multilingual-gsm-symbolic 0.3.0

A package for generating multilingual symbolic GSM math problems

multilingual-gsm-symbolic

A Python package for generating synthetic multilingual math problems from symbolic templates. Allows you to create more than a thousand examples from just one problem and allows you to test if the LLMs actually understand the problem or whether it was just lucky pattern-matching.

⏳ Installation

pip install multilingual-gsm-symbolic

👩‍💻 Get started

from multilingual_gsm_symbolic import load_data, available_languages

# see possible languages
print(available_languages())
# {'eng': {'number of samples': 100}, 'dan': {'number of samples': 100}}

# Load English templates
templates = load_data("eng")

# Generate concrete questions from a template
questions = templates[0].generate_questions(n=10, language="eng")

for q in questions:
    print(q.question)
    print(q.answer)
    print()

📋 Template format

Templates are JSON files with four fields:

Field	Description
question	Concrete question (the original example)
answer	Concrete answer with calculation steps
question_annotated	Template with variable placeholders and #init / #conditions / #answer sections
answer_annotated	Answer template with inline expressions

Annotated question syntax

{variable, default_value}   — placeholder in the question text
#init:
- $var = range(low, high)   — variable sampled from a range
- $var = sample([a, b, c])  — variable sampled from a list
#conditions:
- is_int(x / y)             — constraint that must hold for a combination to be valid
#answer: x * y + z          — Python expression evaluated to produce the numeric answer

Example: fog bank problem

{
  "question": "A fog bank rolls in over a city at 3 miles/hour. The city is 42 miles wide. How many hours will it take for the fog bank to cover the city?",
  "question_annotated": "A fog bank rolls in over a city at {speed,3} miles/hour. The city is {width,42} miles wide. How many hours will it take for the fog bank to cover the city?\n#init:\n- $speed = range(1, 20)\n- $width = range(2, 100)\n#conditions:\n- is_int(width / speed)\n#answer: width // speed",
  "answer": "At 3 miles/hour, it will take 42/3=14 hours for the fog to cover the city.",
  "answer_annotated": "At {speed} miles/hour, it will take {width}/{speed}={width//speed} hours for the fog to cover the city."
}

Example: shopping problem

{
  "question": "A store sells apples for $2 each and oranges for $3 each. If you buy 4 apples and 5 oranges, how much do you spend?",
  "question_annotated": "A store sells apples for ${apple_price,2} each and oranges for ${orange_price,3} each. If you buy {n_apples,4} apples and {n_oranges,5} oranges, how much do you spend?\n#init:\n- $apple_price = range(1, 10)\n- $orange_price = range(1, 10)\n- $n_apples = range(1, 20)\n- $n_oranges = range(1, 20)\n#conditions:\n- True\n#answer: apple_price * n_apples + orange_price * n_oranges",
  "answer": "You spend 4*2 + 5*3 = 8 + 15 = $23.",
  "answer_annotated": "You spend {n_apples}*{apple_price} + {n_oranges}*{orange_price} = {n_apples*apple_price} + {n_oranges*orange_price} = ${apple_price*n_apples + orange_price*n_oranges}."
}

🗃️ Data

The English templates are derived from Apple's GSM-Symbolic paper. The Danish templates are manual translations and localizations of the English set, validated both computationally and manually. The original concrete problems are from GSM8k.

Language	Code	Templates
English	eng	100
Danish	dan	100

Writing a custom template

Here is a complete example — a "speed × time = distance" problem with randomised values and a divisibility constraint:

{
  "question": "A car travels at 60 mph for 3 hours. How far does it travel?",
  "answer": "Distance = speed × time = 60 × 3 = 180 miles.\n#### 180",
  "id_orig": 0,
  "id_shuffled": 0,
  "question_annotated": "A car travels at {speed,60} mph for {hours,3} hours. How far does it travel?\n#init:\n- $speed = range(20, 100, 10)\n- $hours = range(1, 9)\n#conditions:\n- is_int(speed * hours / 10)\n#answer: speed * hours",
  "answer_annotated": "Distance = speed × time = {speed} × {hours} = {speed * hours} miles.\n#### {speed * hours}"
}

Save it as a .json file and load it directly:

from multilingual_gsm_symbolic.gsm_parser import AnnotatedQuestion

template = AnnotatedQuestion.from_json("my_template.json")
questions = template.generate_questions(n=5, language="eng")
for q in questions:
    print(q.question)
    print(q.answer)

Init functions available in #init lines:

Function	Returns
range(start, end[, step])	integers in [start, end)
arange(start, end[, step])	evenly-spaced floats
sample(items[, n])	one item (or n items) from a list
sample_sequential(items, n)	n consecutive items from a list
range_str(start, end, step, word_list)	(word, int) pairs, e.g. ("three", 3)

Condition functions available in #conditions lines:

Function	Returns
is_int(x)	True if x is a whole number
divides(a, b)	True if a % b == 0
Fraction(x)	fraction string, e.g. "3/4"

📖 API reference

function load_data

load_data(language="eng", directory=None) → list[AnnotatedQuestion]

Load symbolic templates.

Argument	Type	Description
language	str	Language code, e.g. "eng" (default) or "dan"
directory	Path | None	Override the bundled data; load templates from this path instead
RETURNS	list[AnnotatedQuestion]	The loaded templates

function load_replacements

load_replacements(language="eng") → dict

Load language-specific named values (e.g. lists of names, places) used inside templates.

Argument	Type	Description
language	str	Language code, e.g. "eng" (default)
RETURNS	dict	Mapping of replacement name → value list

function load_gsm

load_gsm(language="eng", directory=None) → list[GSMProblem]

Load the bundled concrete problems for a given language.

Argument	Type	Description
language	str	Language code, e.g. "eng" (default)
directory	Path | None	Override the bundled data directory
RETURNS	list[GSMProblem]	The loaded concrete problems

class AnnotatedQuestion

Core class representing a symbolic template. Constructed from a JSON template file via AnnotatedQuestion.from_json(path).

^{method AnnotatedQuestion.generate_questions}

Generate concrete Question instances from the template.

Argument	Type	Description
n	int	Number of questions to generate
language	str	Language code for rendered text
replacements	dict	Replacement values from load_replacements
RETURNS	list[Question]	The generated questions

^{method AnnotatedQuestion.get_default_assignments}

Extract the example variable values from the template.

Argument	Type	Description
replacements	dict	Replacement values from load_replacements
RETURNS	dict	Mapping of variable name → default value

^{method AnnotatedQuestion.format_question}

Render the question text for a given variable assignment.

Argument	Type	Description
assignments	dict	Variable name → value mapping
language	str	Language code for rendered text
RETURNS	str	The rendered question string

^{method AnnotatedQuestion.format_answer}

Render the answer text for a given variable assignment.

Argument	Type	Description
assignments	dict	Variable name → value mapping
language	str	Language code for rendered text
RETURNS	str	The rendered answer string

class Question

Dataclass holding a single generated problem.

Attribute	Type	Description
question	str	The rendered question text
answer	str	The rendered answer text
id_orig	int	Index of the original template
id_shuffled	int	Index within the shuffled sample

class GSMProblem

Pydantic model for a concrete problem loaded from disk.

Attribute	Type	Description
question	str	The question text
answer	str	The answer text
id_orig	int	Original problem index
filepath	Path	Path to the source file on disk

Acknowledgement

The symbolic template engine and the danish subset were originally developed as part of the m-gsm-symbolic project at the Centre for Humanities Computing by:

• Kenneth Enevoldsen
• Simon Mosegaard
• Enniw

The initial template format was derived from Apple's GSM-Symbolic paper and the original concrete problems are from GSM8k.