3ViewSense: Spatial and Mental Perspective Reasoning from Orthographic Views in Vision-Language Models
Paper • 2603.07751 • Published • 12
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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
id: string
question: string
answer: string
solution: string
message: string
to
{'id': Value('string'), 'question': Value('string'), 'answer': Value('string'), 'message': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1779, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 299, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 128, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2321, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2249, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
id: string
question: string
answer: string
solution: string
message: string
to
{'id': Value('string'), 'question': Value('string'), 'answer': Value('string'), 'message': Value('string')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1347, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 882, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 943, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1646, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1832, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
id string | question string | answer string | message string |
|---|---|---|---|
00000 | Choose the most appropriate option from the four given to fill in the question mark so that it presents a certain regularity.
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00000.png"}, {"type": "text", "text": "<image>\nChoose the most appropriate option from the four given to fill in the question mark so that it presents a certain ... |
00001 | Please choose the most suitable option from the given choices to fill in the question mark, so that it presents a certain pattern:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00001.png"}, {"type": "text", "text": "<image>\nPlease choose the most suitable option from the given choices to fill in the question mark, so that it presents a ... |
00002 | The left figure shows a polyhedron composed of 3 equally-sized cubes with a black triangle on only one face and 12 white cubes. It is cut into three smaller polyhedrons labeled ①, ②, and ③. The question asks which polyhedron ③ could represent:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00002.png"}, {"type": "text", "text": "<image>\nThe left figure shows a polyhedron composed of 3 equally-sized cubes with a black triangle on only one face and 12... |
00003 | Please select the most appropriate option from the four choices to fill in the question mark, so that the figures display a certain regularity:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00003.png"}, {"type": "text", "text": "<image>\nPlease select the most appropriate option from the four choices to fill in the question mark, so that the figures ... |
00004 | From the four given options, choose the most suitable one to fill in the place of the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00004.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the place of the question mark, so that it pr... |
00005 | Divide the following six figures into two categories, so that each category has its own common characteristics or patterns. The correct classification is:
A: ①③④, ②⑤⑥
B: ①②⑤, ③④⑥
C: ①④⑤, ②③⑥
D: ①⑤⑥, ②③④ | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00005.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category has its own common characteristics or ... |
00006 | Please select the most suitable option to fill in the question mark, so that it conforms to the change pattern of the previous four figures:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00006.png"}, {"type": "text", "text": "<image>\nPlease select the most suitable option to fill in the question mark, so that it conforms to the change pattern of ... |
00007 | On the left is a solid shape composed of a pentagonal prism and a cylinder, in which a pentagonal prism, identical in size to the base of the upper pentagonal prism, is carved out of the cylinder. If the solid is cut from any angle, which of the following cannot be a cross-section of this polyhedron?
A: A
B: B
C: C
D:... | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00007.png"}, {"type": "text", "text": "<image>\nOn the left is a solid shape composed of a pentagonal prism and a cylinder, in which a pentagonal prism, identical... |
00008 | The figure below is a polyhedron composed of 15 white cubes and 4 gray cubes. Now, the polyhedron is to be cut by a plane passing through vertices A, B, and C. The correct cross-section is:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00008.png"}, {"type": "text", "text": "<image>\nThe figure below is a polyhedron composed of 15 white cubes and 4 gray cubes. Now, the polyhedron is to be cut by ... |
00009 | The three-dimensional shape formed by folding the given planar diagram on the left is:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00009.png"}, {"type": "text", "text": "<image>\nThe three-dimensional shape formed by folding the given planar diagram on the left is: \nA: A \nB: B \nC: C \n... |
00010 | From the four given options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00010.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00011 | From the four given options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00011.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00012 | The left side shows the given three-dimensional shape (the upper cylinder is the hollowed-out part). If you cut it from any side, which option on the right cannot be a cross-sectional view of this three-dimensional shape?
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00012.png"}, {"type": "text", "text": "<image>\nThe left side shows the given three-dimensional shape (the upper cylinder is the hollowed-out part). If you cut it... |
00013 | The left illustration is a three-dimensional figure composed of 14 black and white small cubes, and one of the views among the four options on the right is not a view of this three-dimensional figure. Please identify which one it is.
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00013.png"}, {"type": "text", "text": "<image>\nThe left illustration is a three-dimensional figure composed of 14 black and white small cubes, and one of the vie... |
00014 | Choose the most appropriate option from the four given choices to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00014.png"}, {"type": "text", "text": "<image>\nChoose the most appropriate option from the four given choices to fill in the question mark, so that it presents a... |
00015 | Choose the most appropriate option from the four given choices to fill in the question mark, so as to present a certain pattern:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00015.png"}, {"type": "text", "text": "<image>\nChoose the most appropriate option from the four given choices to fill in the question mark, so as to present a ce... |
00016 | Which of the four options on the right side of the image is not the elevation view of the part on the left?
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00016.png"}, {"type": "text", "text": "<image>\nWhich of the four options on the right side of the image is not the elevation view of the part on the left?\n\nA: ... |
00017 | Choose the most suitable option from the four given choices to fill in the question mark, making it appear consistent with a certain pattern:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00017.png"}, {"type": "text", "text": "<image>\nChoose the most suitable option from the four given choices to fill in the question mark, making it appear consist... |
00018 | Choose the most suitable option from the four given choices to fill in the question mark, ensuring it follows a certain pattern:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00018.png"}, {"type": "text", "text": "<image>\nChoose the most suitable option from the four given choices to fill in the question mark, ensuring it follows a ce... |
00019 | Divide the six figures below into two categories so that each category has its own common features or patterns. The correct classification is ( ).
A: ①②④, ③⑤⑥
B: ①⑤⑥, ②③④
C: ①③⑥, ②④⑤
D: ①②⑥, ③④⑤ | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00019.png"}, {"type": "text", "text": "<image>\nDivide the six figures below into two categories so that each category has its own common features or patterns. Th... |
00020 | Divide the six shapes below into two categories, such that each category of shapes has its own common characteristics or patterns. The correct classification is:
A: ①③④, ②⑤⑥
B: ①③⑥, ②④⑤
C: ①④⑤, ②③⑥
D: ①②③, ④⑤⑥ | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00020.png"}, {"type": "text", "text": "<image>\nDivide the six shapes below into two categories, such that each category of shapes has its own common characterist... |
00021 | Choose the most suitable option from the four given choices to fill in the question mark, so that a certain pattern is exhibited:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00021.png"}, {"type": "text", "text": "<image>\nChoose the most suitable option from the four given choices to fill in the question mark, so that a certain patter... |
00022 | From the four given options, select the most suitable one to fill in the question mark, so that a certain pattern is presented:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00022.png"}, {"type": "text", "text": "<image>\nFrom the four given options, select the most suitable one to fill in the question mark, so that a certain pattern ... |
00023 | Divide the following six figures into two categories, so that each category shares its own common characteristics or rules. The correctly categorized option is:
A: ①③⑤, ②④⑥
B: ①③⑥, ②④⑤
C: ①②③, ④⑤⑥
D: ①②④, ③⑤⑥ | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00023.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category shares its own common characteristics ... |
00024 | Choose the appropriate option from the four given choices to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00024.png"}, {"type": "text", "text": "<image>\nChoose the appropriate option from the four given choices to fill in the question mark, so that it presents a cert... |
00025 | Select the most appropriate option from the given four choices to fill in the question mark, so that a certain pattern is presented.
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00025.png"}, {"type": "text", "text": "<image>\nSelect the most appropriate option from the given four choices to fill in the question mark, so that a certain pat... |
00026 | From the given four options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00026.png"}, {"type": "text", "text": "<image>\nFrom the given four options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00027 | From the four given options, choose the most suitable one to fill in the place marked by the question mark so that it presents a certain pattern:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00027.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the place marked by the question mark so that... |
00028 | Choose the most suitable option from the four given choices to fill in the question mark so that a certain pattern is presented:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00028.png"}, {"type": "text", "text": "<image>\nChoose the most suitable option from the four given choices to fill in the question mark so that a certain pattern... |
00029 | Choose the most appropriate option from the four given choices to fill in the question mark, so that a certain pattern is formed:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00029.png"}, {"type": "text", "text": "<image>\nChoose the most appropriate option from the four given choices to fill in the question mark, so that a certain pat... |
00030 | From the four given options, choose the most suitable one to fill in the question mark, creating a certain regularity.
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00030.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, creating a certain regular... |
00031 | The left side shows the net of a cube's outer surface. Which option on the right can be folded to form it?
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00031.png"}, {"type": "text", "text": "<image>\nThe left side shows the net of a cube's outer surface. Which option on the right can be folded to form it?\n\nA: A... |
00032 | Which of the following unfolded views of the outer surface of a box, when folded, results in a box different from the other three?
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00032.png"}, {"type": "text", "text": "<image>\nWhich of the following unfolded views of the outer surface of a box, when folded, results in a box different from ... |
00033 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is:
A: ①③④, ②⑤⑥
B: ①②④, ③⑤⑥
C: ①④⑤, ②③⑥
D: ①③⑥, ②④⑤ | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00033.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00034 | From the four given options, select the most suitable one to fill in the question mark so that a certain pattern is presented:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00034.png"}, {"type": "text", "text": "<image>\nFrom the four given options, select the most suitable one to fill in the question mark so that a certain pattern i... |
00035 | Please choose the most suitable option from the four given choices to fill in the question mark, so that a certain pattern is presented:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00035.png"}, {"type": "text", "text": "<image>\nPlease choose the most suitable option from the four given choices to fill in the question mark, so that a certain... |
00036 | From the four given options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00036.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00037 | Divide the following six figures into two categories, ensuring that each category of figures shares common characteristics or patterns. The option with the correct classification is:
A: ①②⑤, ③④⑥
B: ①③④, ②⑤⑥
C: ①⑤⑥, ②③④
D: ①③⑤, ②④⑥ | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00037.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, ensuring that each category of figures shares common charact... |
00038 | Choose the most appropriate option from the four given choices to fill in the question mark, making sure it follows a certain pattern:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00038.png"}, {"type": "text", "text": "<image>\nChoose the most appropriate option from the four given choices to fill in the question mark, making sure it follow... |
00039 | The following solid figure can be formed by combining ①②③:
<img width="700px" height="449px" src="images/181eca9c1e285eb.png">
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00039.png"}, {"type": "text", "text": "<image>\nThe following solid figure can be formed by combining ①②③: \n<img width=\"700px\" height=\"449px\" src=\"images/1... |
00040 | Divide the following six figures into two categories, ensuring that each category has its own common features or patterns. The correct classification is:
A: ①③⑥, ②④⑤
B: ①③⑤, ②④⑥
C: ①②⑤, ③④⑥
D: ①⑤⑥, ②③④ | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00040.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, ensuring that each category has its own common features or p... |
00041 | Select the only item from the four images to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00041.png"}, {"type": "text", "text": "<image>\nSelect the only item from the four images to fill in the question mark, so that it presents a certain regularity:\... |
00042 | Which of the following options is formed by folding the left figure.
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00042.png"}, {"type": "text", "text": "<image>\nWhich of the following options is formed by folding the left figure.\n\nA: A \nB: B \nC: C \nD: D\nSolve the co... |
00043 | Divide the following six figures into two categories, so that each category of figures has its own common features or patterns. The correct classification is:
A: ①②④, ③⑤⑥
B: ①⑤⑥, ②③④
C: ①③⑥, ②④⑤
D: ①④⑤, ②③⑥ | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00043.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common features... |
00044 | From the four given options, choose the most suitable one to fill in the question mark, making it exhibit a certain regularity:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00044.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, making it exhibit a certai... |
00045 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is:
A: ①③⑥, ②④⑤
B: ①②⑤, ③④⑥
C: ①④⑥, ②③⑤
D: ①③④, ②⑤⑥ | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00045.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00046 | The left side shows a three-dimensional shape made up of several small cubes. Which option on the right represents a view of this shape from a certain direction?
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00046.png"}, {"type": "text", "text": "<image>\nThe left side shows a three-dimensional shape made up of several small cubes. Which option on the right represents... |
00047 | The diagram below shows a rectangular prism composed of 4 black and 8 white cubes. Which option could be its correct exterior surface layout?
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00047.png"}, {"type": "text", "text": "<image>\nThe diagram below shows a rectangular prism composed of 4 black and 8 white cubes. Which option could be its corre... |
00048 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is:
A: ①③⑥, ②④⑤
B: ①②⑤, ③④⑥
C: ①⑤⑥, ②③④
D: ①③⑤, ②④⑥ | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00048.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00049 | Choose the most suitable option from the given four choices to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00049.png"}, {"type": "text", "text": "<image>\nChoose the most suitable option from the given four choices to fill in the question mark, so that it presents a ce... |
00050 | On the left is a three-dimensional shape made up of multiple small cubes. Which option on the right is a view that can be seen from a certain direction?
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00050.png"}, {"type": "text", "text": "<image>\nOn the left is a three-dimensional shape made up of multiple small cubes. Which option on the right is a view that... |
00051 | Among the following three-dimensional figures, the view observed from any angle cannot be a centrally symmetric figure:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00051.png"}, {"type": "text", "text": "<image>\nAmong the following three-dimensional figures, the view observed from any angle cannot be a centrally symmetric fi... |
00052 | Which of the following is the net of the given three-dimensional shape?
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00052.png"}, {"type": "text", "text": "<image>\nWhich of the following is the net of the given three-dimensional shape?\nA: A \nB: B \nC: C \nD: D\nSolve the c... |
00053 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct categorization is:
A: ①③④, ②⑤⑥
B: ①②⑥, ③④⑤
C: ①④⑤, ②③⑥
D: ①③⑥, ②④⑤ | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00053.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00054 | From the four given options, choose the most appropriate one to fill in the question mark to present a certain regularity.
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00054.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark to present a certain reg... |
00055 | Divide the six figures below into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is:
A: ①②④, ③⑤⑥
B: ①②⑥, ③④⑤
C: ①③④, ②⑤⑥
D: ①④⑥, ②③⑤ | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00055.png"}, {"type": "text", "text": "<image>\nDivide the six figures below into two categories, so that each category of figures has its own common characterist... |
00056 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is:
A: ①②④, ③⑤⑥
B: ①④⑤, ②③⑥
C: ①②⑤, ③④⑥
D: ①③⑥, ②④⑤ | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00056.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00057 | Divide the following six figures into two categories, making sure each category has its own common characteristics or patterns. The correctly categorized option is:
A: ①②⑥, ③④⑤
B: ①③⑤, ②④⑥
C: ①③⑥, ②④⑤
D: ①⑤⑥, ②③④ | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00057.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, making sure each category has its own common characteristics... |
00058 | The option that contains cubes which can be combined into a 3×3×3 cube block is:
A: 1, 2, 4
B: 1, 3, 5
C: 1, 3, 4
D: 1, 2, 5 | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00058.png"}, {"type": "text", "text": "<image>\nThe option that contains cubes which can be combined into a 3×3×3 cube block is:\n\nA: 1, 2, 4 \nB: 1, 3, 5 \nC:... |
00059 | From the four given options, select the most appropriate one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00059.png"}, {"type": "text", "text": "<image>\nFrom the four given options, select the most appropriate one to fill in the question mark, so that it presents a c... |
00060 | From the four given options, choose the most suitable one to fill in the question mark so that a certain pattern is formed:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00060.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark so that a certain pattern i... |
00061 | From the four given options, choose the most appropriate one to fill in the question mark so that it presents a certain regularity:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00061.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark so that it presents a ce... |
00062 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is ( ).
A: ①②⑤, ③④⑥
B: ①③⑤, ②④⑥
C: ①③⑥, ②④⑤
D: ①⑤⑥, ②③④ | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00062.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00063 | From the four given options, choose the most appropriate one to fill in the question mark so that it presents a certain regularity:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00063.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark so that it presents a ce... |
00064 | The left side shows the net of a cube's outer surface. Which option on the right can it be folded into? Please identify it.
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00064.png"}, {"type": "text", "text": "<image>\nThe left side shows the net of a cube's outer surface. Which option on the right can it be folded into? Please ide... |
00065 | The following three-dimensional shape can be composed of figures ①, ②, and ③:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00065.png"}, {"type": "text", "text": "<image>\nThe following three-dimensional shape can be composed of figures ①, ②, and ③:\n\nA: A \nB: B \nC: C \nD: D\nSol... |
00066 | From the given four options, select the most appropriate one to fill in the question mark so that it presents a certain pattern:
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00066.png"}, {"type": "text", "text": "<image>\nFrom the given four options, select the most appropriate one to fill in the question mark so that it presents a ce... |
00067 | From the four given options, choose the most suitable one to fill in the question mark so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00067.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark so that it presents a certa... |
00068 | Divide the following six figures into two categories, so that each category of figures has its own common characteristics or patterns. The correct classification is:
A: ①③⑤, ②④⑥
B: ①③④, ②⑤⑥
C: ①②⑤, ③④⑥
D: ①②④, ③⑤⑥ | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00068.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category of figures has its own common characte... |
00069 | As shown in the figure below, fold from Figure 1 to Figure 2, then fold into Figure 3, and then cut out the shaded triangular part from Figure 4. The shape obtained after fully unfolding the paper is. | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00069.png"}, {"type": "text", "text": "<image>\nAs shown in the figure below, fold from Figure 1 to Figure 2, then fold into Figure 3, and then cut out the shaded... |
00070 | Divide the following six figures into two categories, so that each category has its own common features and patterns. The option that categorizes them correctly is:
A: ①②③, ④⑤⑥
B: ①⑤⑥, ②③④
C: ①②④, ③⑤⑥
D: ①③④, ②⑤⑥ | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00070.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, so that each category has its own common features and patter... |
00071 | From the four given options, choose the most appropriate one to fill in the question mark, so that it presents a certain regularity.
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00071.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark, so that it presents a c... |
00072 | Please choose the most appropriate option from the four given to fill in the question mark, so that a certain pattern is presented:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00072.png"}, {"type": "text", "text": "<image>\nPlease choose the most appropriate option from the four given to fill in the question mark, so that a certain patt... |
00073 | From the four given options, choose the most suitable one to fill in the question mark, so that it presents a certain pattern.
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00073.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00074 | The image below shows the front view and the rear view of a polyhedron formed by stacking cubes of the same size. This polyhedron can be divided into a combination of three polyhedrons: ①, ②, and ③. Which of the following options can fill the question mark?
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00074.png"}, {"type": "text", "text": "<image>\nThe image below shows the front view and the rear view of a polyhedron formed by stacking cubes of the same size. ... |
00075 | From the four given options, select the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00075.png"}, {"type": "text", "text": "<image>\nFrom the four given options, select the most suitable one to fill in the question mark, so that it presents a cert... |
00076 | Divide the following six figures into two categories, ensuring that each category of figures has its own common features or patterns. The correct classification is:
A: ①③④, ②⑤⑥
B: ①③⑥, ②④⑤
C: ①②⑤, ③④⑥
D: ①④⑥, ②③⑤ | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00076.png"}, {"type": "text", "text": "<image>\nDivide the following six figures into two categories, ensuring that each category of figures has its own common fe... |
00077 | From the four given options, choose the most suitable one to fill in the question mark, so that a certain pattern is presented:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00077.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, so that a certain pattern ... |
00078 | This question includes two sets of images and four options to choose from. The two sets of images have certain similarities, as well as some differences. You are required to select the most suitable option from the four choices to replace the question mark. The correct answer should not only maximize the similarity bet... | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00078.png"}, {"type": "text", "text": "<image>\nThis question includes two sets of images and four options to choose from. The two sets of images have certain sim... |
00079 | From the four given options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00079.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00080 | From the given four options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00080.png"}, {"type": "text", "text": "<image>\nFrom the given four options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00081 | The following fractal image is generated by iterating which basic shape:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00081.png"}, {"type": "text", "text": "<image>\nThe following fractal image is generated by iterating which basic shape:\nA: A\nB: B\nC: C\nD: D\nSolve the comple... |
00082 | The left image shows the front view and rear view of a polyhedron composed of identical cubes. This polyhedron is made up of three-dimensional shapes ①, ②, and ③. Which of the following options can be placed at the question mark?
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00082.png"}, {"type": "text", "text": "<image>\nThe left image shows the front view and rear view of a polyhedron composed of identical cubes. This polyhedron is ... |
00083 | Choose the most appropriate option from the given four choices to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00083.png"}, {"type": "text", "text": "<image>\nChoose the most appropriate option from the given four choices to fill in the question mark, so that it presents a... |
00084 | From the four given options, choose the most appropriate one to fill in the question mark, so that a certain pattern is presented:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00084.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark, so that a certain patte... |
00085 | The option that best matches the given pattern is ( ).
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00085.png"}, {"type": "text", "text": "<image>\nThe option that best matches the given pattern is ( ).\n\nA: A \nB: B \nC: C \nD: D\nSolve the complex visua... |
00086 | The left diagram shows a given hollow three-dimensional shape. If it is cut from any face, which of the following is not a possible cross-section of the three-dimensional shape?
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00086.png"}, {"type": "text", "text": "<image>\nThe left diagram shows a given hollow three-dimensional shape. If it is cut from any face, which of the following ... |
00087 | From the four given options, choose the most appropriate one to fill in the question mark so as to present a certain pattern:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00087.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark so as to present a certa... |
00088 | Please choose the most appropriate option from the given four to fill in the question mark, so that it presents a certain regularity.
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00088.png"}, {"type": "text", "text": "<image>\nPlease choose the most appropriate option from the given four to fill in the question mark, so that it presents a ... |
00089 | Please select the one graphic from the four below that is different from the other three.
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00089.png"}, {"type": "text", "text": "<image>\nPlease select the one graphic from the four below that is different from the other three.\nA: A \nB: B \nC: C \... |
00090 | Among the following options, the one that cannot be folded into the original shape is:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00090.png"}, {"type": "text", "text": "<image>\nAmong the following options, the one that cannot be folded into the original shape is:\nA: A \nB: B \nC: C \nD:... |
00091 | The left image is the given three-dimensional shape. When cut open from any face, which option on the right cannot be the cross-section of this three-dimensional shape?
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00091.png"}, {"type": "text", "text": "<image>\nThe left image is the given three-dimensional shape. When cut open from any face, which option on the right cannot... |
00092 | Given on the left is the exterior surface of a paper box. Which of the following can be formed by folding it? ( )
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00092.png"}, {"type": "text", "text": "<image>\nGiven on the left is the exterior surface of a paper box. Which of the following can be formed by folding it? ( )... |
00093 | From the four given options, choose the most appropriate one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00093.png"}, {"type": "text", "text": "<image>\nFrom the four given options, choose the most appropriate one to fill in the question mark, so that it presents a c... |
00094 | Among the following options, which one matches the given pattern of changes in the figure:
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00094.png"}, {"type": "text", "text": "<image>\nAmong the following options, which one matches the given pattern of changes in the figure:\nA: A \nB: B \nC: C ... |
00095 | The left side shows the given polyhedron. From any angle, which option on the right cannot be a view of this polyhedron?
A: A
B: B
C: C
D: D | A | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00095.png"}, {"type": "text", "text": "<image>\nThe left side shows the given polyhedron. From any angle, which option on the right cannot be a view of this polyh... |
00096 | Choose the most suitable option from the four given choices to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00096.png"}, {"type": "text", "text": "<image>\nChoose the most suitable option from the four given choices to fill in the question mark, so that it presents a ce... |
00097 | Given below is the external surface of a paper box. Which of the following can be formed by folding it?
A: A
B: B
C: C
D: D | D | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00097.png"}, {"type": "text", "text": "<image>\nGiven below is the external surface of a paper box. Which of the following can be formed by folding it?\nA: A \nB... |
00098 | From the given four options, choose the most suitable one to fill in the question mark, so that it presents a certain regularity:
A: A
B: B
C: C
D: D | B | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00098.png"}, {"type": "text", "text": "<image>\nFrom the given four options, choose the most suitable one to fill in the question mark, so that it presents a cert... |
00099 | The left diagram shows the front view and the rear view of a polyhedron made by stacking identical cubes. This polyhedron can be composed of three polyhedra: ①, ②, and ③. Which of the following can fill the question mark?
A: A
B: B
C: C
D: D | C | [{"role": "system", "content": "你是书生·万象，英文名是InternVL，是由上海人工智能实验室、清华大学及多家合作单位联合开发的多模态大语言模型。"}, {"role": "user", "content": [{"type": "image", "image": "images/00099.png"}, {"type": "text", "text": "<image>\nThe left diagram shows the front view and the rear view of a polyhedron made by stacking identical cubes. This pol... |
End of preview.
YAML Metadata Warning:empty or missing yaml metadata in repo card
Check out the documentation for more information.
请你看一下这里的静态数据，我现在的任务是想要scaling这类的数据，请你广泛的找类有规则的可以通过生成python代码批量生
成vqa，我暂时不用那种已有generator的，我要那个广泛的规则就好，我就要把那些没有generator的。我不用你给我生成VQA，我只要有这些规则，比如网站或者论文之类的，先搜集就好，不用得到VQA
1 大类数据
| 名称 | 数量 | 标签 | 描述 | 备注 |
|---|---|---|---|---|
| 视觉推理 Benchmark / Dataset | ||||
| Visual Sphinx | 多种 | 视觉推理, Benchmark | 视觉归纳/演绎/空间推理，题目分 Inductive/Deductive/Spatial/Extension 四类，含扩展 10 选项版本 | 已整理 |
| ARC-AGI 3 | — | 视觉推理, Benchmark | ARC 抽象视觉推理竞赛第三版 | 已整理 |
| CubeVLM | 3 tiers | 视觉推理, Benchmark | Rubik's Cube 推理，三种表示：Full Symbolic / Full Visual / Partial Visual，12 种动作 | 已整理 |
| TACIT | 10×3 难度 | 视觉推理, Benchmark 生成器 |
空间/逻辑/结构推理，10 tasks × 3 难度，seed 确定性程序生成，完全可复现 | 已整理 |
| Sphinx (maveryn) | 25 | 视觉推理, 生成器 | 程序化生成视觉 puzzle，使用 motifs/tiles/charts/几何基元，规则+参数+随机种子驱动，开源 25 种类型 | 已整理 |
| Kaggle AGI – Dynamic Visual Reasoning | 1 | 视觉推理, Benchmark | 矩形桌面+移动球+命名矩形障碍物，接收棋盘图像+规则，Question-Answer 格式 | 已整理 |
| VR-Bench | 5 类 | 视觉推理, Benchmark | 五种迷宫：规则/不规则/3 D 迷宫/陷阱场 (Trapfield)/推箱子 (Sokoban)，涵盖 2 D 和 3 D 环境 | 已整理 |
| VisualPuzzles | 5 类 | 视觉推理, Benchmark 静态数据集 |
开源数据但未开源生成方法；含 Algorithmic/Inductive/Spatial/Analogical/Deductive 五类 | 已整理 |
| Gym-V | 179 | 视觉推理, 生成器 | 179 个环境，涵盖单回合推理/多回合游戏/空间导航/复古街机游戏，代码完全开源可生产数据 | 已整理 |
| MentisOculi | 5 | 视觉推理, Benchmark | 5 个视觉任务，5 个不同难度 | 已整理 |
| VisuLogic | 6 域 23 子类 | 视觉推理, Benchmark 静态数据集 |
1000 道人工验证题，视觉+逻辑综合推理，强调避免语言模式匹配；6 个 domains：Quantitative/Spatial/Positional/Attribute/Stylistic/Other | 已整理 |
| Enigmata | 36 任务 7 大类 | 视觉推理, 生成器 RL 训练 |
面向逻辑推理的可验证合成数据，generator+verifier，可按参数和难度持续生成并自动验证，适合 RL 训练 | 已整理 |
| VBVR-DataFactory | 300+ gen | 视觉推理, 生成器 | 大规模视频推理生成工厂，300+ generators，按 seed/参数不断生成新样本；含空间/路径/计数/顺序/图表等推理 | 已整理 |
| MIRA | 20 tasks | 视觉推理, Benchmark Visual-CoT |
偏视觉链式推理 (Visual-CoT) 评测；546 个样本，20 种 task types，4 个 domains；涉及几何/类物理/空间逻辑/因果变化 | 已整理 |
| CVR | 103 | 视觉推理, 生成器 | 程序化生成组合视觉推理题，103 个任务；开源自动生成代码和 generalization test set 生成函数 | 已整理 |
| STARE | — | 视觉推理, Benchmark | 空间推理综合评测；任务从 2 D/3 D 几何变换、cube net folding、tangram puzzles 到 temporal frame 和 perspective reasoning | 已整理 |
| SynLogic | 35 | 视觉推理, 生成器 | 合成式逻辑推理数据，35 种 tasks，含 Sudoku/Game of 24/Cipher/Arrow Maze | 已整理 |
| ARC-GEN | — | 视觉推理, 生成器 | Procedural benchmark generator，为 ARC 类抽象推理任务做模仿式程序生成 | 已整理 |
| iVISPAR | — | 视觉推理, Benchmark | 交互式多模态空间推理 benchmark，基于 sliding-tile puzzle 评测 VLM agent 的空间理解/规划/多步推理 | 已整理 |
| Gen-ViRe | — | 视觉推理, 生成器 | Generative visual reasoning benchmark，面向视频生成/世界模拟模型的推理评测 | 已整理 |
| MM-HELIX | 42 tasks | 视觉推理, Benchmark | 多模态长链反思推理 benchmark；42 个 tasks 分 algorithms/graphs/puzzles/games 四类，5 个 difficulty levels | 已整理 |
| RAVEN | 7 | 视觉推理, 生成器 | 7 类 Raven 渐进矩阵 (Progressive Matrices)，程序生成 | 已整理 |
| SpatialViz-Bench | 11 | 视觉推理, Benchmark 生成器 |
11 类空间推理任务，生成器 | 已整理 |
| VisFactor | 20 | 视觉推理, Benchmark 生成器 |
20 类视觉因子推理，生成器 | 已整理 |
| SMART | 101 | 视觉推理, Benchmark 静态数据集 |
101 个 root puzzles，静态数据集 | 已整理 |
| BPS (Bongard Problems) | 400+ | 视觉推理, 静态数据集 | 400 道专家设计视觉推理题，非程序生成 | 已整理 |
| Bongard-LOGO | 12,000 | 视觉推理, 生成器 | NVIDIA 出品，合成 Bongard 概念归纳题，给定正例集合 vs 负例集合归纳抽象视觉规则；含完整 Python 生成库，三类题型：自由形状/基础形状/抽象形状（凸凹/对称等），可自定义生成 | 已整理 |
| KiVA | 1,400 | 视觉推理, Benchmark 生成器 |
Kid-inspired Visual Analogies（UC Berkeley），测颜色/大小/旋转/翻转/数量 5 种变换规则，基于真实 3 D 物体图像；含数据集下载+生成脚本，可指定参数组合生成 compositional 题目 | 已整理 |
| 谜题 / 逻辑推理 | ||||
| pencil-puzzle-bench | 94 种 / 62,231 实例 | 谜题, 生成器 | Python step-level 验证 + 约束求解器生成，含 Sudoku/Nonogram 等，支持交互式多步推理 | 已整理 |
| grilops | 17 | 谜题, 生成器 | 基于约束求解 (SAT/SMT) 的 pencil puzzle 生成器 Python 库，17 类 puzzle | 已整理 |
| Simon Tatham's Puzzles | 40 | 谜题, 生成器 | 40 种经典 puzzle，含完整开源生成器（另见 GitHub 镜像 ghewgill/puzzles） | 已整理 |
| ghewgill/puzzles | 40 | 谜题, 生成器 | Simon Tatham Puzzle Collection 的 GitHub 移植版，同样 40 种 puzzle 生成器 | 已整理 |
| LLM-PuzzleTest | 18 | 谜题, Benchmark 生成器 |
18 种 puzzles，含 generator，面向 LLM 推理评测 | 暂时不用 |
| puzzle-kurodoko / janko系 | 36 | 谜题, 静态数据集 | 36 种逻辑谜题（田鼠挖洞/黑白/阴阳/独棋/温度计/海苔/扫雷/战舰/接水管/数壹/数间/信号旗/珍珠/缝线/水箱/数墙/星之战/方阵和/高楼/不等式/数和/异形数独/杀手数独/黑白/数织/搭桥/数独/点灯等） | 暂时不用 |
| janko.at | 300+ | 谜题, 静态数据集 | 300+种 pencil puzzles，专家设计，无 generator | 暂时不用 |
| Nikoli | 47 | 谜题, 静态数据集 | 47 种专家精心设计的 puzzles，非程序生成 | 暂时不用 |
| BrainBashers | 22 | 谜题, 生成器 | 22 种程序生成 puzzles | 暂时不用 |
| PuzzleMadness | 41 | 谜题, 生成器 | 41 种数独变体 | 暂时不用 |
| VGRP-Bench | 20 | 视觉推理, Benchmark 生成器 |
视觉几何推理，含 generator；任务含迷宫/Raven 矩阵/CA/Logic Grid/图着色/图同构/Unknot Detection 等 | 已整理 |
| CAPTCHA | ||||
| NextGen-CAPTCHAs | 27 | CAPTCHA, 生成器 | 防 AI 验证码，27 种（3 D 视角/背景遮挡层/箱体折叠/颜色计数/骰子路径/动态拼图/洞数计数/幻觉丝带/层叠/镜像/多文字系统/遮挡计数/红点/旋转匹配/阴影方向/阴影可信/幽灵圆等），seed 可复现 | 已整理 |
| OpenCaptchaWorld | 20 | CAPTCHA, Benchmark | 面向 Web Agent 的开源 CAPTCHA 推理平台，20 种类型，较简单，可用于训练数据生成 | 没有开源 |
| RLVR 训练 / 可验证推理数据 | ||||
| Reasoning Gym | 100+ | 生成器 RLVR 训练 可验证 |
NeurIPS 2025 Spotlight。程序化生成 + 自动验证的 RL 训练库，pip 可安装，统一 score_answer 验证接口，直接支持 GRPO 框架。100+ 任务含 maze/graph/Rubik's cube/logic games 等，以 text 为主，视觉部分待扩展 | 已整理 |
| Reason-RFT | 3 类任务 | 视觉推理, 生成器 RLVR 训练 可验证 |
NeurIPS 2025。专为 VLM GRPO 设计，HuggingFace 可直接下载：Spatial Transformation (60 k) / Structure Perception (4.5 k) / Visual Counting (35 k)，含完整 SFT+GRPO 两阶段训练代码 | 已整理 |
| SynthRL | — | 生成器 RLVR 训练 可验证 |
专为 RLVR 训练的数据 scaling pipeline：seed 题目选择 → 自动合成更难变体 → 验证正确性，保证难度提升的同时保留原始答案，代码开源 | 已整理 |
| AlphaMaze (visual-thinker) | — | 视觉推理, 生成器 RLVR 训练 可验证 |
用 GRPO 训练 LLM 做迷宫导航，文本化迷宫表示 + verifiable reward，含数据生成代码和训练脚本；SFT 86% → GRPO 93%，是 puzzle→RL 路线的直接先例 | 已整理 |
| I-RAVEN (SRAN repo) | 7 类 | 视觉推理, 生成器 静态数据集 |
修复了原版 RAVEN 答案 bias 问题的改进版，含完整生成代码（python I-RAVEN/main. Py），可自定义生成数量，适合作为抽象视觉推理的 seed 数据集 | 已整理 |
| raven-gen | 7 类 | 视觉推理, 生成器 | RAVEN 的独立 Python 生成工具，比原版更轻量灵活，pip 可安装，可定制分辨率、配置和难度，适合快速生成 Raven 矩阵类视觉推理数据 | 已整理 |
| Games | ||||
| Odysseus | 1 | 作者以《超级马里奥大陆》为测试环境，要求智能体完成 100+轮的感知-推理-行动协调。 | 待整理 | |
| Enhancing Player Enjoyment with a Two-Tier DRL and LLM-Based Agent System for Fighting Games | 1 | 本文针对格斗游戏 AI 鲜少以"增强玩家乐趣"为设计目标的问题，提出双层智能体（TTA）系统，并在《街头霸王 II》中验证。 | 待整理 | |
| atari-gpt | benchmark | 本文提出 Atari-GPT 基准，首次系统评估多模态大语言模型作为 Atari 游戏低层策略控制器的涌现能力。 | 待整理 | |
| 生成模型 | ||||
| VisionFoundry | N | LLM+Diffusion | 仅需输入一个关键词，LLM 扩充再通过 Diffusion model 生成图像，然后 LLM 验证。无限扩充。 | 待整理 |
| 视觉逻辑场景 / Description Logic | N | 可以生成 |
- LoRA 是一个逻辑推理增强型 VQA 数据集。 简单 2 D 或 3 D 场景：物体、属性、关系、区域 - 10 万个自动生成的逼真厨房场景。 - 20 万道复杂多样的逻辑推理题。 |
待整理-0516 |
2 静态数据的生产以及任务分配
2.1 批次 1-0514
完整的全量分配结果在：
rule_task_assignment_full.jsondocs/rule_task_assignment_full.json的结构是：
{
"规律补全": {
"VisualPuzzles": ["2", "..."],
"SMART101": ["77", "..."],
"VisuLogic-Train": ["00000", "..."]
}
}
另外当前还有一组：
待人工复核
目前只出现在 VisuLogic-Train，共有 92 条。这部分说明只靠题干模板还不够稳，建议最后单独派给一个人做人工归并。
这个 JSON 里保存了三个数据文件的完整 id 列表，按工作包拆分。Markdown 这里只放摘要统计，避免把几千个 id 全塞进文档里。 按照类别整理：
| 工作包 | 覆盖内容 | 主要来源 | 可直接分配的样例 id | 容易混淆的边界 | 示例 |
|---|---|---|---|---|---|
| 规律补全 | 图形序列、矩阵、问号补全、局部到全局规律发现 | VisuLogic V1 2647； VisualPuzzles inductive 一部分 162；SMART pattern 5 |
全量见 JSON。当前统计：VisualPuzzles 162 条；SMART 5 个 root puzzles；VisuLogic 2647 条 |
容易和“六图分类”混；如果任务是从候选中补缺项，归这里 |  |
| 六图分类 | 6 个图形分两组，按共同属性归类 | VisuLogic V2 752；VisualPuzzles inductive 一部分 47 |
全量见 JSON。当前统计：VisualPuzzles 47 条；VisuLogic 752 条 |
容易和“规律补全”混；如果目标是分组而不是补缺，归这里 |  |
| 三维空间 | 折叠/展开、视图、投影、截面、空间拼装、折纸裁切 | VisuLogic V3/V4/V5/V6；806VisualPuzzles spatial 部分 deductive 226；SMART spatial 9 |
全量见 JSON。当前统计：VisualPuzzles 226 条；SMART 9 个 root puzzles；VisuLogic 806 条 |
内部子类很多，但底层表示相近，建议整包处理，不要再按论文拆 |  |
| 路径与计量 | 迷宫、路径追踪、计数、长度、面积、最优化数量 | VisualPuzzles algorithmic/spatial 一部分 358；SMART path/counting/math/measure 60 |
全量见 JSON。当前统计：VisualPuzzles 358 条；SMART 60 个 root puzzles |
容易和“逻辑映射”混；如果核心是算数值、找路径、做约束搜索，归这里 |  |
| 类比与逻辑映射 | 类比关系、编码规则、交换规则、顺序恢复、逻辑排除 | VisualPuzzles analogical/deductive 375 ；SMART algebra/logic/order 27 |
全量见 JSON。当前统计：VisualPuzzles 375 条；SMART 27 个 root puzzles |
容易和“路径与计量”混；如果核心是规则映射或逻辑约束，不是数值搜索，归这里 |  |
2.2 批次 2-0515
筛选标准：
可以静态渲染成图像。
可以自己用 Python 生成局面/图形/图表。
答案可以用规则、公式、枚举、图搜索、线性代数或模拟器自动验证。
尽量避开已有高重复方向：
RAVEN/RPM、Bongard/BPS、Nikoli/Janko/pencil puzzle大类、STARE/cube net/tangram、Sokoban/maze/sliding-tile/Atari/Rubik's cube。Wolfram MathWorld: The Web's Most Extensive Mathematics Resource 有很多例子，但是还没有来得及整理 ✅ 2026-05-16 下面 [[#4 批次 3-0516-MathWorld Scaling Rule Candidates - Collected]]
2.2.1 数学相关
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| BPS (Bongard Problems) 来源：BPS (Bongard Problems) |
400+ 不会重复 |
视觉推理, 静态数据集 | 400 道专家设计视觉推理题，非程序生成 生成方式：LLM 读取规则-（人工筛选）-生成图片的描述-生成代码 |
批次 2 | 待补充 | |
| SynthRL 来源：SynthRL |
数学题 | 生成器 RLVR 训练 可验证 |
专为 RLVR 训练的数据 scaling pipeline：seed 题目选择 → 自动合成更难变体 → 验证正确性，保证难度提升的同时保留原始答案，代码开源 生成方式：数学推理题目，扩展需要 google api。 |
待补充 |
2.2.2 物理、机械与可验证量
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| 机械推理图（148 sample） 来源：Mechanical Reasoning dataset； paper |
低 | 齿轮组、皮带、滑轮、杠杆、液压、电路开关 | 方向、速度比、省力倍数、平衡位置、灯泡亮灭、哪个系统可行 | 有点复杂，不能不能生成 |  |
待补充 |
| Figure Weights / 天平图形重量 来源：WAIS Figure Weights；CORE Figure Weights |
低 | 多个天平等式/不等式、图形砝码、候选补全 | 哪个选项平衡；某图形重量；哪个更重；最少需要几个图形 | 随机采样整数权重，生成线性等式/不等式；用线性方程或枚举验证唯一答案 |  |
待补充 |
2.2.3 符号、属性与约束推理
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Matchstick / 七段数码管 来源：MathSticks；通用规则 |
低 | 火柴数字、运算符、错误等式、几何火柴图 | 移动/添加/删除几根使等式成立；问哪根应移动；问是否有解/有几个解 | 七段数码管状态枚举；操作距离为 1/2/3；用表达式求值或几何连通/方块计数验证 |  |
待补充 |
| SET-like 属性卡片 来源：SET rules；overview |
低 | 12 张卡，每张有颜色/形状/数量/填充属性 | 三张是否成 set；找缺失卡；一屏中有几个 set；哪张参与最多 set | 每张卡是属性向量；每维满足 all-same 或 all-different；穷举三元组验证 |  |
待补充 |
| Mastermind / 颜色密码反馈 来源：Rules；complexity |
低 | 多行颜色猜测 + 黑/白反馈钉 | 哪个候选密码满足所有反馈；还剩几个可能密码；下一猜反馈是什么 | 枚举所有颜色序列；按 exact-position 和 color-only 反馈过滤候选 |  |
待补充 |
| 视觉逻辑场景 / Description Logic 来源：LoRA VQA |
低-中 | 简单 2D 或 3D 场景：物体、属性、关系、区域 | all/exists/not/and/or、计数约束、包含关系、多跳关系 | 自己生成场景图和渲染；答案由一阶逻辑/描述逻辑查询得到；可避免真实图像依赖 |  |
待补充 |
2.2.4 棋盘连接与落子游戏
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Connect Four / 四子棋 来源：MathWorld；Hasbro rules |
低 | 7x6 竖棋盘，红黄棋子受重力落子 | 哪列是合法落子；落子后谁赢；是否已有四连；找立即获胜/防守列 | 用二维数组表示棋盘；合法列为未满列；落子后扫描横/竖/斜四连；可用小深度 minimax 生成战术题 |  |
待补充 |
| Reversi / Othello 来源：Reversi rules |
低 | 8x8 黑白棋盘 | 哪些位置是合法落子；某步会翻转几个子；落子后棋盘变成什么；当前比分 | 检查 8 个方向是否夹住对方棋子；翻转列表可精确计算；随机合法对局采样局面 |  |
待补充 |
| Hex 来源：Hex |
低 | 六边形网格，两色棋子，双方连接对边 | 哪方已经连通；某步是否完成连接；哪块是关键桥；候选落子是否合法 | 把格子看成图节点；同色邻接并查集/BFS 判断是否连接两条边 |  |
待补充 |
| Dots and Boxes 来源：Dots and Boxes |
低 | 点阵、已画边、已完成方格归属 | 当前玩家能否完成盒子；某步得几分；哪些边是安全边；游戏比分 | 网格边集合；每条候选边检查新闭合方格数量；可生成 endgame chain 题 |  |
待补充 |
2.2.5 放置、拼块与空间构型
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Block design / 彩色积木拼图 来源：Block Design；Kohs |
中 | 2x2/3x3/4x4 目标图案、双色对角块、候选块朝向 | 最少块数、某块朝向、哪个候选能拼成目标、缺失区域 | 用方格/三角半格表示块面；枚举块朝向；验证拼接后像素/网格一致 |  |
待补充 |
| 正交三视图/体素重建 来源：3ViewSense；mental rotation |
中 | front/top/right 三视图、体素堆、候选 3D 结构 | 从三视图选可能结构；数隐藏方块；哪个视图不一致 | 随机生成体素集合；投影得到三视图；候选用投影一致性和最小/最大体素数验证 |  |
待补充 |
| Blokus-like polyomino placement 来源：Blokus rules；overview |
中 | 方格棋盘、彩色多连方块、剩余块 | 哪个位置可放；是否只角接触不边接触；最多还能放几个格；哪个候选非法 | 多连方块坐标 + 旋转/翻转；检测越界、重叠、角接触、边接触 |  |
待补充 |
| Tetris board state 来源：Tetris Guideline |
中 | 10x20 堆叠棋盘 + 当前方块 | 当前方块能否放在某列/旋转；放下后消几行；哪列高度最高 | 网格碰撞检测；旋转模板；hard drop 后清行和高度统计 |  |
待补充 |
2.2.6 状态转移与模拟类游戏（games）
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Mancala / Kalah 来源：Kalah rules；overview |
低 | 两排坑位 + 两个得分仓，坑内石子数 | 走某坑后石子如何分布；是否获得额外回合；是否触发 capture；当前得分 | 数组模拟 sowing；最后一粒位置决定 extra turn/capture；适合数值+视觉结合 |  |
待补充 |
| Tower of Hanoi 静态状态 来源：Tower of Hanoi |
低 | 三根柱子、不同大小圆盘、当前状态/目标状态 | 下一步合法移动、最少步数、当前是否有效、目标能否在 k 步内到达 | 状态用 tuple 表示；合法移动图搜索；最短路/BFS 或公式验证 |  |
待补充 |
| Peg Solitaire 来源：Peg Solitaire |
低 | 十字/三角棋盘，有孔和棋子 | 哪些跳跃合法；跳一步后局面；最少剩几个；当前是否无路可走 | 图上跳跃规则：起点有子、中间有子、终点空；BFS/DFS 可生成可解局面 |  |
待补充 |
| Lights Out 来源：Lights Out |
低 | 方格灯阵，亮/灭状态 | 按某格后哪些灯改变；最少几步全灭；哪个按钮必须按 | 状态是 bitset；按键为自身+邻居 XOR；线性代数或 BFS 解 | |
待补充 |
| 2048 来源：2048 |
低 | 4x4 数字方块局面 | 向某方向滑动后的局面；合并后最大块；哪个方向得分最高 | 数组模拟滑动压缩和相同数合并；可固定不生成随机新块来做可验证题 |  |
待补充 |
2.2.7 当前不建议作为新增重点的高重复项
| 规则族 / game | 原因 | data_summary-0515.md 已有对应 |
|---|---|---|
| RPM / Raven 矩阵 | 已有 RAVEN、I-RAVEN、raven-gen，重复高 | RAVEN / I-RAVEN / raven-gen |
| Bongard / 六图分类 | 已有 BPS 和 Bongard-LOGO，重复高 | BPS / Bongard-LOGO |
| Nikoli/Janko/pencil puzzle 大类 | 已有多条 puzzle 来源和 generator 来源，重复高 | pencil-puzzle-bench / grilops / Simon Tatham / janko.at / Nikoli |
| Cube net folding / Tangram | STARE 已明确包含，现有三维空间包也覆盖 | STARE / VisualPuzzles / VisuLogic / SMART |
| Sudoku/Nonogram/Kakuro 变体 | 已被 SynLogic、pencil-puzzle-bench、PuzzleMadness 等覆盖 | SynLogic / pencil-puzzle-bench / PuzzleMadness |
| 迷宫/路径基础题 | 已有 VR-Bench、AlphaMaze、VisualPuzzles、SMART、VGRP-Bench | VR-Bench / AlphaMaze / SMART / VGRP-Bench |
| Sokoban | VR-Bench 已覆盖推箱子 | VR-Bench |
| Sliding tile / 15 puzzle | iVISPAR 已覆盖 sliding-tile 空间规划 | iVISPAR |
| Atari / Mario / fighting games | 现有文档已有相关条目，且更偏动态 agent，不适合静态 VQA 起步 | Odysseus / Atari-GPT / fighting games |
| Rubik's Cube | CubeVLM 已覆盖 | CubeVLM |
2.3 批次 3-0516-MathWorld Scaling Rule Candidates - Collected
目标：专门从 Wolfram MathWorld 中筛选可静态渲染、可用 Python 生成和自动验证的规则型 VQA scaling 候选
筛选标准：
- 来源尽量只使用 MathWorld 条目。
- 可以静态渲染成图像、棋盘、网格、图、几何构型或数表。
- 答案可以用公式、枚举、图算法、线性代数、约束求解、几何计算或状态搜索自动验证。
- 对已经高度重复的方向保留但标注重复度，方便后续取舍。
2.3.1 图论、路径与网络结构
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Eulerian Path / 一笔画图 来源：MathWorld: Eulerian Path |
低 | 无向图、桥图、城市/岛屿连接图、边高亮 | 是否存在一笔画；从哪个点开始可走完所有边；添加/删除哪条边后可一笔画 | 用 NetworkX 统计连通性和奇度顶点数；生成满足 0 或 2 个奇点的图；可枚举一条 Euler trail | 给定 7 个节点 10 条边，问能否从 A 出发每条边恰走一次 | 待补充 |
| Hamiltonian Path / Hamiltonian Cycle 来源：MathWorld: Hamiltonian Path；MathWorld: Hamiltonian Cycle |
低-中 | 一般图、网格图、立体骨架图、候选访问序列 | 某序列是否访问每点一次；是否形成 Hamiltonian cycle；缺失下一点是哪一个 | 小规模图用回溯/bitmask DP；候选序列直接验证顶点唯一性和相邻边存在 | 给出一个 12 点图和访问序列，问是否为 Hamiltonian path | 待补充 |
| Icosian Game / 十二面体 Hamiltonian 游戏 来源：MathWorld: Icosian Game |
低 | 十二面体图、20 点 pegboard、局部路径高亮 | 路径是否已经重复点；下一步哪些点合法；是否能闭合成 Hamiltonian cycle | 固定 dodecahedral graph；用 DFS/DP 验证路径扩展和闭合；可从完整解中截断生成题 | 图上已有 16 个访问点，问哪个候选点能继续保持合法 | 待补充 |
| Graph Path / 最短路径与简单路径 来源：MathWorld: Graph Path |
中 | 节点-边图、带权图、迷宫抽象图 | 两点间是否连通；最短路径长度；某条路径是否合法；有几条长度 k 路径 | BFS/Dijkstra/枚举简单路径；随机图控制路径唯一性或多解数量 | 从 S 到 T 的最短路径经过几个节点 | 待补充 |
| Grid Graph / 方格图路径 来源：MathWorld: Grid Graph |
中 | m x n 方格点阵、障碍边、路径涂色 | 两点最短路；环数量；是否二分图；Hamiltonian path 是否可能 | 构造 P_m x P_n 图；BFS、二分染色、回溯或 DP 验证；障碍可由删边生成 |
在 5x6 网格中，问红色路径是否走到每个格点一次 | 待补充 |
| Maze / 迷宫 来源：MathWorld: Maze |
高 | 方格迷宫、圆形迷宫、入口出口 | 哪条路线能到出口；最少转弯数；死胡同数量；某堵墙移除后是否连通 | 生成 spanning tree maze 或带环迷宫；BFS/DFS 验证路径、距离和连通性 | 从入口到出口最少需要走几步 | 待补充 |
| Vertex Coloring / 图着色 来源：MathWorld: Vertex Coloring |
低 | 平面图、一般图、节点颜色候选 | 当前着色是否合法；最少需要几色；哪个节点颜色冲突 | 对小图用回溯/ILP 求 chromatic number；候选着色检查边两端颜色 | 图中蓝色方案是否是合法 3-coloring | 待补充 |
| Map Coloring / 地图着色 来源：MathWorld: Map Coloring |
低 | 区域地图、平面划分、邻接图 | 相邻区域是否冲突；最少颜色数；某区域可用哪些颜色 | 随机生成 planar graph 或 Voronoi 区域邻接图；图着色验证 | 给定部分着色地图，问区域 R 还能用哪些颜色 | 待补充 |
| Clique / 团检测 来源：MathWorld: Clique |
低 | 图中节点集高亮、社交网络样式图 | 高亮节点是否两两相连；最大 clique 大小；补哪条边形成 clique | 穷举小规模节点子集；Bron-Kerbosch 求最大 clique；生成唯一最大团 | 图中红色 5 个点是否构成 clique | 待补充 |
| Graceful Graph / 优美标号 来源：MathWorld: Graceful Graph |
低 | 图节点数字标签、边差值标注 | 标号是否 graceful；哪条边差值重复；缺失节点标签是多少 | 对边计算绝对差；检查节点标签唯一、边标签覆盖 1..m；可回溯生成题 | 给定 6 条边的树标号，问是否为 graceful labeling | 待补充 |
| Dominating Set / 控制集 来源：MathWorld: Domination Number |
低 | 图节点、被覆盖节点阴影、高亮控制点 | 高亮集合是否 domination set；最少控制点数；哪个节点未被覆盖 | 小图枚举节点子集；验证每个节点在集合中或邻接集合；可用 ILP | 红色节点能否覆盖整张图 | 待补充 |
| Spanning Tree / 生成树 来源：MathWorld: Spanning Tree |
低 | 连通图、候选边集合高亮 | 高亮边是否形成生成树；删哪条边仍连通；有几个环 | 用并查集检测连通和无环；边数应为 n-1；可用 Kirchhoff 矩阵树定理计数小图 | 图中蓝色边是否连接全部节点且没有环 | 待补充 |
| Planar Graph / 平面图判定 来源：MathWorld: Planar Graph |
低 | 节点连线图、交叉边图、平面嵌入候选 | 是否平面；哪个边交叉可重画；是否含 K5/K3,3 结构 | 小图用 planarity test；几何绘制中可检测线段交叉；生成 planar/nonplanar 对照 | 这张图是否可以不交叉地画在平面上 | 待补充 |
| Tree / 树结构 来源：MathWorld: Tree |
低 | 层级树、无根树、根节点高亮 | 是否为树；叶子数；两个节点距离；最近公共祖先 | 检查连通且边数 n-1；BFS 求距离；有根树预处理 LCA | 图中从节点 7 到节点 12 的路径长度是多少 | 待补充 |
2.3.2 棋盘图、棋子移动与棋盘约束
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Knight Graph / 骑士图 来源：MathWorld: Knight Graph |
低 | m x n 棋盘、骑士可达边、路径编号 | 某步是否为骑士移动；哪些格可达；路径是否为 knight's tour | 构造 (±1,±2) 移动图；验证路径邻接和覆盖；小棋盘 DFS 生成 tour 片段 |
从 c3 出发，下一步能否到 d5 | 待补充 |
| King Graph / 王图 来源：MathWorld: King Graph |
低 | 棋盘格点、八邻域连边、王路径 | 某路径是否合法；最少王步数；哪些格一步可达；是否 Hamiltonian | 用 Chebyshev 距离验证一步移动；BFS 求最短路；障碍棋盘可做路径题 | 王从 A1 到 E4 最少几步 | 待补充 |
| Queen Graph / 后图 来源：MathWorld: Queen Graph |
中 | m x n 棋盘、后可攻击连线、棋子摆放 | 两个皇后是否互相攻击；给定摆放是否合法；最少颜色数/着色问题 | 同行/同列/同对角线判断；可转为 graph coloring 或 independent set | 图中 6 个皇后是否两两不攻击 | 待补充 |
| Queens Problem / n 皇后 来源：MathWorld: Queens Problem |
中 | n x n 棋盘、皇后符号、候选落子 | 当前局面是否合法；还能放在哪些格；有几个解；补全一行皇后 | 回溯生成 n-queens 解；局部遮罩验证行列对角线冲突；可控制唯一补全 | 在 8x8 棋盘中，问第 6 行皇后应放哪一列 | 待补充 |
| Rook Graph / 车图与行列约束 来源：MathWorld: Rook Graph |
低 | m x n 棋盘、车攻击线、矩阵格 | 两格是否同行同列；最少颜色数；Latin square 对应着色 | 构造 K_m x K_n rook graph；检查行列邻接；用着色生成 Latin square 题 |
哪些格与红色车在 rook graph 中相邻 | 待补充 |
| Bishop Graph / 象图 来源：MathWorld: Bishop Graph |
低 | 棋盘、对角线连通分量、黑白格分组 | 两格是否同一 bishop component；某移动是否合法；是否连通 | 判断同色且同对角线移动；构造 bishop graph，按颜色分连通分量 | 白格上的象能否到达目标格 | 待补充 |
| Rook Complement Graph / 非同行非同列关系 来源：MathWorld: Rook Complement Graph |
低 | m x n 棋盘、互不同行列连线 | 两格是否在补图相邻；高亮集合是否互相非同行列；匹配/排列题 | 对所有格 (r,c) 建图，边连接 r1!=r2 and c1!=c2；验证 clique/independent set |
红色格子集合是否任意两格都不同行不同列 | 待补充 |
| Leaper Graph / 广义跳棋子 来源：MathWorld: Leaper Graph |
低 | 棋盘、固定跳跃向量、可达图 | 哪些格一步可达；路径是否合法；棋盘是否连通 | 给定 leaper 向量 (a,b)，生成八种符号变换移动；BFS/连通性验证 |
使用 (2,3)-leaper，从中心格能跳到哪些格 | 待补充 |
| Triangular Honeycomb Chess Graphs 来源：MathWorld: Triangular Honeycomb Rook Graph |
低 | 三角网格/六角棋盘、rook/bishop/queen/king 移动线 | 某移动是否合法；连通分量；最短步数；攻击关系 | 用 axial/triangular lattice 坐标建图；按方向集合生成边；BFS 验证 | 在三角蜂窝棋盘中，rook 从 A 到 B 需要几步 | 待补充 |
| Puz-Graph / 滑块置换图 来源：MathWorld: Puz-Graph |
中-高 | 小图上放编号棋子和一个空位、状态转移图 | 某移动是否合法；两个状态是否同连通分量；最短移动步数 | 状态为含空位的排列；沿底图边交换空位和相邻棋子；BFS 最短路 | 从左图状态到右图状态最少移动几次 | 待补充 |
2.3.3 数表、填数与代数约束
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Magic Square / 幻方 来源：MathWorld: Magic Square |
中 | n x n 数字方阵、部分空格、行列对角线标注 | 是否为 magic square；缺失数是多少；magic constant；哪条线不满足 | 检查数字集合、行/列/对角线和；可由 Siamese method 或已知构造生成 | 3x3 方阵中缺失中心数，使所有线和相等 | 待补充 |
| Duerer's Magic Square / Durer 幻方变体 来源：MathWorld: Duerer's Magic Square |
低 | 4x4 幻方、象限/中心 2x2 高亮 | 哪些区域和为 34；哪个数字交换会破坏性质；补缺失格 | 固定 Duerer square 或同构变换；验证行列对角线、象限、中心块和 | 问高亮的四个角数字之和是否为 34 | 待补充 |
| Pandiagonal Magic Square / 泛对角幻方 来源：MathWorld: Pandiagonal Magic Square |
低 | 带环绕对角线的方阵、对角线高亮 | 某条环绕对角线和；是否 pandiagonal；缺失数 | 用模索引计算 wraparound diagonal；候选方阵直接验证 | 高亮环绕对角线的和是否等于 magic constant | 待补充 |
| Multiplication Magic Square / 乘法幻方 来源：MathWorld: Multiplication Magic Square |
低 | n x n 数字方阵、乘积标注 | 行列对角线乘积是否相等；缺失因子；最小乘积比较 | 用整数乘积或质因数向量验证；随机生成乘法一致方阵 | 缺失格填几能让三行乘积相同 | 待补充 |
| Prime Magic Square / 素数幻方 来源：MathWorld: Prime Magic Square |
低 | 方阵中全为素数、空格和候选素数 | 是否全素且 magic；哪个候选能填入；magic constant | 素性测试 + 幻方和约束；用回溯或模板生成小阶题 | 哪个候选素数放入空格后仍为幻方 | 待补充 |
| Semimagic Square / 半幻方 来源：MathWorld: Semimagic Square |
低 | 方阵、只要求行列和 | 是否 semimagic；哪条对角线不满足 magic；行列缺失值 | 行列求和验证；对角线作为干扰项；可从 Latin/排列矩阵生成 | 该方阵是 magic square 还是只满足 semimagic | 待补充 |
| Latin Square / 拉丁方 来源：MathWorld: Latin Square |
高 | n x n 符号/颜色/数字方阵、部分空格 | 某行列是否合法；缺失符号；是否 reduced Latin square；两个格能否同符号 | 检查每行每列是否为 1..n；用群表或随机置换生成；回溯补全 | 4x4 拉丁方中空格应填哪个颜色 | 待补充 |
| Partial Latin Square / 局部符号集合拉丁方 来源：MathWorld: Partial Latin Square |
低 | 每格有候选符号小列表、已填符号 | 哪个符号可填；是否违反局部候选或行列唯一性；是否可补全 | 每格有 allowed set；用 CSP/回溯验证唯一解；可生成比 Sudoku 更泛化的题 | 中心格只能从 {1,3,5} 选，问哪个选项合法 | 待补充 |
| Euler Square / Graeco-Latin Square 来源：MathWorld: Euler Square |
中 | 两套符号叠加方阵、颜色+形状组合 | 两个 Latin squares 是否正交；是否每个组合只出现一次；缺失组合 | 分别验证行列唯一；组合 pair 全局唯一；可用有限域构造 | 哪个颜色-形状组合应填入空格 | 待补充 |
| Cryptarithmetic / 字母算式 来源：MathWorld: Cryptarithmetic |
低 | 竖式加减乘、字母替代数字、候选映射 | 哪个数字映射满足竖式；某字母是多少；是否唯一解 | 约束每字母唯一数字、首字母非零；按列进位回溯或 brute force | SEND + MORE = MONEY 中，问 M 是多少 | 待补充 |
| Alphametic / 有意义词语字母算式 来源：MathWorld: Alphametic |
低 | 单词竖式、主题词、字母表 | 映射是否有效；哪个选项为唯一解；进位位置判断 | 与 cryptarithmetic 相同，增加单词模板生成；可控制字母数不超过 10 | TWO + TWO = FOUR 中，哪个数字可对应 O | 待补充 |
| Skeleton Division / 骨架除法 来源：MathWorld: Skeleton Division |
低 | 长除法版式、星号/空格、部分数字 | 缺失数字；商是否正确；某一步乘积是否匹配 | 枚举被除数/除数/商；用长除法中间步骤约束过滤 | 长除法中第二个部分积应是多少 | 待补充 |
| Talisman Square / 相邻差约束方阵 来源：MathWorld: Talisman Square |
低 | 方阵、相邻格差值条件、候选填数 | 是否满足相邻差至少 k；哪个格冲突；补一个数字 | 检查横竖斜邻域绝对差；回溯生成满足条件的排列方阵 | 空格填 8 是否会和邻格差值太小 | 待补充 |
| Magic Circle / 圆环幻数 来源：MathWorld: Magic Circles |
低 | 圆周节点、弦/线组合、节点数字 | 每条直线和是否相等；缺失节点；magic constant | 固定 incidence hypergraph；验证每条线的和；回溯生成唯一补全 | 圆上哪个数字能让所有直线和相等 | 待补充 |
2.3.4 拼块、铺砌、拆分与空间构型
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Polyomino / 多连方 来源：MathWorld: Polyomino |
中 | 方格拼块轮廓、旋转/翻转候选、编号格 | 该形状是几连方；两个形状是否等价；是否含洞；周长/面积 | 坐标集合标准化；旋转/翻转归一；连通性、洞、周长计算 | 两个 pentomino 是否只差旋转或翻转 | 待补充 |
| Polyomino Tiling / 多连方铺砌 来源：MathWorld: Polyomino Tiling |
中 | 棋盘区域、多块 polyomino、部分覆盖 | 某块能否放入；是否完整覆盖；最少/最多剩余格；候选铺法是否合法 | Exact cover/DLX 或回溯；检测重叠、越界、覆盖完整性 | 用 5 块 pentomino 能否铺满给定 5x5 缺口区域 | 待补充 |
| Tetromino / 四连方 来源：MathWorld: Tetromino |
中 | Tetris-like 四连方、候选朝向、棋盘区域 | 形状名称；旋转后占哪些格；能否填入空洞；消行数 | 预定义 5/7/19 种 tetromino；旋转模板和碰撞检测 | 当前 L tetromino 旋转后会覆盖哪些格 | 待补充 |
| Pentomino / 五连方 来源：MathWorld: Pentomino |
中 | 12 种 pentomino、矩形区域、候选拼法 | 某块名称；是否能铺矩形；哪个候选位置非法；剩余空洞形状 | 12 个坐标模板；exact cover 验证；可用已知矩形尺寸生成题 | 哪个 pentomino 能填入右上角空洞 | 待补充 |
| T-Polyomino / T 型多连方 来源：MathWorld: T-Polyomino |
低 | T 形块、不同阶数、网格占格 | 阶数是多少；能否由若干 T-polyomino 铺满区域；旋转合法性 | 按阶数生成 T 形坐标；回溯铺砌；检查面积整除和覆盖 | 图中 T-polyomino 的 order 是几 | 待补充 |
| Polycube / 多立方体 来源：MathWorld: Polycube |
中 | 体素块、三视图、候选 3D 形状 | 由几块小立方体组成；两个 polycube 是否同构；能否装箱 | 3D 坐标集合；24 种旋转归一；体素投影和装箱回溯 | 哪个 3D 候选与左侧三视图一致 | 待补充 |
| Soma Cube / Soma 立方 来源：MathWorld: Soma Cube |
中 | 7 个 Soma pieces、3x3x3 目标体、候选放置 | 某块放置是否合法；缺失块是哪一块；是否填满 3x3x3 | 体素 exact cover；固定 7 件 Soma pieces；旋转枚举 | 最后一块应选哪个才能补成 3x3x3 立方 | 待补充 |
| Slothouber-Graatsma Puzzle 来源：MathWorld: Slothouber-Graatsma Puzzle |
低 | 3x3x3 盒子、6 个 1x2x2 块和 3 个小立方 | 哪个块位置合法；空洞是否可填；是否完整装箱 | 3D exact cover；长方体块旋转；枚举装箱状态 | 还剩两个 1x1x1 空位，问当前装法是否可能完成 | 待补充 |
| Conway Puzzle / 立方装箱 来源：MathWorld: Conway Puzzle |
低 | 多块长方体/立方体拼成大立方 | 组件是否能放；当前局面是否可完成；缺失体素数 | 体素化块；exact cover/DFS；从完整解移除部分块生成题 | 哪个候选块能放入中央空腔 | 待补充 |
| Cube Dissection / 立方体拆分 来源：MathWorld: Cube Dissection |
低 | 大立方切成若干块、爆炸图、体素图 | 这些块能否重组成立方；哪个切面面积最大；体积是否一致 | 体素或多面体布尔运算；体积守恒；装箱验证 | 图中 4 个部件总体积是否等于 3x3x3 立方 | 待补充 |
| Dissection Puzzles / 平面拆分拼图 来源：MathWorld: Dissection Puzzles |
中 | 多边形分割、候选重排目标形 | 哪些碎片可拼成目标；面积是否相等；边长是否匹配 | 多边形面积、边长、角度；允许旋转/翻转；小规模 exact cover 或几何配准 | 这些碎片能否拼成右侧正方形 | 待补充 |
| T-Puzzle 来源：MathWorld: T-Puzzle |
低 | T puzzle 四块/多块、目标轮廓、候选摆放 | 哪块应旋转；当前拼法是否重叠；能否组成 T 形 | 多边形刚体变换；碰撞检测和目标覆盖；可用离散化辅助验证 | 哪个选项把碎片放进 T 形轮廓且无重叠 | 待补充 |
| Tangram / 七巧板 来源：MathWorld: Tangram |
高 | 七巧板碎片、目标剪影、候选摆放 | 哪块位置错误；是否完整覆盖剪影；面积比例 | 固定 7 块多边形；离散网格或多边形布尔验证；可生成 silhouette matching | 右侧摆法中哪一块超出了目标轮廓 | 待补充 |
| Rep-Tile / 自相似拼块 来源：MathWorld: Rep-Tile |
低 | 大形状由若干小相似形组成、缩放网格 | 缩放倍数；小块数量；是否为 rep-tile 分割 | 多边形相似变换；面积比等于块数；边界覆盖验证 | 该图是否把一个三角形分成 4 个相似三角形 | 待补充 |
2.3.5 铺砌、蜂窝、packing 与 covering
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Tiling / 一般铺砌 来源：MathWorld: Tiling |
中 | 平面 tile 图案、周期单元、缺失 tile | 哪块 tile 应填；是否周期；某 tile 的 corona 数量 | 规则 tile 坐标生成；检查邻接、覆盖、重复单元；可从周期 tiling 抽空 | 空白处应放哪种 tile 才能延续图案 | 待补充 |
| Tessellation / 正则与半正则镶嵌 来源：MathWorld: Tessellation |
低 | 正多边形铺面、顶点周围多边形序列 | 顶点配置；是否 regular/semiregular；缺失多边形边数 | 用角度和为 360 度验证；生成 3 regular 和 8 semiregular 图案 | 某顶点周围的配置是 3.6.3.6 还是 3.4.6.4 | 待补充 |
| Hexagon Tiling / 六边形铺砌 来源：MathWorld: Hexagon Tiling |
低 | 正六边形网格、非正六边形周期铺砌、菱形填充六边形 | 哪些格相邻；路径距离；菱形铺法数量小例；缺失 tile | axial/cube 坐标生成 hex grid；邻接和距离公式；小区域 exact cover | 在六边形网格中，从 A 到 B 的最短步数 | 待补充 |
| Square Tiling / 方形铺砌 来源：MathWorld: Square Tiling |
中 | 正方形网格、不同大小方块填矩形 | 是否无重叠覆盖；缺失方块边长；面积和 | 矩形 packing/exact cover；用扫描线检测重叠；面积和验证 | 空白矩形应用哪个边长的正方形填补 | 待补充 |
| Domino Tiling / 多米诺铺砌 来源：MathWorld: Domino Tiling |
高 | 黑白棋盘区域、2x1 domino 覆盖 | 是否可铺；某摆法是否合法；铺法数小例；黑白格数量必要条件 | 二分图完美匹配或 DP；棋盘染色快速判定；exact cover 验证候选 | 去掉两个同色角的棋盘能否用 domino 铺满 | 待补充 |
| Penrose Tiles / 非周期铺砌 来源：MathWorld: Penrose Tiles |
低 | kite/dart 或 rhombus tiles、匹配规则标记 | 哪个 tile 可接在边上；局部匹配是否违反规则；图案是否可扩展 | 用 edge colors/arrows 作为约束；局部 CSP；substitution rules 生成 patches | 哪个候选菱形能接在红色箭头边旁 | 待补充 |
| Wang Tile / 边色方块铺砌 来源：MathWorld: Wang Tile |
低 | 方块 tile 四边颜色、网格空格 | 哪个 tile 可放；是否所有相邻边匹配；有几种补全 | 每个 tile 为四元组颜色；CSP/回溯；局部唯一解生成 | 空白格上方为红、左方为蓝，应选哪个 tile | 待补充 |
| Circle Packing / 圆 packing 来源：MathWorld: Circle Packing |
低 | 容器内多个圆、相切图、圆心标注 | 是否重叠；哪些圆相切；packing density；最大可放半径 | 计算圆心距离与半径和；面积密度；优化或采样生成非重叠布局 | 图中圆 A 和圆 B 是否相切 | 待补充 |
| Rigid Circle Packing / 稳定圆 packing 来源：MathWorld: Rigid Circle Packing |
低 | 圆接触网络、可移动圆高亮 | 哪个圆可移动；接触图是否刚性局部条件；相切邻居数量 | 建 contact graph；局部用约束或几何自由度近似判断；生成简单稳定/不稳定例 | 哪个圆没有被邻居固定住 | 待补充 |
| Circle Covering / 圆覆盖 来源：MathWorld: Circle Covering |
低 | 平面区域、多个重叠圆、未覆盖点 | 某点是否被覆盖；区域是否全覆盖；最少还需几个圆 | 点采样 + 精确圆覆盖判断；小区域可用网格验证；生成可视化覆盖漏洞 | 黑点是否落在任一圆内 | 待补充 |
| Sphere Packing / 球 packing 来源：MathWorld: Sphere Packing |
中 | 3D 球堆、投影视图、接触网络 | 哪些球相切；层数；投影中遮挡关系；packing density | 3D 坐标距离验证；投影渲染；固定 FCC/HCP 小块生成 | 中心球接触了几个球 | 待补充 |
| Kissing Number / 接吻数 来源：MathWorld: Kissing Number |
低 | 中心圆/球与周围圆/球接触图 | 中心对象接触数量；哪个对象不相切；维度对应数值 | 2D/3D 坐标距离验证；计数与中心距离等于半径和的邻居 | 图中有几个圆与中心圆相切 | 待补充 |
2.3.6 计算几何、平面构造与度量题
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Voronoi Diagram / Voronoi 图 来源：MathWorld: Voronoi Diagram |
低 | 点集、Voronoi 区域、查询点 | 查询点属于哪个站点；两区域是否相邻；边界由哪些点决定 | scipy.spatial.Voronoi 或半平面裁剪；最近点验证；邻接由 ridge_points 得到 | 黑点落在哪个 Voronoi cell 中 | 待补充 |
| Delaunay Triangulation / Delaunay 三角剖分 来源：MathWorld: Delaunay Triangulation |
低 | 点集三角网、候选边、外接圆 | 哪条边是 Delaunay；某三角形是否合法；与 Voronoi 邻接关系 | scipy.spatial.Delaunay；空圆条件验证；随机点集避免共圆退化 | 红色边是否属于 Delaunay triangulation | 待补充 |
| Convex Hull / 凸包 来源：MathWorld: Convex Hull |
低 | 平面点集、外壳多边形、高亮候选点 | 哪些点在凸包上；凸包面积；某点是否内部 | Graham scan/Monotonic chain；点在多边形内；shoelace 面积 | 哪个蓝点不是凸包顶点 | 待补充 |
| Triangulation / 多边形三角剖分 来源：MathWorld: Triangulation |
低 | 简单多边形、对角线、三角形区域 | 某条对角线是否合法；三角形数量；面积和是否匹配 | ear clipping 或 shapely triangulate；检查对角线在多边形内且不交叉 | 七边形三角剖分应有几个三角形 | 待补充 |
| Art Gallery Theorem / 多边形守卫 来源：MathWorld: Art Gallery Theorem |
低 | 多边形房间、守卫点、可见区域阴影 | 几个守卫足够；某点是否被看见；哪个角未覆盖 | 多边形可见性计算；小 n 用三角剖分和 3-coloring 构造；采样验证覆盖 | 图中哪个区域没有被任一守卫看到 | 待补充 |
| Point in Polygon / 点在多边形内 来源：MathWorld: Point in Polygon |
低 | 多边形、查询点、射线 | 点在内/外/边界；射线交点数；哪个点被包含 | ray casting 或 winding number；避免边界退化或单独标注 | 黑点是在多边形内部还是外部 | 待补充 |
| Polygon Area / 多边形面积 来源：MathWorld: Polygon Area |
低 | 网格多边形、顶点坐标、三角分割 | 面积是多少；哪个多边形面积更大；Pick 定理小题 | shoelace formula；网格点可用 Pick theorem；自动渲染坐标 | 图中格点多边形面积是多少 | 待补充 |
| Pick's Theorem / 格点多边形 来源：MathWorld: Pick's Theorem |
低 | 格点多边形、边界点/内部点标记 | 内部格点数；面积；边界点数；缺失点分类 | 计算 lattice polygon 面积和边界 gcd；用 A = I + B/2 - 1 验证 |
已知面积 12、边界点 10，问内部点几个 | 待补充 |
| Euler Characteristic / 欧拉示性数 来源：MathWorld: Euler Characteristic |
低 | 平面图、多面体网格、顶点边面标注 | V-E+F 是多少；是否满足凸多面体公式；缺失面数 | 计数 vertices/edges/faces；多面体/平面图拓扑验证 | 该多面体有 8 顶点 12 边，问面数是多少 | 待补充 |
| Polyhedron / 多面体骨架 来源：MathWorld: Polyhedron |
中 | 3D 多面体、展开图、顶点边面 | 顶点/边/面数量；哪个展开图可折叠；邻接面判断 | 用预定义 polyhedron mesh；投影渲染；图结构验证邻接 | 正十二面体每个面邻接几个面 | 待补充 |
| Platonic Solid / 柏拉图立体 来源：MathWorld: Platonic Solid |
中 | 五种正多面体、骨架图、面展开图 | 识别立体；面数/顶点数/边数；对偶是谁 | 固定五种 mesh 参数；欧拉公式和对偶映射验证 | 由 20 个三角形面组成的是哪种正多面体 | 待补充 |
| Frustum / 截台体积 来源：MathWorld: Frustum |
低 | 截锥/截棱锥、尺寸标注 | 体积/侧面积；哪个截面更大；高度缺失 | 公式计算；随机尺寸生成；图中标注参数 | 上底半径 2、下底半径 5、高 6 的截锥体积是多少 | 待补充 |
2.3.7 数列、图案、自动机与视觉化规则
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Cellular Automaton / 元胞自动机 来源：MathWorld: Cellular Automaton |
低 | 1D/2D 网格时间演化、初态和规则 | 下一行/下一代是什么；某格 t 步后状态；规则号识别 | 按邻域规则迭代 bit grid；固定随机 seed；答案直接模拟 | Rule 30 的下一行中第 5 格是黑还是白 | 待补充 |
| Elementary Cellular Automaton 来源：MathWorld: Elementary Cellular Automaton |
低 | 1D 二值 CA 三邻域、规则表、时空图 | 给定规则表求下一行；识别规则号；补缺失像素 | 8 个邻域到 bit 输出；规则号二进制编码；逐行模拟 | 规则 110 下，当前 001110 的下一行是什么 | 待补充 |
| Game of Life / 生命游戏 来源：MathWorld: Life |
中 | 二维黑白格、当前代和候选下一代 | 下一代某格状态；图案是否仍生命；几代后数量 | 按 8 邻域计数应用 Life 规则；模拟多步；可生成 oscillator/still life | 这个 blinker 下一代是横线还是竖线 | 待补充 |
| Pascal's Triangle / 杨辉三角 来源：MathWorld: Pascal's Triangle |
低 | 三角数表、缺失数字、模颜色图 | 缺失项；某行和；奇偶颜色模式；组合数位置 | 用 C(n,k) 公式或递推；模 p 着色；自动生成空格 |
第 7 行第 3 个数是多少 | 待补充 |
| Ulam Spiral / 素数螺旋 来源：MathWorld: Ulam Spiral |
低 | 数字方格螺旋、素数高亮、坐标标注 | 某格数字；某数字坐标；是否素数；高亮数列规律 | 生成方形螺旋映射；素性测试；可问坐标和数值互查 | 螺旋中数字 37 位于中心的哪个方向 | 待补充 |
| Fibonacci Word / 斐波那契词 来源：MathWorld: Fibonacci Word |
低 | 二值字符串/条纹递推图 | 下一段字符串；第 n 位字符；替换规则是否正确 | 字符串 morphism 迭代；直接索引或递推；渲染条纹 | 按 0->01, 1->0，第三次迭代结果是什么 | 待补充 |
| Lindenmayer System / L-system 来源：MathWorld: Lindenmayer System |
低 | 迭代曲线、重写规则、候选下一步 | 下一代字符串；哪幅图是第 k 代；转角数量 | 字符串重写 + turtle graphics；验证 token counts 和渲染路径 | Koch 规则迭代两次后有几段线 | 待补充 |
| Koch Snowflake / Koch 雪花 来源：MathWorld: Koch Snowflake |
低 | 分形曲线迭代图、边段数量 | 第 n 代边数/周长；哪幅图是下一代；面积增长 | 递推 segments=3*4^n；turtle 生成；多边形面积公式 |
第 3 次迭代后共有多少条小线段 | 待补充 |
| Sierpinski Sieve / Sierpinski 三角 来源：MathWorld: Sierpinski Sieve |
低 | 三角递归图、缺失子三角、迭代阶数 | 黑/白区域数量；某子区域是否被移除；第几阶图 | 递归三角划分或 Pascal mod 2；坐标判断；计数公式 | 第 4 阶图中有多少个最小黑三角 | 待补充 |
| Hilbert Curve / 空间填充曲线 来源：MathWorld: Hilbert Curve |
低 | 方格中的递归路径、编号点、方向箭头 | 下一步方向；两编号点是否相邻；第 n 阶覆盖格数 | Hilbert index <-> xy 映射；路径邻接验证；递归绘制 | Hilbert 曲线第 12 步走向哪个方向 | 待补充 |
| Dragon Curve / 龙曲线 来源：MathWorld: Dragon Curve |
低 | 折纸曲线、左右转序列、迭代图 | 下一次折叠序列；末端位置；哪幅图是第 k 阶 | 生成 turn sequence；turtle path；检测自交/端点 | 第 5 次迭代的最后一个转向是左还是右 | 待补充 |
| Penrose Tiling Substitution / Penrose 递归图案 来源：MathWorld: Penrose Tiles |
低 | 菱形/风筝飞镖替换步骤、局部 patch | 哪个子 tile 出现；下一阶 tile 数；边匹配是否正确 | substitution matrix 计数；几何替换渲染；边箭头约束验证 | 下一阶中胖菱形数量会变成多少 | 待补充 |
2.3.8 经典 puzzle 与状态搜索
| 候选规则种类 | 和已有数据重复度 | 静态图形式 | 可生成的 VQA 类型 | Python 生成/验证思路 | 示例 | 负责人/完成情况 |
|---|---|---|---|---|---|---|
| Tower of Hanoi / 汉诺塔 来源：MathWorld: Tower of Hanoi |
低 | 三柱圆盘、当前状态和目标状态 | 哪个移动合法；最少步数；下一步应移动哪盘；是否可在 k 步内到达 | 状态 tuple 表示每盘柱号；合法移动 BFS 或公式 2^n-1；从解路径采样 |
当前状态下，最小盘能移到哪根柱子 | 待补充 |
| 15 Puzzle / 十五数码 来源：MathWorld: 15 Puzzle |
高 | 4x4 滑块、空格、目标状态 | 哪些滑块可移动；是否可解；最少步数小局面；移动后状态 | 置换逆序奇偶性判可解；A*/IDA* 解小扰动状态；候选移动验证 | 当前空格旁边哪些数字可以滑入 | 待补充 |
| Baguenaudier / 九连环 来源：MathWorld: Baguenaudier |
低 | 环扣开关序列、二进制状态、步骤图 | 下一步合法操作；最少解开步数；某状态编号 | 用 Gray code/状态图模拟；合法翻转规则；BFS 验证 | 当前 01011 状态下哪个环能被翻转 | 待补充 |
| Tic-Tac-Toe Multiway / 井字棋多路状态 来源：MathWorld: Multicomputation |
中 | 3x3 棋盘、game tree 小图、候选落子 | 当前谁赢；哪些落子合法；下一状态数；是否已经终局 | 枚举棋盘状态；胜线检测；生成 game tree 或 multiway graph | 轮到 X，哪个格落子后立即获胜 | 待补充 |
| Conway's Game of Life Patterns 来源：MathWorld: Life |
中 | still life/oscillator/glider 静态序列 | 该图案是静物还是振荡子；几代回到原样；下一代活细胞数 | Life 模拟并检测周期；固定 pattern 库；可自动渲染多帧为静态图 | 这个 5x5 图案两代后是否回到原样 | 待补充 |
| Theta-0 Graph Puzzle 来源：MathWorld: Theta-0 Graph |
低 | 特定 puzzle graph、边/节点路径 | 能否从指定状态到目标；路径是否合法；图结构属性 | 将 puzzle 抽象为图搜索；按条目图结构固定生成；BFS 验证 | 从红点到蓝点是否存在不重复边路径 | 待补充 |
| Caliban Puzzle 来源：MathWorld: Caliban Puzzle |
低 | 棋盘/图形 puzzle 布局、候选移动 | 哪步合法；是否达到目标；最短步数小实例 | 若条目规则固定，可编码状态转移；BFS/DFS 自动验证 | 哪个选项是当前局面的合法下一步 | 待补充 |
| Diabolical Cube 来源：MathWorld: Diabolical Cube |
低 | 小立方体组合块、目标立方、候选装配 | 哪个部件位置合法；能否组成立方；缺失块 | 体素 exact cover；旋转枚举；固定 puzzle pieces | 哪个候选部件能填入剩余空间 | 待补充 |
2.3.9 现阶段优先级备注
| 规则族 / 方向 | 建议 | 原因 |
|---|---|---|
| 最值得优先补充 | Eulerian/Hamiltonian、棋盘图、Voronoi/Delaunay/Convex Hull、Magic/Latin/cryptarithmetic、circle packing、Wang/Penrose tiles | 与现有数据重复较低，视觉形式清楚，Python 验证直接，能形成大量参数化题 |
| 可作为中期扩展 | polyomino/pentomino/polyclube/Soma、dissection、Art Gallery、L-system/fractal | 生成和渲染成本稍高，但题型质量高，适合做中等难度 scaling |
| 需要谨慎避免重复 | Maze、15 Puzzle、Tangram、Domino Tiling、Sudoku-like Latin squares、Tower of Hanoi | 现有 benchmark 或总表已有近邻，除非设计出明显不同的视觉/推理切面 |
| 不太适合第一批 | 过深的数论条目、纯公式条目、大规模 NP-hard 最优题 | 静态图像信息量弱，或自动生成唯一答案成本高，容易变成文本数学题 |
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Papers for Yezixiao/Visual_scaling_static
CubeBench: Diagnosing Interactive, Long-Horizon Spatial Reasoning Under Partial Observations
Paper • 2512.23328 • Published
MathSticks: A Benchmark for Visual Symbolic Compositional Reasoning with Matchstick Puzzles
Paper • 2510.00483 • Published
VisualSphinx: Large-Scale Synthetic Vision Logic Puzzles for RL
Paper • 2505.23977 • Published • 10
Enhancing Player Enjoyment with a Two-Tier DRL and LLM-Based Agent System for Fighting Games
Paper • 2504.07425 • Published