Improving Multilingual Math Reasoning for African Languages

Akintunde Oladipo; David Ifeoluwa Adelani; Esther Adenuga; Jimmy Lin; Kelechi Ogueji; Odunayo Ogundepo

REVIEW 4 major objections 7 minor 27 references

Improving Multilingual Math Reasoning for African Languages

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read For mathematical reasoning in African languages, translating a diverse English instruction dataset outperforms directly generating synthetic native-language data at the same budget, and the two together perform best.

desk verdict Useful datasets and ablations, but the headline 'translated data wins' is likely inflated by GSM8K contamination shared with the evaluation benchmark. read the letter →

arxiv 2505.19848 v1 pith:TQ5JAMIW submitted 2025-05-26 cs.CL

Odunayo Ogundepo , Akintunde Oladipo , Kelechi Ogueji , Esther Adenuga , David Ifeoluwa Adelani , Jimmy Lin This is my paper · ORCID

classification cs.CL

keywords Africanlanguagesmathematicalreasoninglow-resourcesyntheticdatagenerationmachinetranslationinstructiontuningsupervisedfine-tuningLLM-as-judgeevaluation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks a practical question: when you extend a modern LLM to African languages, which data strategy actually teaches mathematical reasoning? Fine-tuning Llama 3.1 8B on machine-translated OpenMathInstruct reaches an average of 51.4 on AfriMGSM, a human-translated 16-language math test set, beating the same 30,000-sample budget of directly generated native-language synthetic data (39.4); training on both together does best overall (57.7, and 52.3 on African languages alone). The authors further find that source-dataset breadth decides whether translation pays off, that a single multilingual model beats per-language experts, and that retaining prompt tokens in the loss signal helps rather than hurts. A reader should care because the winning recipes are cheap and concrete: one 8B model, modest data, and no frontier-scale compute.

What carries the argument

The argument is carried by a controlled experimental setup rather than a single mathematical object. Three data pipelines are placed on equal footing: the persona-based synthetic pipeline that builds AfriPersona-Instruct from text-to-persona and persona-to-persona generation seeded by Wikipedia and WURA articles; GPT-4o translation of two English math datasets, BigMath and OpenMathInstruct V2, into nine target languages; and an LLM-as-judge evaluation in which GPT-4o, an automatic judge, decides whether a generated response matches the golden answer, replacing exact-match scoring that the authors find unreliable in multilingual settings. The load-bearing comparisons hold the model (Llama 3.1 8B instruct or base), the generating model (GPT-4o), and the training recipe (10,000–30,000 samples, two epochs, batch size 128, learning rate $5\times10^{-5}$) fixed, so observed differences are attributable to data type, training stage, or configuration. The mechanism identified is source-data diversity: the breadth of OpenMathInstruct is what lets translation outperform direct generation, while the narrow BigMath translation fails.

What would settle it

Have fluent human speakers of the target languages score a few hundred model responses from the translated-data and synthetic-data models and compare their verdicts with the GPT-4o judge's verdicts; if agreement is low in any language, or if extracting the final numeric answer exactly reverses the translated-versus-synthetic ordering on the same 30,000-sample budget, then the paper's central claim does not survive.

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Extended reading notes

Core claim

On the paper's own terms, the core discovery is that the type and diversity of training data, not its origin, governs how well an LLM learns multilingual math reasoning. With the base model, the translation model, the sample budget, and the training schedule all held fixed, a model fine-tuned on 30,000 machine-translated samples of OpenMathInstruct V2 reaches 51.4 average accuracy on AfriMGSM, while the same budget of AfriPersona-Instruct—problems generated directly in nine African languages through a persona-driven GPT-4o pipeline—reaches 39.4. Translated BigMath, a narrower, specialized source, drops to 11.2, indicating that source breadth is what makes translation pay off. Combining translated and synthetic data (60,000 samples) yields the best result, 57.7 overall and 52.3 on African languages, with the 8B model approaching or exceeding GPT-4 on Yorùbá, Igbo, and Swahili. The paper further reports that joint multilingual fine-tuning outperforms monolingual experts, that masking prompt tokens during supervised fine-tuning slightly hurts, and that continual pretraining on general African text does not transfer to math.

Load-bearing premise

Every accuracy number and ranking in the paper is produced by GPT-4o acting as an automatic judge, calibrated on only a couple of samples, with no human validation of judge accuracy across the nine languages and varied response styles; if that judge is biased or unreliable, the reported scores and the ranking of data strategies could change.

Editorial extensions

If this is right

Teams building math-capable models for African languages should lead with machine translation of a broad, diverse English instruction dataset; native-language synthetic data is a complement rather than a substitute, and the two together give the largest gains.
Source breadth is the deciding constraint: a translated dataset is only as useful as the diversity of the original, so narrow specialized collections may not justify the translation budget.
A single multilingual model fine-tuned on several African languages outperforms per-language experts and also generalizes to unseen African languages, making joint multilingual training the deployment strategy of choice.
The common practice of masking prompt tokens in the supervised fine-tuning loss should be reconsidered for low-resource multilingual settings, where computing loss over the full input gave higher math accuracy.
With only 30,000 translated samples, an open 8B model approaches or beats GPT-4 on several African languages, showing that frontier-level math reasoning in low-resource languages does not require frontier-scale resources.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the paper's own qualitative audit (Section 5.1) found frequent lexical and grammatical errors in AfriPersona-Instruct, and its limitations section concedes that the synthetic reasoning steps are not formally verified; if data quality is what drives the translated-data advantage, improving generation fidelity (human correction or grammar feedback) could close the gap more cheaply
Beyond the paper: because every comparative number flows through a GPT-4o judge calibrated on only a couple of samples, the ordering should be treated as provisional until human speakers confirm the judge's verdicts in each language; re-running the 30,000-sample comparison with exact-match extraction of final numeric answers is a cheap robustness check.
Beyond the paper: the recipe of translating a diverse instruction set and then adding native synthetic data likely transfers to other low-resource language groups and other reasoning domains, but the paper demonstrates it only for mathematics in nine African languages, so that extrapolation is a hypothesis.
Beyond the paper: the negative continual-pretraining result points to one concrete next experiment the authors hint at—pretraining on math-focused African-language text instead of general news and literary text—which would test whether domain alignment rather than language adaptation is what math reasoning needs.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Read the paper. The most useful things here are the two released artifacts — AfriPersonaHub and AfriPersona-Instruct — and a set of controlled ablations that a low-resource practitioner can actually use: prompt masking hurt, multilingual fine-tuning beat monolingual experts, 10k→30k scaling helped, and continual pretraining on Lugha-Llama actually made math worse. Those findings don't depend on the paper's most questionable comparison.

The headline result, that translated OpenMathInstruct beats persona-based synthetic data (51.4 vs 39.4 at 30k samples), is suspect for a concrete reason the paper doesn't address: OpenMathInstruct-1 was built by generating solutions for GSM8K problems, and V2 likely inherits that grade-school subset; AfriMGSM is a human translation of GSM8K. So the translated training data likely overlaps with the test set in the original English source. The LSH deduplication described in §4.2 only catches surface-level near-duplicates; it can't remove a GPT-4o translation of a GSM8K problem that a human translator rendered differently in Yoruba. A model trained on that data can memorize answers, and a perfect judge would still report inflated accuracy. This is more load-bearing than the unvalidated LLM judge, which the reader flagged. Judge bias would have to correlate with training-data type to flip the ranking; contamination is structurally built into the winning condition.

Other soft spots are real but smaller: no error bars and one run per condition; the continual pretraining comparison is confounded because Lugha-Llama differs from Llama Base in pretraining data and procedure; the manual audit in §5.1 found the synthetic data has quality problems, which the authors honestly acknowledge.

None of this kills the paper. The datasets are reusable, the ablations on masking and multilingual training are still informative, and the limitations section is honest. But the central claim needs another experiment — evaluate on a math benchmark not derived from GSM8K, or filter the training set for GSM8K-derived prompts and re-run the comparison. Without that, I'd be very cautious about citing the 51.4 vs 39.4 result as evidence that translated data is better.

I'd send it to review, but with a note that the contamination issue must be addressed in the revision.

Referee Report

4 major / 7 minor

Summary. The paper systematically compares strategies for adapting Llama 3.1 8B models to mathematical reasoning in nine African languages, focusing on: (i) translated versus directly generated synthetic training data, (ii) prompt-masking during SFT, (iii) scaling the amount of synthetic data, (iv) monolingual versus multilingual fine-tuning, and (v) continual pretraining. The main empirical claims are that translated OpenMathInstruct V2 data outperforms directly generated AfriPersona-Instruct at the same 30k-sample budget (51.4 vs 39.4 on AfriMGSM), that combining both data types gives the best results (57.7), that prompt masking hurts performance slightly, and that multilingual fine-tuning beats monolingual experts. The authors release AfriPersonaHub and AfriPersona-Instruct datasets. Evaluation uses GPT-4o as an LLM judge on AfriMGSM, a human-translated version of GSM8K.

Significance. If the findings are robust, the paper provides actionable guidance for building multilingual math reasoning models in low-resource African languages: translate diverse English instruction data rather than only generating synthetic data in the target language, and combine both sources for best results. The release of the persona hub and instruction dataset is a concrete contribution to the community. The comparative framing across data types, training stages, and model configurations is valuable and goes beyond typical single-pipeline studies. However, the central claims currently rest on an unvalidated LLM judge and on a training/test overlap risk that are both load-bearing; the paper needs additional validation and decontamination evidence before the conclusions can be accepted.

major comments (4)

[§4.2, Appendix A, Tables 2–3] The evaluation relies entirely on GPT-4o as an LLM judge, and Appendix A states only that the prompt was 'calibrated using a couple of samples from different languages.' No human-validated accuracy, agreement rate, or per-language reliability of the judge is reported. Since every accuracy in Tables 2 and 3 and all cross-condition comparisons depend on this judge, please provide a human-validated sample (e.g., 50–100 responses per language, or at least across the five trained languages) and report judge accuracy per language, or compare against exact-match extraction on a subset. Without this, the headline differences (e.g., 51.4 vs 39.4) could be artifacts of judge bias rather than genuine capability differences.
[§3.2 and §4.2, Table 2 rows 8 vs 11] The central comparison between translated OpenMathInstruct and AfriPersona-Instruct is at risk of training/test contamination. OpenMathInstruct V2 is generated by Mixtral from seed problems that, per the cited OpenMathInstruct-1 paper, include GSM8K; AfriMGSM is a human translation of GSM8K. The LSH de-duplication described in §4.2 operates on surface shingles and cannot detect cross-lingual or paraphrased duplicates. If the translated training data contains translated versions of GSM8K problems, the 51.4 vs 39.4 gap may reflect memorization rather than superior reasoning. Please quantify the overlap between translated training prompts and AfriMGSM (e.g., embedding-based retrieval), or retrain on a translated dataset that provably excludes GSM8K-derived items, and show that the ranking persists.
[§4.1, Table 2 rows 6–9] All experiments are reported from a single training run with no variance information. Some conclusions rest on small differences: prompt masking (rows 8 vs 9: 39.4 vs 38.7 overall; 31.8 vs 29.7 African-only) and scaling from 10k to 20k samples (rows 6 vs 7: 34.9 vs 34.7 overall). These gaps are within plausible seed-level noise. Report results over at least three seeds for the key comparisons (translated vs synthetic, masking, scaling) and provide confidence intervals or significance tests.
[§4.3.5, Table 2 rows 14–15] The continual pretraining ablation compares Llama 3.1 8B Base with Lugha-Llama 8B, a different model with its own pretraining corpus (WURA + OpenWebMath) and training procedure. This design does not isolate the effect of continual pretraining; any performance difference could stem from the data mix, training order, or other hyperparameters. The conclusion that continual pretraining 'may not directly benefit multilingual math reasoning' is therefore not supported. A controlled comparison would require continually pretraining Llama 3.1 Base on the same data, or re-framing the result as a property of the specific Lugha-Llama model rather than a general conclusion about continual pretraining.

minor comments (7)

[Abstract, §1] There are typos: 'todyas' should be 'today's' and 'Our experiments focuses' should be 'Our experiments focus.'
[§5.3] The row references in the text are off by one: 'Row 11' for translated BigMath should be Row 10, and 'Row 12' for translated OpenMathInstruct should be Row 11. Please correct these references.
[Table 2] Please specify the composition of Row 12 'All Data 60,000' — presumably 30k translated OpenMathInstruct plus 30k AfriPersona-Instruct, but the text should state this explicitly.
[Table 2, Row 5] The monolingual SFT row does not report the number of training samples per language. Please state the sample size and whether it matches the 30k multilingual budget in total or per language.
[§4.2] Please describe the LSH de-duplication details for the training/test split: what language(s) the shingles were computed on, the shingle size and similarity threshold, and whether it was applied cross-lingually or only within the same language.
[§5.1] The manual audit of AfriPersona-Instruct is qualitative. Please provide quantitative counts of the identified error types (unnatural phrasing, lexical inaccuracies, ambiguity) and the number of prompts affected.
[§3.2, References] The paper uses OpenMathInstruct V2 but cites the OpenMathInstruct-1 paper (Toshniwal et al., 2024). Please clarify the relationship between the two and provide a citation or description for V2, especially regarding whether GSM8K was used as a seed source.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the headline comparisons are empirical measurements on an external human-translated benchmark; self-citations supply data sources and baselines but are not load-bearing.

full rationale

The paper's central claims are empirical comparisons of training-data strategies, not derivations. AfriMGSM is described as an external human-translated version of GSM8K, so the evaluation benchmark is not defined in terms of the training data or the models' outputs. The headline numbers in Table 2 (AfriPersona-Instruct 30k = 39.4, Open Instruct Translated 30k = 51.4, All Data 60k = 57.7) are measurements; no parameter is fitted to these scores and then renamed as a prediction. The self-citations that appear (AfriMGSM/Adelani et al. 2025, WURA/Oladipo et al. 2023a, Lugha-Llama/Buzaaba et al. 2025) supply the benchmark, a persona source, and a comparison model, but the conclusions do not reduce to those citations. The most serious concerns are external-validity threats rather than circularity: GPT-4o both generates/translates the training data and serves as the evaluation judge, and Appendix A admits the judge was only calibrated on 'a couple of samples'; Section 4.2's LSH de-duplication is token-level and may miss semantic overlap between OpenMathInstruct's grade-school subset and AfriMGSM's human-translated GSM8K. These issues could bias or invalidate the comparison, but they do not make any reported result true by construction.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper's empirical comparisons rely on benchmark validity, judge reliability, translation fidelity, and the representativeness of the base model. No free parameters are fitted in the sense of numerical curve fitting; hyperparameters are fixed across conditions. No new theoretical entities are introduced.

assumptions (5)

domain assumption AfriMGSM is a valid human-translated measure of mathematical reasoning in African languages.
Used as the sole evaluation benchmark; if translations are noisy or the benchmark has artifacts, all numbers shift. Section 4.2.
domain assumption GPT-4o judge reliably determines answer correctness across languages.
No human validation beyond a few calibration samples; the judge may be biased by style or language. Section 4.2, Appendix B.6.
domain assumption Machine translation preserves problem difficulty and answer semantics.
They translate BigMath and OpenMathInstruct and assume equivalence; no post-hoc verification of translations is reported. Section 3.2.
ad hoc to paper Lugha-Llama continual pretraining is a controlled comparison for base Llama 3.1.
The paper compares Llama Base with Lugha-Llama, which differs in pretraining data distribution and procedure; any performance difference may not be attributable to continual pretraining alone. Section 4.3.5 and Section 5.5.
domain assumption The LLM used for synthetic generation produces linguistically acceptable native-language data.
The manual audit in Section 5.1 found grammatical and lexical errors, so this assumption is only partially met.

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Cite this review

Pith. "Pith review of Improving Multilingual Math Reasoning for African Languages." pith.science (2026). https://pith.science/paper/TQ5JAMIW

@misc{pith2026250519848,
  author       = {Pith},
  title        = {Pith review of: Improving Multilingual Math Reasoning for African Languages},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TQ5JAMIW}},
  note         = {Machine review of arXiv:2505.19848}
}

read the original abstract

Researchers working on low-resource languages face persistent challenges due to limited data availability and restricted access to computational resources. Although most large language models (LLMs) are predominantly trained in high-resource languages, adapting them to low-resource contexts, particularly African languages, requires specialized techniques. Several strategies have emerged for adapting models to low-resource languages in todays LLM landscape, defined by multi-stage pre-training and post-training paradigms. However, the most effective approaches remain uncertain. This work systematically investigates which adaptation strategies yield the best performance when extending existing LLMs to African languages. We conduct extensive experiments and ablation studies to evaluate different combinations of data types (translated versus synthetically generated), training stages (pre-training versus post-training), and other model adaptation configurations. Our experiments focuses on mathematical reasoning tasks, using the Llama 3.1 model family as our base model.

Figures

Figures reproduced from arXiv: 2505.19848 by the authors.

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Reference graph

Works this paper leans on

27 extracted references · 17 canonical work pages

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Preprint, arXiv:2502.17387

Big-math: A large-scale, high-quality math dataset for reinforcement learning in language models. Preprint, arXiv:2502.17387. Viraat Aryabumi, John Dang, Dwarak Talupuru, Saurabh Dash, David Cairuz, Hangyu Lin, Bharat Venkitesh, Madeline Smith, Kelly Marchisio, Sebas- tian Ruder, Acyr Locatelli, Julia Kreutzer, Nick Frosst, Phil Blunsom, Marzieh Fadaee, A...

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countries

**Diversity of Contexts**: - Ensure a variety of regions, languages, and cultural perspectives are represented to reflect diverse African contexts. # Output Format - Provide a list of 3 personas in JSON format, each with fields: "countries", "languages", and "persona". - Ensure that each persona includes a narrative description in the "persona" field that...

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Provide the prompt JSON format, each with fields: "prompt", "language" B.4 Math Problem Generation Create a math problem that a given user persona, who is a native speaker of a given language, might ask you to solve. Ensure the problem requires between 2 and 8 steps to solve, and the solution involves performing a sequence of elementary calculations using...

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1/2" versus

Llama 2: Open foundation and fine-tuned chat models.arXiv preprint arXiv:2307.09288. Kosei Uemura, Mahe Chen, Alex Pejovic, Chika Madu- abuchi, Yifei Sun, and En-Shiun Annie Lee. 2024. Afri- Instruct: Instruction tuning of African languages for diverse tasks. InFindings of the Association for Compu- tational Linguistics: EMNLP 2024, pages 13571–13585, Mia...

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countries

**Persona Detailing**: Write a brief description for each persona, including how they would engage with the content and their potential impact or interaction within the African context. # Output Format Express each user persona in a structured JSON format with the following attributes: ```json { "countries": ["Kenya"], "languages": ["Swahili"], "persona":...

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- Understand potential interpersonal relationships based on shared activities or values

**Analyze the Given Persona**: - Identify key characteristics such as country, language, role, and interests. - Understand potential interpersonal relationships based on shared activities or values
[14]

Consider roles that would naturally support or collaborate with their interests or goals

**Generate Interpersonal Personas**: - Create personas that could interact or share goals with the given persona. Consider roles that would naturally support or collaborate with their interests or goals
[15]

**Create Similar Personas from Different African Communities**: - Maintain the essence of the original persona but adapt cultural, geographic, or linguistic attributes to fit another African context
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The above example is not tied to any particular persona, but you should create one that is unique and specific to the given persona
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The instruction should contain all the verifiable contraint(s)
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User instruction:

Your output should start with "User instruction:"
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Your output should not include the answer to the instruction
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Your output should be in the provided language
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You should make full use of the persona description to create the math problem to ensure that the math problem is unique and specific to the persona
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Each math problem created should require between 2 and 8 steps to solve, involving elementary calculations using only basic arithmetic operations
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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

**Content Analysis**: Break down the text to identify primary topics, themes, and connections to African contexts

work page

[2] [2]

**Persona Generation**: For each theme, create diverse personas by: - Specifying a broad range of demographic characteristics, avoiding repetitive structures - Identifying relevant professions or industries prevalent in Africa - Outlining specific interests or hobbies related to the text and befitting diverse African cultures - Highlighting potential chal...

work page

[3] [3]

Preprint, arXiv:2502.17387

Big-math: A large-scale, high-quality math dataset for reinforcement learning in language models. Preprint, arXiv:2502.17387. Viraat Aryabumi, John Dang, Dwarak Talupuru, Saurabh Dash, David Cairuz, Hangyu Lin, Bharat Venkitesh, Madeline Smith, Kelly Marchisio, Sebas- tian Ruder, Acyr Locatelli, Julia Kreutzer, Nick Frosst, Phil Blunsom, Marzieh Fadaee, A...

arXiv 2024

[4] [4]

countries

**Diversity of Contexts**: - Ensure a variety of regions, languages, and cultural perspectives are represented to reflect diverse African contexts. # Output Format - Provide a list of 3 personas in JSON format, each with fields: "countries", "languages", and "persona". - Ensure that each persona includes a narrative description in the "persona" field that...

work page

[5] [5]

InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 5843– 5862, Miami, Florida, USA

Pretraining language models using translationese. InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 5843– 5862, Miami, Florida, USA. Association for Computa- tional Linguistics. Bonaventure FP Dossou, Atnafu Lambebo Tonja, Oreen Yousuf, Salomey Osei, Abigail Oppong, Iyan- uoluwa Shode, Oluwabusayo Olufunke Awo...

arXiv 2024

[6] [6]

prompt",

Provide the prompt JSON format, each with fields: "prompt", "language" B.4 Math Problem Generation Create a math problem that a given user persona, who is a native speaker of a given language, might ask you to solve. Ensure the problem requires between 2 and 8 steps to solve, and the solution involves performing a sequence of elementary calculations using...

work page

[7] [9]

1/2" versus

Llama 2: Open foundation and fine-tuned chat models.arXiv preprint arXiv:2307.09288. Kosei Uemura, Mahe Chen, Alex Pejovic, Chika Madu- abuchi, Yifei Sun, and En-Shiun Annie Lee. 2024. Afri- Instruct: Instruction tuning of African languages for diverse tasks. InFindings of the Association for Compu- tational Linguistics: EMNLP 2024, pages 13571–13585, Mia...

arXiv 2024

[8] [12]

countries

**Persona Detailing**: Write a brief description for each persona, including how they would engage with the content and their potential impact or interaction within the African context. # Output Format Express each user persona in a structured JSON format with the following attributes: ```json { "countries": ["Kenya"], "languages": ["Swahili"], "persona":...

work page