Analysing Mathematical Reasoning Abilities of Neural Models
Paper • 1904.01557 • Published
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The dataset generation failed because of a cast error
Error code: DatasetGenerationCastError
Exception: DatasetGenerationCastError
Message: An error occurred while generating the dataset
All the data files must have the same columns, but at some point there are 4 new columns ({'question', 'options', 'correct', 'rationale'}) and 4 missing columns ({'text', 'meta', 'subset', 'file_path'}).
This happened while the json dataset builder was generating data using
hf://datasets/rayvex/Maths/aqua_rat.jsonl (at revision 9284b80d25f7c1a959eae9baf454b7de8c6ec801)
Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1831, in _prepare_split_single
writer.write_table(table)
File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 714, in write_table
pa_table = table_cast(pa_table, self._schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2218, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
question: string
options: list<item: string>
child 0, item: string
rationale: string
correct: string
to
{'text': Value('string'), 'subset': Value('string'), 'meta': {'id': Value('string'), 'language_detection_score': Value('float64')}, 'file_path': Value('string')}
because column names don't match
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1455, 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 1054, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 894, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 970, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1702, 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 1833, in _prepare_split_single
raise DatasetGenerationCastError.from_cast_error(
datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
All the data files must have the same columns, but at some point there are 4 new columns ({'question', 'options', 'correct', 'rationale'}) and 4 missing columns ({'text', 'meta', 'subset', 'file_path'}).
This happened while the json dataset builder was generating data using
hf://datasets/rayvex/Maths/aqua_rat.jsonl (at revision 9284b80d25f7c1a959eae9baf454b7de8c6ec801)
Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
text string | subset string | meta dict | file_path string |
|---|---|---|---|
\begin{document}
\title [Power numerical radius inequalities]
{{ Power numerical radius inequalities from an extension of Buzano's inequality }}
\author[P. Bhunia]{Pintu Bhunia}
\address{ {Department of Mathematics, Indian Institute of Science, Bengaluru 560012, Karnataka, India}}
\email{pintubhunia... | arXiv | {
"id": "2305.17657.tex",
"language_detection_score": 0.4445488452911377
} | arXiv/math_arXiv_v0.2.jsonl |
\begin{document}
\title{Attractors of Sequences of Function Systems \\ and their relation to Non-Stationary Subdivision} \author[David Levin]{David Levin} \author[Nira Dyn]{Nira Dyn} \address{D. Levin, N. Dyn, School of Mathematical Sciences, Tel Aviv University, Israel} \author[P. V. Viswanathan]{Puthan Veedu Viswana... | arXiv | {
"id": "1612.00630.tex",
"language_detection_score": 0.6515102386474609
} | arXiv/math_arXiv_v0.2.jsonl |
\begin{document}
\title{Generic rigidity of reflection frameworks} \author{Justin Malestein\thanks{Temple University, \url{justmale@temple.edu}} \and Louis Theran\thanks{Institut für Mathematik, Diskrete Geometrie, Freie Universität Berlin, \url{theran@math.fu-berlin.de}}} \date{} \maketitle \begin{abstract} \begin{no... | arXiv | {
"id": "1203.2276.tex",
"language_detection_score": 0.7831615805625916
} | arXiv/math_arXiv_v0.2.jsonl |
\begin{document}
\title{Controlled deflection of cold atomic clouds and of Bose-Einstein condensates}
\author{N. Gaaloul}
\affiliation{Laboratoire de Spectroscopie Atomique, Mol\'{e}culaire et Applications, D\'{e}partement de Physique, Facult\'{e} des Sciences de Tunis, Universit\'{e} Tunis El Manar, 2092 Tunis, Tun... | arXiv | {
"id": "0709.2636.tex",
"language_detection_score": 0.7808927297592163
} | arXiv/math_arXiv_v0.2.jsonl |
"\\begin{document}\n\n\\title{Isomorphy classes of $k$-involutions of $G_2$}\n\n\\begin{abstract} Is(...TRUNCATED) | arXiv | {
"id": "1211.1874.tex",
"language_detection_score": 0.6350813508033752
} | arXiv/math_arXiv_v0.2.jsonl |
"\\begin{document}\n\n\\noindent {\\footnotesize }\\\\[1.00in]\n\n\\title[ On globally symmetric Fin(...TRUNCATED) | arXiv | {
"id": "1101.4288.tex",
"language_detection_score": 0.7402070164680481
} | arXiv/math_arXiv_v0.2.jsonl |
"\\begin{document}\n\n\\title[Poloids]{Poloids from the Points of View of Partial Transformations an(...TRUNCATED) | arXiv | {
"id": "1710.04634.tex",
"language_detection_score": 0.5051230788230896
} | arXiv/math_arXiv_v0.2.jsonl |
"\\begin{document}\n\n\\begin{frontmatter}\n\n\\title{Hyperbolicity in the corona and join of graphs(...TRUNCATED) | arXiv | {
"id": "1410.2938.tex",
"language_detection_score": 0.7075411081314087
} | arXiv/math_arXiv_v0.2.jsonl |
"\\begin{document}\n\n\\begin{abstract} We revisit Vasy's method \\cite{vasy1},\\cite{vasy2} for sho(...TRUNCATED) | arXiv | {
"id": "1511.03352.tex",
"language_detection_score": 0.5529550909996033
} | arXiv/math_arXiv_v0.2.jsonl |
"\\begin{document}\n\n\\title{Upper bounds for number of removed edges in the Erased Configuration M(...TRUNCATED) | arXiv | {
"id": "1507.05008.tex",
"language_detection_score": 0.8079072833061218
} | arXiv/math_arXiv_v0.2.jsonl |
End of preview.
YAML Metadata Warning:empty or missing yaml metadata in repo card
Check out the documentation for more information.
Mathematics Dataset
This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.
Original paper: Analysing Mathematical Reasoning Abilities of Neural Models (Saxton, Grefenstette, Hill, Kohli).
Example questions
Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.
Answer: 4
Question: Calculate -841880142.544 + 411127.
Answer: -841469015.544
Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).
Answer: 54*a - 30
Question: Let e(l) = l - 6. Is 2 a factor of both e(9) and 2?
Answer: False
Question: Let u(n) = -n**3 - n**2. Let e(c) = -2*c**3 + c. Let l(j) = -118*e(j) + 54*u(j). What is the derivative of l(a)?
Answer: 546*a**2 - 108*a - 118
Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql.
Answer: 1/110
Pre-generated data
Version 1.0
This is the version released with the original paper. It contains 2 million (question, answer) pairs per module, with questions limited to 160 characters in length, and answers to 30 characters in length. Note the training data for each question type is split into "train-easy", "train-medium", and "train-hard". This allows training models via a curriculum. The data can also be mixed together uniformly from these training datasets to obtain the results reported in the paper. Categories:
- algebra (linear equations, polynomial roots, sequences)
- arithmetic (pairwise operations and mixed expressions, surds)
- calculus (differentiation)
- comparison (closest numbers, pairwise comparisons, sorting)
- measurement (conversion, working with time)
- numbers (base conversion, remainders, common divisors and multiples, primality, place value, rounding numbers)
- polynomials (addition, simplification, composition, evaluating, expansion)
- probability (sampling without replacement)
Getting the source
PyPI
The easiest way to get the source is to use pip:
$ pip install mathematics_dataset
From GitHub
Alternately you can get the source by cloning the mathematics_dataset repository:
$ git clone https://github.com/deepmind/mathematics_dataset
$ pip install --upgrade mathematics_dataset/
Generating examples
Generated examples can be printed to stdout via the generate script. For
example:
python -m mathematics_dataset.generate --filter=linear_1d
will generate example (question, answer) pairs for solving linear equations in one variable.
We've also included generate_to_file.py as an example of how to write the
generated examples to text files. You can use this directly, or adapt it for
your generation and training needs.
Dataset Metadata
The following table is necessary for this dataset to be indexed by search engines such as Google Dataset Search.
| property | value | ||||||
|---|---|---|---|---|---|---|---|
| name | Mathematics Dataset |
||||||
| url | https://github.com/deepmind/mathematics_dataset |
||||||
| sameAs | https://github.com/deepmind/mathematics_dataset |
||||||
| description | This dataset consists of mathematical question and answer pairs, from a range
of question types at roughly school-level difficulty. This is designed to test
the mathematical learning and algebraic reasoning skills of learning models.\n
\n
## Example questions\n
\n
```\n
Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.\n
Answer: 4\n
\n
Question: Calculate -841880142.544 + 411127.\n
Answer: -841469015.544\n
\n
Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).\n
Answer: 54*a - 30\n
```\n
\n
It contains 2 million
(question, answer) pairs per module, with questions limited to 160 characters in
length, and answers to 30 characters in length. Note the training data for each
question type is split into "train-easy", "train-medium", and "train-hard". This
allows training models via a curriculum. The data can also be mixed together
uniformly from these training datasets to obtain the results reported in the
paper. Categories:\n
\n
* **algebra** (linear equations, polynomial roots, sequences)\n
* **arithmetic** (pairwise operations and mixed expressions, surds)\n
* **calculus** (differentiation)\n
* **comparison** (closest numbers, pairwise comparisons, sorting)\n
* **measurement** (conversion, working with time)\n
* **numbers** (base conversion, remainders, common divisors and multiples,\n
primality, place value, rounding numbers)\n
* **polynomials** (addition, simplification, composition, evaluating, expansion)\n
* **probability** (sampling without replacement) |
||||||
| provider |
|
||||||
| citation | https://identifiers.org/arxiv:1904.01557 |
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