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Which Language Should a Skeleton Speak? Language Choices in Multilingual Reasoning

HyeonSeok Lim, SeungWoo Song, Inho Won, Hoyun Song, Jihyo Kim, KyungTae Lim

arXiv:2610.09607v1cs.CLcs.AI

TL;DR

Prior work largely assumes English skeletons, leaving the choice of skeleton language and its interaction with query and answer languages insufficiently explored. LASEF empirically examines those configurations in multilingual mathematical reasoning. The findings indicate context-dependent effects rather than a universally optimal skeleton language.

  • Problem

    Prior work largely fixes skeleton language to English and has not systematically examined how query, skeleton, and reasoning languages combine in multilingual mathematical reasoning.

    Source: §1 · pp. 1–2, §2 · p. 2

  • Method

    LASEF empirically varies language configurations while holding skeleton structure and format fixed, combining greedy decoding, multi-rollout evaluation, translation ablation, and cross-benchmark validation.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    Skeleton-language effects are context-dependent and follow directionally consistent, evaluation- and benchmark-dependent, or asymmetric-negative patterns rather than a universal optimum.

    Source: §1 · p. 2, §6 · p. 9

  • Takeaways & Limitations

    Skeleton language is a design variable that requires multi-level exploration rather than a single universally optimal choice.

    Source: §1 · p. 2, §6 · p. 9

    The study focuses on mathematical reasoning, and its full configuration search is computationally expensive and intended as an offline diagnostic requiring revalidation when benchmark, model, or task changes.

    Source: Limitations · p. 9

Abstract

from arXiv · show

Skeleton-based reasoning prompting is a promising training-free approach for structuring LLM reasoning, but prior work largely assumes an English-centric setting. We propose the Language-Aware Skeleton Exploration Framework (LASEF) to study skeleton-language choice in multilingual mathematical reasoning. Across math benchmarks, model scales, and languages, we show that English skeletons yield a small positive tendency on average, most visible for smaller models and low-resource languages. However, few language-level gains remain significant after correction, and English is not universally optimal. Combining greedy decoding, multi-rollout evaluation, translation ablation, and cross-benchmark validation, we further find three patterns of skeleton-language effects: directionally consistent, evaluation- and benchmark-dependent, and asymmetric negative. These effects cannot be fully explained by generation quality alone. Overall, skeleton language is a context-dependent design variable that requires multi-level exploration. All resources are released at https://github.com/lhsstn/LASEF.

1 Introduction

The introduction frames skeleton language as an underexplored choice in multilingual reasoning and proposes a training-free framework to examine it. Its findings argue for conditional, rather than universal, guidance on which language to use.

1 Introduction

  • A skeleton is a concise, high-level representation of a problem-solving flow that guides later reasoning and answer generation, without requiring training.The paper uses the term for explicit representations of reasoning flow; this training-free property supports use in low-resource language scenarios.Source: §1 · p. 1
  • Prior work largely fixed skeleton language to English, leaving combinations of query, skeleton, and answer languages insufficiently explored for multilingual deployment.These combinations may engage different linguistic priors and reasoning trajectories, and the paper highlights low-resource languages as a particular question.Source: §1 · pp. 1–2
  • LASEF formalizes input, skeleton, and reasoning languages as design variables and empirically compares configurations while holding skeleton structure and format fixed.The framework characterizes when language choices help or hurt rather than prescribing one universally optimal skeleton language.Source: §1 · p. 2
  • Skeleton-language effects fall into directionally consistent, evaluation- and benchmark-dependent, and asymmetric-negative patterns, with consistency assessed across decoding protocols and benchmarks.The study combines greedy decoding and multi-rollout evaluation and uses translation ablation to distinguish skeleton generation quality from cross-lingual alignment.Source: §1 · p. 2

2 Related Work

Related work spans structured reasoning prompts and multilingual or English-pivot approaches. The paper positions its study as an examination of language combinations while holding the skeleton structure fixed.

2 Related Work

  • English-pivot strategies use English priors to address non-English reasoning gaps, but may reduce interpretability and practical utility for native-language users.Prior work reports persistent performance gaps in non-English contexts, particularly in mathematical tasks.Source: §2 · p. 2
  • Structured reasoning methods range from Zero-shot CoT to Skeleton-of-Thought, Plan-and-Solve, and Program-of-Thought, with prior studies reporting improved logical consistency.Multilingual extensions exist, but prior work has predominantly fixed skeleton language to English or overlooked language combinations between the guide and final response.Source: §2 · p. 2
  • The study adopts Qi et al. (2025c)’s inference structure as a baseline and varies skeleton language to analyze its relation to multilingual reasoning performance.This design keeps the structure fixed to provide experimental control.Source: §2 · pp. 2–3

3 Language-Aware Skeleton Exploration Framework

LASEF empirically compares language configurations while keeping skeleton structure and format fixed. It defines the query, skeleton, and answer-language dimensions and describes skeletons as short structural guides rather than solution steps.

3 Language-Aware Skeleton Exploration Framework

  • LASEF is an empirical framework for analyzing skeleton-language configurations within an evaluation environment, not a training or algorithmic-search method.It varies language configurations while holding skeleton structure and format fixed to identify effective configurations in that environment.Source: §3 · p. 3

3.1 Problem Setup and Language Dimensions

  • A skeleton-based process is characterized by query language, skeleton language, and detailed-reasoning and answer language, which may be identical or distinct.LASEF isolates the effects of these configurations while keeping the skeleton generation method and structure fixed; the effective combination may vary by benchmark or domain.Source: §3.1 · p. 3
  • For a given benchmark, LASEF compares language configurations to identify relatively effective skeleton-language choices in that evaluation environment.The setup assumes inference without additional training or parameter updates.Source: §3.1 · p. 3

3.2 Skeleton Construction and Usage

  • The study’s skeletons are concise intermediate structural guides that avoid giving core answers, calculation procedures, or specific solution steps.Their generation principle is to describe what the problem structure is, not how to solve it.Source: §3.2 · p. 3
  • The representative English skeleton for a Swahili query averages approximately 120 tokens and omits direct answers and core solution steps.The paper reports skeleton length as approximately 120 tokens on average regardless of language.Source: §3.2 · p. 3

4 Experiments

The experiments vary skeleton-language configurations across models, benchmarks, and target languages. English skeletons tend to help more for smaller models, easier tasks, and low-resource languages, but their effects are not uniform.

4.1 Experimental Setup

  • LASEF varies model scale, problem difficulty, and language resource levels while keeping skeleton structure and generation fixed; evaluation uses exact match and greedy or multi-rollout decoding.The study includes QWEN2.5 models at 7B, 14B, and 72B; MGSM, MATH-500, and PolyMath; and high- and low-resource languages.Source: §4 · pp. 3–4, §4.1 · p. 4

4.2 Baseline Configurations

  • The baselines compare target-language CoT with English-pivot CoT, which translates the query into English before target-language reasoning and answering.English skeletons are the default skeleton configuration in the baseline comparisons.Source: §4.2 · pp. 4–5

4.3 Performance across Diverse Dimensions

  • With QWEN2.5-7B on MGSM, Swahili rises from 63.1 to 71.7 (+8.6), while Chinese gains +0.0 and Spanish +1.6; larger models benefit less consistently.QWEN2.5-7B and 14B improve across benchmarks (+0.9 to 2.5), whereas QWEN2.5-72B averages a 0.2 drop in the specified settings.Source: §4.3 · p. 5, Table 1 · p. 5

Does Benchmark Difficulty Limit the Gains?

4.4 Effect of English Skeletons in Low-Resource Languages

  • On low-resource MGSM, English skeletons improve 13 of 19 languages, but only Kazakh and Uyghur show significant language-level gains after FDR correction.In the target-language input setting, effects vary substantially by language, including gains for Kazakh and Uyghur and degradation for Maltese.Source: Table 2 · p. 6, §4.4 · p. 6

Does Benchmark Difficulty Limit the Gains?

  • In low-resource settings, translation contributes more than skeletons (+24.07 vs. +2.02 pp), while English-skeleton gains are most pronounced for smaller models and easier tasks.Across the reported conditions, English skeletons’ benefits also depend on model scale, task difficulty, and language resources.Source: Does Benchmark Difficulty Limit the… · p. 6

4.5 Is English the Only Solution for Low-Resource Languages?

  • For QWEN2.5-7B, non-English skeletons reduce average performance by 0.63 to 2.60 points, though some language pairs improve under greedy and multi-rollout evaluation.Lao–Thai, Basque–Korean, and Armenian–Korean retain positive direction across the two evaluation protocols; Maltese gains are evaluation-sensitive.Source: Figure 2 · p. 7, §4.5 · pp. 7–8
  • Shared surface affinity does not guarantee positive transfer: Russian skeletons hurt Mongolian and Chinese skeletons hurt Uyghur, with negative effects persisting across decoding protocols.The authors group observed effects as directionally consistent, evaluation- and benchmark-dependent, or asymmetric negative, and argue one protocol is insufficient to characterize them.Source: §4.5 · p. 8

5 Analysis

The translation ablation holds skeleton content fixed to examine surface-language effects. Some language-pair effects retain their direction, while others remain sensitive to evaluation or benchmark.

Directionally Consistent Pairs Persist

  • Basque–Korean (+6.32 → +4.42), Armenian–Korean (+5.17 → +1.61), and Lao–Thai (+2.81 → +0.40) stay positive with translated skeletons.Their reduced magnitudes suggest the effects are not solely attributable to skeleton generation quality.Source: §5 · p. 8

Maltese: A Fragile Surface Effect

  • With content fixed, Maltese–Russian and Maltese–Korean gains remain positive (+5.15 and +5.06), yet Maltese–Russian reverses on MSVAMP.The passage describes this surface-form effect as sensitive to decoding protocol and benchmark, rather than a generation-quality artifact.Source: §5 · pp. 8–9

Asymmetric Negatives Persist

  • Mongolian–Russian (−3.43) and Uyghur–Chinese (−6.94) remain negative with translated skeletons, indicating these negative effects are not quality artifacts.The pairs share surface affinity but lack structural alignment.Source: §5 · p. 9

Analysis

  • Across the tested pairs, skeleton-language effects reflect skeleton–target interactions that cannot be reduced to generation quality and must be identified empirically.The translation ablation compares LLM-generated skeletons with translations of English skeletons, holding semantic content fixed.Source: §5 · pp. 8–9

6 Conclusion

The paper studies skeleton-language selection in multilingual mathematical reasoning through LASEF, an empirical analysis framework rather than an automatic selector. Its results show that skeleton language is context-dependent and requires multi-level exploration.

6 Conclusion

  • English skeletons are a reasonable default, but their average gains are small and they are not a one-size-fits-all solution.The conclusion frames the answer to which skeleton language to use as conditional rather than universal.Source: §6 · p. 9
  • The study identifies directionally consistent, evaluation- and benchmark-dependent, and asymmetric negative skeleton-language effects.These patterns are examined using greedy decoding, multi-rollout evaluation, translation ablation, and cross-benchmark validation.Source: §6 · p. 9

Limitations

This section outlines the study’s scope and methodological constraints, including its focus on mathematical reasoning, a fixed skeleton, and offline configuration search. It also describes the translation-selection and round-trip validation procedures, without providing the table’s accuracy values.

Limitations

  • The study’s findings are limited to mathematical reasoning, a fixed skeleton structure, and an expensive configuration search intended for offline diagnosis rather than deployment.The training-free design precludes potential gains from fine-tuning, and the interaction between skeleton design and language choice remains unexplored. Existing benchmark results can flag risky candidates, but they should be revalidated when the benchmark, model, or task changes; efficient search prediction remains future work.Source: Limitations · p. 9

C.2.2 Stage 2: Back-Translation Quality Selection (BTQS)

  • BTQS selects the numerically checked candidate whose English back-translation has higher cosine similarity to the source, measured with the BAAI/bge-m3 encoder.Each candidate is back-translated using the model that generated it.Source: §C.2.2 · p. 17
  • The round-trip check evaluates Qwen2.5-7B on MGSM after translating English through target-language pivots and back to English.The caption says the setup validates translated-dataset semantic consistency; its table values are not supplied.Source: Table 5 · p. 17

C.3 Quality Control and Verification Results

The verification pipeline checks translated data through quality filtering and round-trip reasoning, while the typology section defines surface affinity and structural alignment as descriptive categories for comparing language pairs.

C.3 Quality Control and Verification Results

  • Samples below the 0.8 BTQS similarity threshold were regenerated, and selected samples were checked for logical consistency using QWEN2.5-7B.The check reused back-translated English text rather than requiring another translation.Source: §C.3 · p. 17
  • Tamil-pivot round-trip reasoning accuracy was 93.6% versus the 90.0% baseline, while Kazakh reached 89.2%.The authors interpret the results as evidence that problem-solving information and logical structure were preserved through round-trip conversion.Source: §C.3 · pp. 17–18
  • Round-trip reasoning accuracy does not establish grammatical completeness, and the method may benefit from a model correcting noise in back-translated text.The authors present it as a scalable proxy for logical information loss where native evaluators are difficult to obtain.Source: §C.3 · p. 18
  • The final dataset contains 8,500 samples, with 62.1% from Gemini and 37.9% from GPT.Table 6 presents the final dataset statistics.Source: §C.3 · p. 18, Table 6 · p. 18

D Linguistic Typology and Affinity/Alignment Classification

  • Surface affinity means sharing a language family, script, or macroregion; structural alignment requires sharing both morphological type and basic constituent order.The typological features are listed for target and skeleton languages in Table 7.Source: D Linguistic Typology and… · p. 18, Table 7 · p. 18
  • These typology labels are descriptive, not causal rules: affinity does not prevent negative transfer, and alignment does not guarantee positive transfer.The reported examples include negative transfer for affine but misaligned pairs and evaluation-sensitive results for Maltese.Source: D Linguistic Typology and… · p. 18

E Computational Cost Analysis

Skeletons add a modest token overhead, while skeleton quality varies with model scale and language. Cross-lingual results show that intrinsic generation quality alone does not explain skeleton-language effects.

E Computational Cost Analysis

F.1 Quality Assessment of English Skeletons

  • Skeleton quality rises with model scale, reaching an average score of 6.7 for models of 70B or larger.Figure 6 also reports positive correlations between final performance and coherence (r = 0.82) and completeness (r = 0.74), versus specificity (r = 0.40).Source: §F.1 · p. 19, Figure 6 · p. 19

F.2 Cross-Lingual Skeleton Quality and the Quality–Performance Gap

  • English skeletons have the highest average quality score (7.57), ahead of Spanish (7.35), Chinese (7.24), Russian (7.13), Korean (6.69), and Thai (5.65).Figure 7 presents the quality comparison across language pairs.Source: Figure 7 · p. 19, §F.2 · p. 19
  • Lao’s Thai skeleton scored 6.48 versus English’s 7.77 yet improved accuracy by +2.81; Basque’s Korean skeleton scored 6.18 versus 7.37 yet improved accuracy by +6.32.These structurally aligned pairs show higher performance despite lower intrinsic skeleton quality.Source: §F.2 · pp. 19–20
  • Uyghur’s Chinese skeleton had comparable quality (7.40 vs. 7.54) but performance fell by −6.45; Mongolian’s Russian skeleton scored 7.22 vs. 7.19 yet fell by −5.00.Both pairs share surface affinity without structural alignment.Source: §F.2 · p. 20
  • Together with the translation ablation, the findings support treating skeleton language as an exploratory design variable, not a causal rule.The authors conclude that structural alignment can offset lower intrinsic quality, whereas its absence is not offset by high quality.Source: §F.2 · p. 20

F.3 Error Analysis: Impact of Skeleton

The error analysis compares error frequencies before and after skeleton use. It reports fewer reasoning and calculation errors for some languages, while comprehension errors rise for others.

F.3 Error Analysis: Impact of Skeleton

  • Table 8 compares error frequencies across reasoning stages; for Kazakh, reasoning errors fell from 129 to 105 (−18.6%) and calculation errors from 33 to 18 (−45.5%).The authors interpret these reductions as consistent with skeletons acting as cognitive scaffolding.Source: Table 8 · p. 20, §F.3 · p. 20
  • An automated GPT-5-mini classifier assigned incorrect samples to five error types and returned presence labels and descriptions for quantitative comparison.The categories were problem comprehension, conceptual, reasoning, calculation, and output generation errors.Source: §F.3 · p. 20
  • For languages with marginal or declining performance, increased problem-comprehension errors were a main failure factor; Lao’s count tended to rise from 115 to 133 (+15.7%).The authors interpret this as possible semantic interference from English skeleton instructions, rather than a change in reasoning errors.Source: §F.3 · pp. 20–21

G Llama 3.1 Experimental Results

Across Llama 3.1 and Ministral, English-skeleton effects are small and vary by model scale, benchmark, and language. On harder PolyMath problems, gains generally shrink, with QWEN2.5-14B an exception.

G Llama 3.1 Experimental Results

  • In Llama 3.1, Swahili on MATH-500 improves from 32.5 to 38.8 (+6.3) with an English skeleton, while 70B effects are minimal or sometimes negative, including Spanish’s 88.0 →81.5.MATH-500 shows the most consistent improvements; MGSM and PolyMath vary substantially by language.Source: G Llama 3.1 Experimental Results · p. 21
  • Llama-3.1-8B averages +0.81 pp on target-language queries and +0.75 pp on English-translated queries, versus −0.43 and −0.81 pp for 70B.The effect varies by model and evaluation condition; its qualitative tendency to shrink with model size and baseline performance also appears in Qwen2.5.Source: G Llama 3.1 Experimental Results · p. 21

H Additional Model Family: Ministral

  • Across Ministral’s 30 cells, baseline accuracy correlates negatively with skeleton effect (Spearman ρ = −0.568, nominal p = 0.0011); effects are not consistently positive across model variants and benchmarks.Average effects are +1.29 pp for Ministral-3B and +0.11 pp for Ministral-14B; excluding Swahili, they are +0.38 and −0.12 pp.Source: Table 10 · p. 21, H Additional Model Family: Ministral · p. 22

I PolyMath Difficulty-Level Analysis

J Statistical Significance Analysis

English skeletons outperform the no-skeleton baseline significantly in the pooled low-resource MGSM results, but few language-level gains survive correction. Comparisons between English and non-English skeletons include both positive and negative cases, with some effects sensitive to evaluation protocol.

J Statistical Significance Analysis

  • Six of 95 English-versus-non-English skeleton pairs reach nominal significance before correction, including both positive and negative effects.All three positive cases are for Maltese; negative cases include Uyghur–Thai, Mongolian–Thai, and Kazakh–Korean.Source: Table 12 · p. 22, J Statistical Significance Analysis · pp. 22–23
  • Directionally consistent pairs eu–ko, hy–ko, and lo–th do not reach nominal significance in McNemar’s test, which tests item-level transitions in a single decoding setting.Their direction remains stable across greedy and multi-rollout evaluation, a distinct robustness criterion.Source: J Statistical Significance Analysis · p. 23
  • Maltese gains that are nominally significant under greedy decoding attenuate or reverse under multi-rollout evaluation and are benchmark-dependent.The authors therefore treat Maltese as evaluation-sensitive rather than directionally consistent.Source: J Statistical Significance Analysis · p. 23
  • After FDR correction, English skeletons significantly improve only Kazakh and Uyghur among 19 low-resource MGSM languages; pooled across 4,628 items, the effect is +2.27 pp (p = 0.0014).The mean language-level change is +2.38 pp, but only two languages retain corrected significance.Source: J Statistical Significance Analysis · p. 23

K Cross-Benchmark Generalization on MSVAMP

Across 35 target–skeleton pairs, MGSM and MSVAMP effects show moderate rank correlation, but transfer is uneven: negative patterns transfer better than positive ones. The authors treat existing-benchmark results as useful for prioritizing evaluation, not for specifying an optimal skeleton language in advance.

K Cross-Benchmark Generalization on MSVAMP

  • Across 35 cells, effect sizes on MGSM and MSVAMP have Spearman ρ = 0.383 (nominal p = 0.023), and signs agree in 23/35 (66%; binomial p = 0.090).Pairs were selected using MGSM results before MSVAMP evaluation.Source: Table 13 · p. 23, K Cross-Benchmark Generalization on… · p. 23
  • Among 15 cells for Mongolian, Uyghur, and Kazakh, 14 remain negative on MSVAMP; positive Maltese effects are mixed, with one reversing and another largely diminishing.Hy–ko, lo–zh, and lo–th retain positive direction, while eu–ko becomes 0.00.Source: K Cross-Benchmark Generalization on… · p. 24
  • Prior-benchmark results can help identify risky candidates and prioritize evaluation, but do not specify an optimal skeleton language for a new benchmark, model, or task.Both evaluated benchmarks focus on elementary arithmetic; transfer to harder benchmarks remains future work.Source: K Cross-Benchmark Generalization on… · p. 24

L.2 Results on All Low-Resource Languages

  • Although the experiments cover 34 languages, the main analysis focuses on 19 where target-language CoT is stable; Figure 8 reports results for all 34.Several target languages show gains with specific non-English skeletons, indicating language-dependent effectiveness.Source: §L.2 · p. 24, Figure 8 · p. 25

L.1 Results on Telugu

  • Table 14 reports Telugu accuracy changes from applying a skeleton on MATH-500, PolyMath, and MGSM.The supplied passage identifies the table’s scope but does not state its result values.Source: Table 14 · p. 24, §L.1 · p. 24
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