PhysCount

PhysCount: Do MLLMs Count Visual Appearances or Physical Entities?

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.

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:

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:

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:

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

$$\mathrm{N}\mathrm{A}\mathrm{E}(p,y)=\min \text{\hspace{0.17em}⁣}(1,\frac{\mathrm{\mid }p-y\mathrm{\mid }}{\max (y,1)})\mathrm{.}\backslash mathrm\{NAE\}(p,y)=\backslash min\backslash !\backslash left(1,\backslash frac\{|p-y|\}\{\backslash max(y,1)\}\backslash right).$$

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

@misc{lu2026physcount,
  title  = {PhysCount: Do MLLMs Count Visual Appearances or Physical Entities?},
  author = {Lidong Lu and Jiaxin Lv and Liangrui Dong and Xinyi Mao and
            Lidong Zou and Zhenquan Li and Tong Lu and Guo Chen},
  year   = {2026},
  url    = {https://physcount.github.io}
}