-5.6 Terra | 3.395 | 26.06 | 2.726 | 36.39 | 3.227 | 37.30 | 1.863 | 50.99 | 20.42 | 4.30 | 53.43 |
| Gemma 4-12B | 3.490 | 26.05 | 3.044 | 44.56 | 3.057 | 37.08 | 1.982 | 45.70 | 19.03 | 3.07 | 46.10 |
| Qwen3.5-4B | 3.321 | 22.19 | 4.379 | 39.57 | 2.729 | 32.93 | 3.274 | 57.03 | 18.57 | 3.38 | 48.20 |
| InternVL3.5-30B-A3B | 4.152 | 29.51 | 3.036 | 38.94 | 3.359 | 37.29 | 2.108 | 52.08 | 17.76 | 2.61 | 53.91 |
| MiniMax-M3-428B-A23B | 3.888 | 29.28 | 2.989 | 39.05 | 3.739 | 39.57 | 1.975 | 52.65 | 17.43 | 3.69 | 52.50 |
| GPT-5.6 Luna | 3.536 | 28.24 | 3.368 | 42.24 | 2.992 | 35.07 | 2.283 | 55.98 | 16.87 | 2.92 | 46.98 |
| InternVL3.5-38B | 4.078 | 32.36 | 4.520 | 39.75 | 10.133 | 36.59 | 3.837 | 57.92 | 15.55 | 2.61 | 47.23 |
| InternVL3.5-14B | 4.158 | 29.13 | 2.855 | 40.02 | 3.483 | 38.22 | 2.099 | 57.32 | 15.20 | 1.84 | 44.22 |
| Molmo2-4B | 4.284 | 27.98 | 3.442 | 38.45 | 3.372 | 34.68 | 2.200 | 63.45 | 14.96 | 1.84 | 47.21 |
| Ovis2.6-80B-A3B | 4.132 | 31.39 | 3.089 | 39.59 | 3.313 | 37.88 | 2.302 | 58.70 | 14.93 | 2.15 | 46.79 |
| MiniCPM-V 4.5-8B | 4.528 | 32.52 | 2.828 | 38.82 | 3.426 | 39.32 | 2.176 | 58.40 | 14.90 | 2.76 | 51.28 |
| Cosmos3-Super-64B | 4.144 | 28.29 | 3.003 | 37.39 | 3.051 | 33.50 | 2.339 | 64.08 | 14.69 | 1.38 | 45.67 |
| InternVL3.5-8B | 3.938 | 27.82 | 3.011 | 41.68 | 3.670 | 42.16 | 2.233 | 57.78 | 14.29 | 1.84 | 47.08 |
| Molmo2-8B | 4.174 | 29.30 | 3.209 | 37.50 | 2.996 | 34.35 | 2.484 | 65.41 | 13.13 | 0.92 | 42.99 |
| ERNIE 4.5 VL-28B-A3B | 4.682 | 32.62 | 3.269 | 43.29 | 3.621 | 40.53 | 2.537 | 58.93 | 13.08 | 1.69 | 42.92 |
| MiniCPM-V 4.6-1.3B | 5.720 | 39.90 | 3.340 | 43.56 | 3.694 | 42.36 | 2.252 | 57.22 | 12.40 | 2.15 | 45.11 |
| Cosmos3-Nano-16B | 6.002 | 30.81 | 3.239 | 41.23 | 3.311 | 36.84 | 2.548 | 68.01 | 12.08 | 2.15 | 36.23 |
| Phi-4-Reasoning-Vision-15B | 3.779 | 30.31 | 3.461 | 47.21 | 3.681 | 43.79 | 2.425 | 60.20 | 11.25 | 0.61 | 38.63 |
| LLaVA-OneVision 2-8B | 3.690 | 28.70 | 2.948 | 42.56 | 3.475 | 39.05 | 2.749 | 67.94 | 10.51 | 1.08 | 33.74 |
| InternVL3.5-4B | 7.018 | 38.11 | 3.452 | 48.83 | 3.685 | 39.85 | 2.773 | 65.97 | 9.53 | 1.23 | 36.93 |
| Cosmos3-Edge-4B | 5.332 | 37.23 | 4.005 | 43.59 | 3.555 | 41.68 | 3.209 | 65.98 | 9.27 | 0.77 | 32.42 |
| Granite Vision 4.1-4B | 4.152 | 34.73 | 3.437 | 45.38 | 3.836 | 41.51 | 2.266 | 67.96 | 9.02 | 0.61 | 32.62 |
| Mistral Small 4-119B | 5.582 | 44.59 | 3.526 | 53.29 | 3.908 | 49.46 | 2.660 | 69.42 | 5.87 | 0.00 | 26.18 |
| Gemma 4-E2B | 20.343 | 48.02 | 8.357 | 55.57 | 11.088 | 55.82 | 4.146 | 62.93 | 4.76 | 0.15 | 21.13 |
| Ovis2.6-30B-A3B | 8.207 | 58.71 | 5.285 | 66.79 | 5.397 | 64.98 | 2.404 | 63.92 | 3.80 | 0.46 | 32.38 |
| Gemma 4-E4B | 37.605 | 50.27 | 22.506 | 64.37 | 22.469 | 69.95 | 9.344 | 65.25 | 2.93 | 0.00 | 11.90 |

Higher resolution improves individual counts more readily than complete-group correctness. Presenting related questions together produces larger gains on entity and correspondence questions:

| Qwen3.8-27B setting | Appearance NAE ↓ | Entity NAE ↓ | Formation NAE ↓ | Correspondence NAE ↓ | Score ↑ | Group-Acc ↑ | Phys-Gnd ↑ |
|---|---:|---:|---:|---:|---:|---:|---:|
| 512 px | 28.36 | 37.95 | 37.08 | 49.31 | 21.04 | 5.38 | 62.50 |
| 1,024 px | 21.53 | 33.88 | 32.12 | 46.85 | 26.41 | 7.37 | 63.10 |
| 2,048 px | 19.42 | 33.09 | 31.69 | 44.22 | 27.86 | 7.37 | 61.26 |
| 4,096 px / Independent QA | 19.89 | 32.42 | 29.66 | 44.68 | 28.84 | 7.37 | 65.96 |
| 4,096 px / Joint QA | 19.37 | 26.26 | 32.76 | 33.39 | 40.17 | 23.96 | 78.56 |

## Data Format

The release includes the source images, counting questions and answers, and appearance–entity annotations. Images are numbered sequentially from `000001` through `000546`, retaining their JPEG or PNG format.

### Questions

`data/questions.jsonl` contains one question per line.

| Field | Description |
|---|---|
| `question_id` | Unique question ID. |
| `group_id` | Annotation group shared by questions about the same image and counting target. |
| `image_id` | Image identifier. |
| `image` | Relative path to the image. |
| `question_type` | `appearance`, `entity`, `image_formation`, or `correspondence`. |
| `question` | English counting question. |
| `answer` | Ground-truth integer count. |

### Appearance–Entity Annotations

`data/annotations.jsonl` contains one annotation group per line. Each group stores its `group_id`, `image_id`, image path, original width and height, and a list of `appearances`.

| Appearance field | Description |
|---|---|
| `appearance_id` | Identifier of one annotated occurrence within the group. |
| `entity_id` | Shared identifier for appearances depicting the same physical entity. |
| `mode` | `direct`, `reflection`, or `through_glass`. |
| `x`, `y` | Point coordinates normalized to the image width and height. |

One entity may have several appearances or be visible only in reflection or through glass. Appearances with the same `entity_id` belong to the same physical object.

## Evaluation

### Running GPT Evaluation

Download the benchmark and install the evaluator dependencies:

```bash
hf download lulidong/PhysCount --repo-type dataset --local-dir PhysCount
cd PhysCount
python -m pip install -r evaluation/requirements.txt
export OPENAI_API_KEY="YOUR_KEY"
```

Run independent question answering, then compute the metrics:

```bash
python evaluation/evaluate_gpt.py \
  --data-root . \
  --model YOUR_MODEL_ID \
  --reasoning-effort high \
  --output predictions.jsonl
python evaluation/score.py \
  --data-root . \
  --predictions predictions.jsonl \
  --output metrics.json
```

Use the strongest reasoning setting supported by the selected model, such as `high` or `xhigh`. The generation limit is 32,768 tokens. Optional sampling controls are supplied through `--temperature` and `--top-p` when supported by the model endpoint.

### Prompt

Each image–question pair is evaluated independently. The image and the following prompt are supplied in one user message, with no additional system instruction:

```text
Answer the following counting question about this image. Carefully distinguish
visual appearances from physical entities, including appearances formed by
reflections or seen through glass, and use appearance-entity correspondences
when required by the question. Follow the counting target specified in the
question. Return exactly one non-negative integer, with no labels or prose.
Question: {question}
```

Images retain their native resolution up to a 4,096-pixel long edge. Larger images are resized proportionally without cropping or upsampling. Use `--long-edge` to change the resolution limit.

### Metrics

For a valid predicted count $p$ and ground truth $y$, bounded normalized absolute error is

$$
\mathrm{NAE}(p,y)=\min\!\left(1,\frac{|p-y|}{\max(y,1)}\right).
$$

MAE and NAE are first averaged within each question family in an annotation group, then averaged across groups containing that family. This gives each group equal weight regardless of how many questions it contains.

- **Score:** multiply the available question-family accuracies within each group, then average the products across groups.
- **Group-Acc:** the percentage of groups in which every question is answered exactly.
- **Phys-Gnd:** on groups containing all four families with an exact appearance answer, average the harmonic mean of entity, image-formation, and correspondence accuracy.

MAE is measured in counts. NAE and the three aggregate metrics use a 0–100 scale. Missing, malformed, negative, or extreme predictions receive maximum NAE and fail exact-match evaluation; they are excluded from raw MAE. The evaluator preserves raw responses and parsed predictions.

## Citation

```bibtex
@article{lu2026physcount,
  title={PhysCount: Do MLLMs Count Visual Appearances or Physical Entities?},
  author={Lu, Lidong and Lv, Jiaxin and Dong, Liangrui and Mao, Xinyi and Zou, Lidong and Li, Zhenquan and Lu, Tong and Chen, Guo},
  journal={arXiv preprint arXiv:2610.40530},
  year={2026}
}
```

	---
	pretty_name: PhysCount
	language:
	- en
	task_categories:
	- visual-question-answering
	size_categories:
	- 1K<n<10K
	tags:
	- visual-counting
	- multimodal
	- physical-reasoning
	- reflection
	- transparency
	configs:
	- config_name: questions
	data_files:
	- split: test
	path: data/questions.jsonl
	- config_name: annotations
	data_files:
	- split: test
	path: data/annotations.jsonl
	---
	# PhysCount

	PhysCount: Do MLLMs Count Visual Appearances or Physical Entities?

	![PhysCount overview](assets/teaser.png)

	## Summary

	PhysCount evaluates whether multimodal large language models distinguish visible appearances from the physical objects they depict. Mirrors and glass can make one entity appear several times, while some objects are visible only through reflection or transmission. Counting these scenes requires identifying appearances, recognizing how they are observed, and determining which appearances belong to the same physical entity.

	The benchmark contains 4,595 human-written counting questions from 546 real-world images, organized into 651 target-specific annotation groups. Each group pairs questions with appearance locations, image-formation labels, and same-entity assignments. Four question families examine complementary quantities derived from the same annotated scene:

	- Appearance: enumerate every visible occurrence of the target.
	- Entity: count physical objects, merging appearances of the same entity when required.
	- Image formation: count reflected appearances or appearances seen through glass.
	- Correspondence: count shared identities, intersections, exclusive sets, and reflection multiplicities.

	Experiments with 40 MLLMs show a substantial gap between enumerating appearances and answering counts defined by physical identity. Even the strongest evaluated model answers every question correctly in only 13.36% of groups.

	![PhysCount statistics](assets/benchmark_statistics.png)

	## Dataset Statistics

	\| Property \| Value \|
	\|---\|---:\|
	\| Images \| 546 \|
	\| Annotation groups \| 651 \|
	\| Counting questions \| 4,595 \|
	\| Annotated appearances \| 7,086 \|
	\| Counting targets \| 137 \|
	\| Groups covering all four question families \| 599 \|
	\| Appearance questions \| 651 \|
	\| Entity questions \| 1,150 \|
	\| Image-formation questions \| 711 \|
	\| Correspondence questions \| 2,083 \|

	Each group includes one appearance question. The appearance annotations comprise 2,416 direct appearances, 3,996 reflected appearances, and 674 appearances seen through glass. PhysCount provides a test split with factual counting questions.

	## Results

	All 40 evaluated models are reported below. Score is the primary ranking metric; Group-Acc measures complete-group correctness, and Phys-Gnd measures physical reasoning after an exact appearance count.

	\| Model \| A-MAE ↓ \| A-NAE ↓ \| E-MAE ↓ \| E-NAE ↓ \| I-MAE ↓ \| I-NAE ↓ \| C-MAE ↓ \| C-NAE ↓ \| Score ↑ \| Group-Acc ↑ \| Phys-Gnd ↑ \|
	\|---\|---:\|---:\|---:\|---:\|---:\|---:\|---:\|---:\|---:\|---:\|---:\|
	\| Gemini 3.7 Flash \| 2.724 \| 20.08 \| 2.046 \| 27.36 \| 2.467 \| 30.62 \| 1.396 \| 33.88 \| 36.45 \| 13.36 \| 73.00 \|
	\| Muse-Glimmer-30B \| 2.943 \| 20.31 \| 2.478 \| 32.10 \| 2.405 \| 28.69 \| 1.608 \| 43.04 \| 29.61 \| 7.83 \| 65.51 \|
	\| Qwen3.8-27B \| 3.149 \| 19.89 \| 2.511 \| 32.42 \| 2.702 \| 29.66 \| 1.685 \| 44.68 \| 28.84 \| 7.37 \| 65.96 \|
	\| Qwen3.5-397B-A17B \| 2.836 \| 18.99 \| 2.442 \| 33.28 \| 2.386 \| 26.88 \| 1.859 \| 46.73 \| 27.95 \| 5.84 \| 62.16 \|
	\| Qwen3.5-27B \| 4.103 \| 20.64 \| 3.216 \| 34.58 \| 3.017 \| 26.78 \| 2.942 \| 48.56 \| 26.32 \| 6.30 \| 60.83 \|
	\| Gemma 4-31B \| 3.307 \| 21.83 \| 2.700 \| 36.88 \| 2.814 \| 33.71 \| 1.879 \| 41.86 \| 26.32 \| 6.61 \| 60.07 \|
	\| Qwen3.5-122B-A10B \| 4.192 \| 17.96 \| 2.527 \| 34.40 \| 2.603 \| 27.80 \| 2.068 \| 49.00 \| 26.03 \| 5.99 \| 57.13 \|
	\| Qwen3.5-35B-A3B \| 3.143 \| 18.81 \| 2.425 \| 33.44 \| 2.621 \| 28.49 \| 2.011 \| 51.51 \| 25.70 \| 5.99 \| 58.76 \|
	\| Gemma 4-26B-A4B \| 3.257 \| 22.70 \| 2.852 \| 39.22 \| 2.936 \| 36.53 \| 1.888 \| 44.02 \| 23.79 \| 5.53 \| 57.17 \|
	\| Qwen3.5-9B \| 2.845 \| 20.04 \| 3.708 \| 36.09 \| 3.805 \| 30.05 \| 4.816 \| 53.38 \| 23.54 \| 5.07 \| 55.41 \|
	\| GPT-5.6 Sol \| 3.028 \| 22.82 \| 2.808 \| 36.58 \| 2.544 \| 31.94 \| 2.113 \| 52.11 \| 21.73 \| 3.84 \| 55.65 \|
	\| InternVL3.5-241B-A28B \| 4.135 \| 30.21 \| 2.825 \| 36.24 \| 4.597 \| 36.63 \| 1.983 \| 48.11 \| 21.04 \| 4.92 \| 60.27 \|
	\| GPT-6 Astra \| 3.049 \| 24.87 \| 2.673 \| 37.72 \| 2.517 \| 30.99 \| 1.905 \| 47.83 \| 20.77 \| 3.38 \| 51.89 \|
	\| DeepSeek-V4-Flash-Vision \| 4.321 \| 30.52 \| 2.814 \| 36.12 \| 3.406 \| 37.19 \| 1.864 \| 48.56 \| 20.74 \| 5.22 \| 61.61 \|
	\| GPT-5.6 Terra \| 3.395 \| 26.06 \| 2.726 \| 36.39 \| 3.227 \| 37.30 \| 1.863 \| 50.99 \| 20.42 \| 4.30 \| 53.43 \|
	\| Gemma 4-12B \| 3.490 \| 26.05 \| 3.044 \| 44.56 \| 3.057 \| 37.08 \| 1.982 \| 45.70 \| 19.03 \| 3.07 \| 46.10 \|
	\| Qwen3.5-4B \| 3.321 \| 22.19 \| 4.379 \| 39.57 \| 2.729 \| 32.93 \| 3.274 \| 57.03 \| 18.57 \| 3.38 \| 48.20 \|
	\| InternVL3.5-30B-A3B \| 4.152 \| 29.51 \| 3.036 \| 38.94 \| 3.359 \| 37.29 \| 2.108 \| 52.08 \| 17.76 \| 2.61 \| 53.91 \|
	\| MiniMax-M3-428B-A23B \| 3.888 \| 29.28 \| 2.989 \| 39.05 \| 3.739 \| 39.57 \| 1.975 \| 52.65 \| 17.43 \| 3.69 \| 52.50 \|
	\| GPT-5.6 Luna \| 3.536 \| 28.24 \| 3.368 \| 42.24 \| 2.992 \| 35.07 \| 2.283 \| 55.98 \| 16.87 \| 2.92 \| 46.98 \|
	\| InternVL3.5-38B \| 4.078 \| 32.36 \| 4.520 \| 39.75 \| 10.133 \| 36.59 \| 3.837 \| 57.92 \| 15.55 \| 2.61 \| 47.23 \|
	\| InternVL3.5-14B \| 4.158 \| 29.13 \| 2.855 \| 40.02 \| 3.483 \| 38.22 \| 2.099 \| 57.32 \| 15.20 \| 1.84 \| 44.22 \|
	\| Molmo2-4B \| 4.284 \| 27.98 \| 3.442 \| 38.45 \| 3.372 \| 34.68 \| 2.200 \| 63.45 \| 14.96 \| 1.84 \| 47.21 \|
	\| Ovis2.6-80B-A3B \| 4.132 \| 31.39 \| 3.089 \| 39.59 \| 3.313 \| 37.88 \| 2.302 \| 58.70 \| 14.93 \| 2.15 \| 46.79 \|
	\| MiniCPM-V 4.5-8B \| 4.528 \| 32.52 \| 2.828 \| 38.82 \| 3.426 \| 39.32 \| 2.176 \| 58.40 \| 14.90 \| 2.76 \| 51.28 \|
	\| Cosmos3-Super-64B \| 4.144 \| 28.29 \| 3.003 \| 37.39 \| 3.051 \| 33.50 \| 2.339 \| 64.08 \| 14.69 \| 1.38 \| 45.67 \|
	\| InternVL3.5-8B \| 3.938 \| 27.82 \| 3.011 \| 41.68 \| 3.670 \| 42.16 \| 2.233 \| 57.78 \| 14.29 \| 1.84 \| 47.08 \|
	\| Molmo2-8B \| 4.174 \| 29.30 \| 3.209 \| 37.50 \| 2.996 \| 34.35 \| 2.484 \| 65.41 \| 13.13 \| 0.92 \| 42.99 \|
	\| ERNIE 4.5 VL-28B-A3B \| 4.682 \| 32.62 \| 3.269 \| 43.29 \| 3.621 \| 40.53 \| 2.537 \| 58.93 \| 13.08 \| 1.69 \| 42.92 \|
	\| MiniCPM-V 4.6-1.3B \| 5.720 \| 39.90 \| 3.340 \| 43.56 \| 3.694 \| 42.36 \| 2.252 \| 57.22 \| 12.40 \| 2.15 \| 45.11 \|
	\| Cosmos3-Nano-16B \| 6.002 \| 30.81 \| 3.239 \| 41.23 \| 3.311 \| 36.84 \| 2.548 \| 68.01 \| 12.08 \| 2.15 \| 36.23 \|
	\| Phi-4-Reasoning-Vision-15B \| 3.779 \| 30.31 \| 3.461 \| 47.21 \| 3.681 \| 43.79 \| 2.425 \| 60.20 \| 11.25 \| 0.61 \| 38.63 \|
	\| LLaVA-OneVision 2-8B \| 3.690 \| 28.70 \| 2.948 \| 42.56 \| 3.475 \| 39.05 \| 2.749 \| 67.94 \| 10.51 \| 1.08 \| 33.74 \|
	\| InternVL3.5-4B \| 7.018 \| 38.11 \| 3.452 \| 48.83 \| 3.685 \| 39.85 \| 2.773 \| 65.97 \| 9.53 \| 1.23 \| 36.93 \|
	\| Cosmos3-Edge-4B \| 5.332 \| 37.23 \| 4.005 \| 43.59 \| 3.555 \| 41.68 \| 3.209 \| 65.98 \| 9.27 \| 0.77 \| 32.42 \|
	\| Granite Vision 4.1-4B \| 4.152 \| 34.73 \| 3.437 \| 45.38 \| 3.836 \| 41.51 \| 2.266 \| 67.96 \| 9.02 \| 0.61 \| 32.62 \|
	\| Mistral Small 4-119B \| 5.582 \| 44.59 \| 3.526 \| 53.29 \| 3.908 \| 49.46 \| 2.660 \| 69.42 \| 5.87 \| 0.00 \| 26.18 \|
	\| Gemma 4-E2B \| 20.343 \| 48.02 \| 8.357 \| 55.57 \| 11.088 \| 55.82 \| 4.146 \| 62.93 \| 4.76 \| 0.15 \| 21.13 \|
	\| Ovis2.6-30B-A3B \| 8.207 \| 58.71 \| 5.285 \| 66.79 \| 5.397 \| 64.98 \| 2.404 \| 63.92 \| 3.80 \| 0.46 \| 32.38 \|
	\| Gemma 4-E4B \| 37.605 \| 50.27 \| 22.506 \| 64.37 \| 22.469 \| 69.95 \| 9.344 \| 65.25 \| 2.93 \| 0.00 \| 11.90 \|

	Higher resolution improves individual counts more readily than complete-group correctness. Presenting related questions together produces larger gains on entity and correspondence questions:

	\| Qwen3.8-27B setting \| Appearance NAE ↓ \| Entity NAE ↓ \| Formation NAE ↓ \| Correspondence NAE ↓ \| Score ↑ \| Group-Acc ↑ \| Phys-Gnd ↑ \|
	\|---\|---:\|---:\|---:\|---:\|---:\|---:\|---:\|
	\| 512 px \| 28.36 \| 37.95 \| 37.08 \| 49.31 \| 21.04 \| 5.38 \| 62.50 \|
	\| 1,024 px \| 21.53 \| 33.88 \| 32.12 \| 46.85 \| 26.41 \| 7.37 \| 63.10 \|
	\| 2,048 px \| 19.42 \| 33.09 \| 31.69 \| 44.22 \| 27.86 \| 7.37 \| 61.26 \|
	\| 4,096 px / Independent QA \| 19.89 \| 32.42 \| 29.66 \| 44.68 \| 28.84 \| 7.37 \| 65.96 \|
	\| 4,096 px / Joint QA \| 19.37 \| 26.26 \| 32.76 \| 33.39 \| 40.17 \| 23.96 \| 78.56 \|

	## Data Format

	The release includes the source images, counting questions and answers, and appearance–entity annotations. Images are numbered sequentially from `000001` through `000546`, retaining their JPEG or PNG format.

	### Questions

	`data/questions.jsonl` contains one question per line.

	\| Field \| Description \|
	\|---\|---\|
	\| `question_id` \| Unique question ID. \|
	\| `group_id` \| Annotation group shared by questions about the same image and counting target. \|
	\| `image_id` \| Image identifier. \|
	\| `image` \| Relative path to the image. \|
	\| `question_type` \| `appearance`, `entity`, `image_formation`, or `correspondence`. \|
	\| `question` \| English counting question. \|
	\| `answer` \| Ground-truth integer count. \|

	### Appearance–Entity Annotations

	`data/annotations.jsonl` contains one annotation group per line. Each group stores its `group_id`, `image_id`, image path, original width and height, and a list of `appearances`.

	\| Appearance field \| Description \|
	\|---\|---\|
	\| `appearance_id` \| Identifier of one annotated occurrence within the group. \|
	\| `entity_id` \| Shared identifier for appearances depicting the same physical entity. \|
	\| `mode` \| `direct`, `reflection`, or `through_glass`. \|
	\| `x`, `y` \| Point coordinates normalized to the image width and height. \|

	One entity may have several appearances or be visible only in reflection or through glass. Appearances with the same `entity_id` belong to the same physical object.

	## Evaluation

	### Running GPT Evaluation

	Download the benchmark and install the evaluator dependencies:

	```bash
	hf download lulidong/PhysCount --repo-type dataset --local-dir PhysCount
	cd PhysCount
	python -m pip install -r evaluation/requirements.txt
	export OPENAI_API_KEY="YOUR_KEY"
	```

	Run independent question answering, then compute the metrics:

	```bash
	python evaluation/evaluate_gpt.py \
	--data-root . \
	--model YOUR_MODEL_ID \
	--reasoning-effort high \
	--output predictions.jsonl

	python evaluation/score.py \
	--data-root . \
	--predictions predictions.jsonl \
	--output metrics.json
	```

	Use the strongest reasoning setting supported by the selected model, such as `high` or `xhigh`. The generation limit is 32,768 tokens. Optional sampling controls are supplied through `--temperature` and `--top-p` when supported by the model endpoint.

	### Prompt

	Each image–question pair is evaluated independently. The image and the following prompt are supplied in one user message, with no additional system instruction:

	```text
	Answer the following counting question about this image. Carefully distinguish
	visual appearances from physical entities, including appearances formed by
	reflections or seen through glass, and use appearance-entity correspondences
	when required by the question. Follow the counting target specified in the
	question. Return exactly one non-negative integer, with no labels or prose.

	Question: {question}
	```

	Images retain their native resolution up to a 4,096-pixel long edge. Larger images are resized proportionally without cropping or upsampling. Use `--long-edge` to change the resolution limit.

	### Metrics

	For a valid predicted count $p$ and ground truth $y$, bounded normalized absolute error is

	$$
	\mathrm{NAE}(p,y)=\min\!\left(1,\frac{\|p-y\|}{\max(y,1)}\right).
	$$

	MAE and NAE are first averaged within each question family in an annotation group, then averaged across groups containing that family. This gives each group equal weight regardless of how many questions it contains.

	- Score: multiply the available question-family accuracies within each group, then average the products across groups.
	- Group-Acc: the percentage of groups in which every question is answered exactly.
	- Phys-Gnd: on groups containing all four families with an exact appearance answer, average the harmonic mean of entity, image-formation, and correspondence accuracy.

	MAE is measured in counts. NAE and the three aggregate metrics use a 0–100 scale. Missing, malformed, negative, or extreme predictions receive maximum NAE and fail exact-match evaluation; they are excluded from raw MAE. The evaluator preserves raw responses and parsed predictions.

	## Citation

	```bibtex
	@article{lu2026physcount,
	title={PhysCount: Do MLLMs Count Visual Appearances or Physical Entities?},
	author={Lu, Lidong and Lv, Jiaxin and Dong, Liangrui and Mao, Xinyi and Zou, Lidong and Li, Zhenquan and Lu, Tong and Chen, Guo},
	journal={arXiv preprint arXiv:2610.40530},
	year={2026}
	}
	```