Emulated-Inc/multilingual-grade-school-math-training-pool

Multilingual grade school math training pool

Grade-school math word problems in eleven languages, each with the number that answers it, from four public datasets read at the pinned revisions named below and laid out twice. Train on either layer or on both.

pool.jsonl

Every source rewritten into one shape, 261160 rows, one JSON object per line, with these fields.

Field	What it holds
id	a row identifier unique within this file
question	the problem text, as its source publishes it
answer	the final answer, a number written as a string
solution	a worked solution in the language of the problem, or empty
language	the language the problem is written in
problem_group	the same value for every language of one problem
source	the name of the source directory the row came from
source_repo, source_revision	the dataset and the revision it was read at
source_subset, source_split, source_id	where the row sits in that set
provenance_class	how the row came to exist
licence	the licence of the source it came from

Two of the four sources carry a worked solution and two do not, so solution is written for 64384 rows and empty for the rest, while answer is written for every row. A row with a solution is usable as a supervised pair, a row without one is usable with a verifier that checks the number, and every row is usable the second way. The solutions keep the calculator annotations their sources write, an arithmetic step in double angle brackets before its result, which a model trained on them will learn to write too. Rows are deduplicated on the language together with the problem text and the answer, keeping the first source that carries the problem in the order of the sections below.

The answer of a translated row is the answer key of the English problem it was translated from, which a translation does not change, and such a row is written here only when its own worked solution still ends in that number. Rows whose stated answer is a fraction or an expression rather than a number are not written here. Both kinds are still in the untouched sources.

sources/

The same data untouched, 274195 rows, one directory per source, holding the files at the paths, in the format and with the columns its own repository publishes. Nothing here was renamed, reshaped, reordered or deduplicated. Use this layer if you want a field the rewritten one drops, such as the calculator traces and equations of the large Chinese corpus or the fixed rejected response of the translated set, if you want the rows the rewritten layer left out, or if you would rather pair the problems with their answers yourself.

Languages

One source is English, one is that same English problem set rendered into nine more languages by a language model, and two are Chinese, so the pool is not balanced across its languages and the Chinese share is the largest. The counts are here so that a mixture can be chosen deliberately. One line of the table is an accident rather than coverage: Telugu has 1 rewritten row, which is what the translated set happens to carry in it, and nothing else in the pool reaches that language, so it is not one this pool can train.

Language	Rows in pool.jsonl	Rows in sources/
English (en)	7449	14383
Bengali (bn)	5570	6013
German (de)	6442	6927
Spanish (es)	6419	6931
French (fr)	6420	6930
Japanese (ja)	6513	6932
Russian (ru)	6374	6824
Swahili (sw)	6408	6933
Telugu (te)	1	1
Thai (th)	6399	6934
Chinese (zh)	203165	205387

The sources

sources/gsm8k

Grade-school math word problems written by paid crowdworkers, each with a worked solution in plain English and a final numeric answer, the train split only. From openai/gsm8k at revision 740312add88f781978c0658806c59bc2815b9866, files main/train-00000-of-00001.parquet. 7449 rows here, of which 7449 also appear in pool.jsonl. Languages: English. Provenance class human, licence mit. Its own fields are question, answer holding the worked solution and the final number after ####.

Worth knowing. English only, and its problems are widely present in web pretraining corpora, so a model pretrained on web text may have met them already.

sources/mathoctopus_parallel

The same English train problems and their worked solutions rendered into nine more languages by a language model, question and solution in the same language, published with rule-based calibration and human verification of the numbers by its authors. From Mathoctopus/GSM8KInstruct_Parallel at revision dd8076b83bacd7c6ade2829317e8a500c6ffbec4, files MGSM8KInstruct_Parallel.json. 68186 rows here, of which 56935 also appear in pool.jsonl. Languages: ten languages, English and nine others. Provenance class model-generated, licence apache-2.0. Its own fields are prompt holding an instruction wrapper that names the language and carries the problem, chosen holding the worked solution, reject holding a fixed refusal string that is the same for every row.

Worth knowing. The surface is machine translation, so a quantity inside a problem can be corrupted even where the final answer survives, which is why the rewritten layer keeps only the rows whose worked solution still ends in the human answer key of the English problem it came from. Its English rows are the English source set itself and are deduplicated away in the rewritten layer.

sources/ape210k

Chinese elementary school math word problems collected from an online education service, each with the equation that solves it and the value that equation evaluates to. From MU-NLPC/Calc-ape210k at revision 5142d8cea9154be7f1825c3956b176bea8270d68, files data/train-00000-of-00001-b9f022a8492442e4.parquet, data/validation-00000-of-00001-b9c45633c2837e3b.parquet. 196862 rows here, of which 195266 also appear in pool.jsonl. Languages: Chinese, with a machine translation of each problem into English beside it. Provenance class collected, licence mit. Its own fields are id, question holding a machine translation of the problem into English, question_chinese holding the problem as it was collected, chain holding a calculator trace, result and result_float holding the answer, equation.

Worth knowing. The mit tag sits on this derivative rather than on the collected problems themselves, whose own terms the upstream release does not state. The rewritten layer takes the Chinese column, since the English one is machine translation of it and the Chinese is what people wrote, and the source's own test split is left out.

sources/cmath

Chinese elementary school math word problems taken from real workbooks and school examinations, annotated with the school grade they come from and the number of reasoning steps their solution takes. From weitianwen/cmath at revision 6a626b7266f7c84fd2d2421ad695ffb34b8f9d69, files cmath_dev.jsonl, cmath_test.jsonl. 1698 rows here, of which 1510 also appear in pool.jsonl. Languages: Chinese. Provenance class collected, licence cc-by-4.0. Its own fields are grade, question, golden holding the answer, reasoning_step, num_digits.

Worth knowing. It was published to measure models rather than to train them and it ships both of its files as evaluation splits, so hold it out if you want an untouched Chinese check of your own. Its answer is written as a plain number for all but a few dozen rows, whose fraction answers the rewritten layer leaves out.

Provenance and licences

Every problem in the pool was written by a person and every answer key descends from one, and the class on each row says how the text in front of you came to exist. human is a problem written by paid crowdworkers for the dataset it sits in, which is the English source set. collected is a problem that people wrote for real teaching and was gathered afterwards, which is both Chinese corpora, one gathered from an online education service and one from workbooks and school examinations. model-generated is the nine non-English surfaces of the translated set, where a language model rendered a human problem and a human solution into another language: the problem and the number are human work, the sentences you read are not. No row in the pool was produced from a rule or a template. There is no human-written or human-translated multilingual set of grade-school problems in public data, so a pool that reaches these languages is machine-translated on that side or it does not exist.

The pool as a whole is offered under cc-by-4.0, which is the most restrictive term its sources compose to. The sources themselves are mit for the English source set and for the large Chinese corpus, apache-2.0 for the translated set and cc-by-4.0 for the small Chinese corpus. None of them is non-commercial and none of them is undeclared. Each rewritten row carries its own in the licence field and each directory under sources/ is one source, so a subset under a single licence can be selected. Attribution goes to the authors of each source: the English problems to OpenAI, the translations to the MathOctopus project, the large Chinese corpus to the Ape210K authors and the derivative that carries it, and the small Chinese corpus to the CMATH authors under its attribution licence. A licence tag covers the packaging of a dataset rather than the copyright in the teaching material some of these problems were collected from.

Filtering

Rows whose problem duplicated or overlapped a problem in a held-out evaluation set were removed before publication, from both layers alike: an exact-match check (0 rows), then a word 8-gram overlap check on languages that write spaces and a character n-gram check of the equivalent width on Chinese, Japanese and Thai (585 rows), then a check on the English original a row came from, which removes a problem in every language at once when its English side is caught (4912 rows). That evaluation set is not distributed here. The overlap checks are blunt and cost honest rows, most of all in the languages that write more space-separated tokens per problem than English does. Nothing else was filtered: no grade, no length, no difficulty and no language was selected for or against.