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).
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
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)
The easiest way to get the source is to use pip:
$ pip install mathematics_datasetAlternately you can get the source by cloning the mathematics_dataset repository:
$ git clone https://github.com/deepmind/mathematics_dataset
$ pip install --upgrade mathematics_dataset/Generated examples can be printed to stdout via the generate script. For
example:
python -m mathematics_dataset.generate --filter=linear_1dwill 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.
The following table is necessary for this dataset to be indexed by search engines such as Google Dataset Search.
| property | value | ||||||
|---|---|---|---|---|---|---|---|
| name | Mathematics Dataset |
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| url | https://github.com/deepmind/mathematics_dataset |
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| sameAs | https://github.com/deepmind/mathematics_dataset |
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| 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) |
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| provider |
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| citation | https://identifiers.org/arxiv:1904.01557 |