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)
Getting the source
The easiest way to get the source is to use pip:
$ pip install mathematics_dataset
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/
Generated examples can be printed to stdout via the
generate script. For
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.