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Hidden Language Consistency Phenomena in Reasoning LLMs
Muhammad Ali Shafique, Kelly Marchisio
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
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Summary
This paper investigates multilingual reasoning in Large Language Models (LLMs) by evaluating task accuracy, thinking-language consistency (TC), and answer-language consistency (AC) across the PolyMath benchmark. The authors identify a 'language consistency breakdown effect' where increasing task difficulty causes sudden drops in language consistency, particularly for non-Latin and lower-resource languages. This breakdown can paradoxically improve accuracy as models shift to their dominant internal language. Additionally, the study finds that quantization methods (GPTQ, AWQ, AutoRound) affect language consistency independently of accuracy.
Entities (10)
Relation Signals (7)
Thinking-Language Consistency â measuredon â PolyMath
confidence 95% · We measure final-answer accuracy, thinking-language consistency (TC)... using PolyMath benchmark
PolyMath â usedby â DeepSeek-R1-Distill-Qwen-7B
confidence 95% · We evaluate the models on PolyMath... DeepSeek-R1-Distill-Qwen-7B
PolyMath â usedby â Olmo-3-7B-Think
confidence 95% · We evaluate the models on PolyMath... OLMo-3-7B-Think
DeepSeek-R1-Distill-Qwen-7B â exhibits â Language Consistency Breakdown Effect
confidence 92% · For DeepSeek-R1-Distill-Qwen-7B, Bengali TC drops... Similar breakdowns occur for Arabic, French, Swahili, and Telugu
Language Consistency Breakdown Effect â causes â Accuracy Improvement
confidence 90% · Due to this breakdown effect, accuracy can be preserved or even improved at a harder difficulty level as the model shifts to its internal dominant language.
GPTQ â outperforms â AutoRound
confidence 85% · GPTQ and AWQ often outperform AutoRound under tolerance-based voting
AWQ â outperforms â AutoRound
confidence 85% · GPTQ and AWQ often outperform AutoRound under tolerance-based voting
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Abstract
Abstract:Multilingual reasoning models are commonly evaluated by whether they arrive at the correct answer, but not by whether they preserve the intended language while reasoning and responding. This omission conceals important multilingual behaviors that emerge as tasks become harder. In this paper, we study task difficulty, task accuracy, thinking-language consistency (TC), and answer-language consistency (AC) across reasoning models using PolyMath benchmark in eight languages and four difficulty levels. We uncover four findings: (1) language consistency exhibits four difficulty-dependent behaviors: output-language consistency remains aligned with input, remains misaligned, degrades gradually, or collapses abruptly. (2) We identify the language consistency breakdown effect, where increasing difficulty can cause a sudden drop in output-language consistency, especially in less strongly represented and non-Latin-script languages. (3) Due to this breakdown effect, accuracy can be preserved or even improved at a harder difficulty level as the model shifts to its internal dominant language. (4) Quantization can improve or degrade output-language consistency independently of its effect on accuracy, with GPTQ and AWQ often outperforming AutoRound under tolerance-based voting with {\epsilon} = 1.0. These results show that multilingual capability cannot be characterized by accuracy alone; reliable evaluation should jointly consider task accuracy, language consistency, and task difficulty for multilingual benchmarks.
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- Source: https://arxiv.org/abs/2608.08447v1
- Canonical: https://arxiv.org/abs/2608.08447v1
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Hidden Language Consistency Phenomena in Reasoning LLMs Muhammad Ali Shafique Kansas State University alishafique@ksu.edu Kelly Marchisio Cohere kelly@cohere.com Abstract Multilingual reasoning models are commonly evaluated by whether they arrive at the cor- rect answer, but not by whether they pre- serve the intended language while reasoning and responding. This omission conceals im- portant multilingual behaviors that emerge as tasks become harder. In this paper, we study task difficulty, task accuracy, thinking-language consistency (TC), and answer-language con- sistency (AC) across reasoning models us- ing PolyMath benchmark in eight languages and four difficulty levels. We uncover four findings: (1) language consistency exhibits four difficulty-dependent behaviors: output- language consistency remains aligned with in- put, remains misaligned, degrades gradually, or collapses abruptly. (2) We identify the lan- guage consistency breakdown effect, where in- creasing difficulty can cause a sudden drop in output-language consistency, especially in less strongly represented and non-Latin-script lan- guages. (3) Due to this breakdown effect, ac- curacy can be preserved or even improved at a harder difficulty level as the model shifts to its internal dominant language. (4) Quantiza- tion can improve or degrade output-language consistency independently of its effect on accu- racy, with GPTQ and AWQ often outperform- ing AutoRound under tolerance-based voting with Δ = 1.0. These results show that multilin- gual capability cannot be characterized by ac- curacy alone; reliable evaluation should jointly consider task accuracy, language consistency, and task difficulty for multilingual benchmarks. 1 Introduction Recent large language models (LLMs) with en- hanced reasoning capabilities have achieved strong performance on mathematical, scientific, and competition-level reasoning tasks (Jaech et al., 2024; Team et al., 2025b; Guo et al., 2025; Team, 2025b; Rein et al., 2023; Lightman et al., 2024; Cobbe et al., 2021). These gains often rely on Low MediumHigh Top 0 20 40 60 80 100 Difficulty Level Score (%) AccuracyACTC Figure 1: Difficulty-wise accuracy, thinking-language consistency (TC), and answer-language consistency (AC) of OLMo-3-7B-Think on Chinese PolyMath prob- lems. While accuracy decreases progressively with task difficulty, AC exhibits a sharp breakdown from 77.6% to 13.9% between the low and medium levels. TC remains consistently low across all difficulty levels. long chain-of-thought reasoning (Wei et al., 2022), which can improve accuracy but also increase in- ference cost and lead models to âoverthinkâ sim- ple problems (Chen et al., 2024b). As reason- ing models are increasingly used across languages, evaluation must consider not only whether the fi- nal answer is correct, but also whether the model preserves the requested language in its reasoning and/or response. Multilingual reasoning is commonly evaluated through accuracy across languages and difficulty levels. However, accuracy alone can conceal impor- tant multilingual behavior. A model may produce a correct answer while reasoning or responding in an unintended input language, or preserve the requested language while producing an incorrect answer. Final-answer accuracy, thinking-language consistency (TC), and answer-language consis- tency (AC) therefore capture distinct but comple- mentary dimensions of multilingual reasoning. 1 arXiv:2608.08447v1 [cs.CL] 9 Aug 2026 Four InputâOutput Language-Consistency Cases across Task Difficulty Levels (a) The model switches to Chinese for reasoning despite being instructed to think in English, while answering cor- rectly in English. Model AccuracyInput ConsistencyOutput Consistency Low Med.High Top 0 20 40 60 80 100 Difficulty Level Score (%) Case 1: Output remains consistent. Low Med.High Top 0 20 40 60 80 100 Difficulty Level Case 2: Output remains inconsistent. Low Med.High Top 0 20 40 60 80 100 Difficulty Level Score (%) Case 3: Consistency declines gradually. Low Med.High Top 0 20 40 60 80 100 Difficulty Level Case 4: Consistency collapses abruptly. (b) Four difficulty-dependent language-consistency cases. Figure 2: Illustration and taxonomy of inputâoutput language consistency in thinking traces. (a) An example of language switching within a thinking trace. (b) Four representative difficulty-dependent cases: Case 1, persistent alignment for English with Phi-4-mini-reasoning; Case 2, persistent misalignment for Arabic with Qwen3-30B- A3B-Thinking; Case 3, gradual degradation for Russian with DeepSeek-R1-Distill-Qwen-7B; and Case 4, abrupt collapse for Telugu with DeepSeek-R1-Distill-Qwen-7B. Task difficulty may further shape this relation- ship. Harder problems often require longer and more complex reasoning, increasing the likelihood of language drift. Language-specific factors, in- cluding script, tokenizer coverage, writing direc- tion, and multilingual representation, may further amplify this behavior (Ogueji et al., 2022; Team et al., 2022; Khondaker et al., 2023; Pozzobon et al., 2024). PolyMath (Wang et al., 2026) re- ports language-level output consistency scores and aggregate output consistency score across difficulty levels, but does not characterize how each output- language consistency scores evolves across diffi- culty levels. We fill this gap with a four-case tax- onomy and language-level consistencyâdifficulty analysis. As difficulty increases, output-language consis- tency may remain aligned with the input language, decline gradually, or collapse abruptly as models shift toward a dominant internal language (Fig- ure 1). We term this abrupt decline the language consistency breakdown effect. In this paper, we investigate how task difficulty affects multilingual language consistency and how this behavior interacts with task accuracy. We eval- uate five reasoning models and three non-reasoning models on PolyMath (Wang et al., 2026), cover- ing eight languages and four difficulty levels. The selected languages span diverse scripts and lev- els of multilingual representation. We measure final-answer accuracy, thinking-language consis- tency (TC), and answer-language consistency (AC) at each difficulty level, identify various language consistency behaviors, language-consistency break- down effect, prompt control, and systematically ex- amine how quantization changes output-language consistency scores. We find that: 1.Language consistency exhibits four distinct difficulty-dependent behaviors (§4.1): We identify a taxonomy of multilingual generation behavior across task difficulty: (1) output stays consistent with input language-consistency, (2) output stays inconsistent, (3) output-language consistency declines gradually, and (4) output- language consistency collapses abruptly. This taxonomy shows that output-language consis- tency degradation is not a single uniform phe- nomenon, but can emerge differently across 2 models and languages (Figure 2). 2.Increasing task difficulty degrades output- language consistency and can trigger abrupt drop (§4.2): As problems become harder, output-language consistency generally declines. When it exhibits a sudden and sub- stantial drop between consecutive difficulty levels, we term this the language consistency breakdown effect, which is more prevalent in lower-resource and non-Latin-script languages (Case 4 in Figure 2b). 3.Language consistency breakdown breaks the expected monotonic accuracyâdifficulty relationship (§4.3): Model accuracy is gener- ally expected to decline monotonically as task difficulty increases. We uncover non-linear behavior that breaks this rule: accuracy can preserve or improve at a higher difficulty level due to language consistency breakdown effect in thinking-language consistency (TC) and/or answer-language consistency (AC). 4.Quantization affects output-language con- sistency (§5.1): To the best of our knowledge, this is the first study to systematically exam- ine how quantization affects output-language consistency in multilingual reasoning models. We find that quantization can either improve or degrade language consistency, independently of its effect on task accuracy. Under tolerance- based voting withΔ = 1.0, GPTQ and AWQ often preserves or improves output-language consistency more effectively than AutoRound. Overall, our work highlights that multilingual models cannot be evaluated by final-answer accu- racy alone; task difficulty, thinking-language con- sistency, and answer-language consistency should be considered jointly to better understand multilin- gual reasoning behavior. 2 Preliminary and Related Work Multilingual Reasoning.Multilingual reasoning requires models to solve problems correctly while preserving the requested language in the reasoning trace, final answer, or both. Prior work shows that multilingual LLM performance varies substantially across languages because of differences in training data, tokenizer coverage, script, and degree of mul- tilingual representation (Ahia et al., 2021; Ogueji et al., 2022; Team et al., 2022; Khondaker et al., 2023; Pozzobon et al., 2024). These differences may become more pronounced in reasoning tasks, where longer and more complex generations create additional chances for language drift. Recent reasoning-oriented LLMs, such as Ope- nAI o1 (Jaech et al., 2024), DeepSeek-R1 (Guo et al., 2025), QwQ (Team, 2025b; Yang et al., 2024), and Kimi (Team et al., 2025b), have shown strong performance on mathematical and multi- step reasoning tasks. However, their evaluation commonly emphasizes final-answer accuracy, with less attention to whether the reasoning trace and final answer remain in the requested language. Code-Switching.Code-switching refers to natu- ral alternation between languages within an utter- ance or conversation (Do Ì gruöz et al., 2021). Prior work has evaluated code-switched language un- derstanding and generation on tasks such as senti- ment analysis, machine translation, summarization, and language identification (Khanuja et al., 2020; Winata et al., 2023). These studies typically use human-produced data where switching between English and another language is intentional and linguistically meaningful. Despite this progress, current models still strug- gle to understand and generate code-switched text for several languages (Yong et al., 2023; Zhang et al., 2023). Our focus differs from natural code- switching because we study unintended language changes in model generations. Language Confusion.Unintended generation in the wrong language has been studied as source- language hallucination in zero-shot cross-lingual transfer (Vu et al., 2022; Li and Murray, 2023; Pfeiffer et al., 2023; Chirkova and Nikoulina, 2024) and as off-target translation in multilingual ma- chine translation (Chen et al., 2023; Sennrich et al., 2024). These behaviors occur when multilingual models generate in a language different from the requested target language in input prompt. Similar language confusion has also been ob- served in LLM responses (Marchisio et al., 2024; Kew et al., 2024; Faisal and Anastasopoulos, 2023; Chen et al., 2024a; Holtermann et al., 2024). Most prior work studies this behavior at the response level. In contrast, we separately evaluate language consistency in reasoning traces and final answers. This distinction is important because a model may reason in one language and answer in another. 3 ModelTypeAvg. Acc.TC belowÏ cons @ TopAC belowÏ cons @ Top DeepSeek-R1-Distill-Qwen-1.5BReasoning20.36/86/8 DeepSeek-R1-Distill-Qwen-7BReasoning36.56/86/8 OLMo-3-7B-ThinkReasoning42.76/87/8 Phi-4-mini-reasoningReasoning32.56/86/8 Qwen3-30B-A3B-Thinking-2507Reasoning62.35/80/8 Gemma-3-12b-itNon-reasoning31.3N/A0/8 Phi-4-mini-instructNon-reasoning15.6N/A1/8 Qwen3-30B-A3B-Instruct-2507Non-reasoning50.4N/A0/8 Table 1: Overall task accuracy and language-consistency behavior across reasoning and non-reasoning models using forced-target-language prompting. Avg. Acc. denotes average PolyMath accuracy across eight languages. TC BelowÏ cons @ Top and AC BelowÏ cons @ Top count the languages with thinking- and answer-language consistency scores below Ï cons = 90% at Top difficulty. The threshold Ï cons is an analysis hyperparameter. 3 Experimental Setup and Dataset Evaluation Benchmark. We evaluate the mod- els on PolyMath (Wang et al., 2026), a multilingual mathematical benchmark spanning broad difficulty ranges: âlowâ: K-12 Mathematics, âmediumâ: High-School and University Level, âhighâ: com- petition math, and âtop": Top Olympiad and Fron- tier Mathematics. We evaluate model performance across eight languages and study the effect of diffi- culty levels on accuracy and language consistency in reasoning and answer traces. PolyMath is se- lected because it spans diverse languages and dif- ficulty levels and provides standard scripts 1 for evaluating final-answer correctness and language consistency. Models. We evaluate five reasoning models and three non-reasoning models: DeepSeek-R1-Distill- Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B (Guo et al., 2025), OLMo-3-7B-Think (Olmo et al., 2026), Phi-4-mini-reasoning (Abdin et al., 2025), andQwen3-30B-A3B-Thinking-2507(Team, 2025a) for reasoning, and Gemma-3-12B-it (Team et al., 2025a), Phi-4-mini-instruct, and Qwen3- 30B-A3B-Instruct-2507 as non-reasoning models. This model selection allows comparison of multilingual behavior across reasoning and non-reasoning settings, and model scales. Inference Setup and Prompting Strategy. All inference is performed using thevLLM(Kwon et al., 2023) framework. We use the same inference set- tings as (Liu et al., 2025), with temperature= 0.6 and top-p = 0.95. Our setup differs only in the maximum model sequence length; we use65,536 instead of32,768because multilingual generations 1 The official PolyMath scripts are used to compute final- answer correctness and language-consistency scores. may require more tokens to express the same se- mantic content. To reduce generation variation, models are evaluated using consistent inference set- tings across languages and difficulty levels with three seed values. For each problem, we use forced-target- language prompting in which model is instructed to reason and answer in the target language. The prompting strategy is explained in Appendix B. Evaluation Metrics. In addition to the stan- dard accuracy reported on PolyMath, we evaluate thinking-language consistency (TC) and answer- language consistency (AC) scores. Let Ë â ,r denote the detected language of the reasoning trace andâ i the requested language. We define TC as: TC = 1 N X 1[ Ë â ,r i = â i ].(1) Similarly, let Ë â ,a denote the detected language of the final answer. We define AC as: AC = 1 N X 1[ Ë â ,a i = â i ].(2) We report overall and difficulty-wise accuracy, TC, and AC scores across languages and models to study whether increasing task difficulty affects final-answer correctness and language consistency differently. Further hardware and software details are reported in Appendix D. 4 Results Table 1 summarizes these difficulty-dependent behaviors across five reasoning and three non- reasoning models.Figures 3 and 4 re- port final-answer accuracy, thinking-language consistency (TC), and answer-language consis- tency (AC) across four difficulty levels for 4 DeepSeek-R1-Distill-Qwen-7B AccuracyAnswer Consistency (AC)Thinking Consistency (TC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 3: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language con- sistency (AC) of DeepSeek-R1-Distill-Qwen-7B across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. Results: accuracy generally decreases with task-difficulty, but thinking- and answer-language consistency are language-dependent: accurate in English and Chinese, but breaking down for languages like Arabic, Bengali, French, Swahili, and Telugu. OLMo-3-7B-Think AccuracyAnswer Consistency (AC)Thinking Consistency (TC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 4: Analogous plot to Figure 3, for OLMo-3-7B-Think. English and Russian maintain language consistency, while other languages consistency degrades rapidly with task difficulty. 5 ModelMethodW-A-KV BitsAvg. âAcc.Avg. âTCTC Co-winsTC Co-winner Lang. DeepSeek-R1 Distill-Qwen-7B GPTQ4-16-16 -3.39-5.406/8en, zh, ar, fr, sw, te AWQ4-16-16-2.53-3.835/8en, ar, bn, fr, ru AutoRound4-16-16-0.80-6.753/8en, ar, bn OLMo-3-7B-Think GPTQ4-16-16-2.33+4.287/8en, zh, ar, bn, ru, sw, te AWQ4-16-16-2.39+2.046/8en, ar, bn, fr, ru, sw AutoRound4-16-16-1.14-0.195/8en, ar, fr, sw, te Table 2: Summary of accuracy and thinking-language consistency (TC)âscores relative to Baseline across eight languages for DeepSeek-R1-Distill-Qwen-7B and OLMo-3-7B-Think. Avg.âAcc. and Avg.âTC report average changes over the eight shown languages. Green/red cells mark the best/worst average values among GPTQ, AWQ, and AutoRound within each model. Yellow cells summarize tolerance-based TC voting co-winners withΔ = 1.0, i.e., methods within one TC point of the bestâTC for each model-language group. Full per-language Acc./TC and âAcc./âTC results are reported in Table 6, 7, and 8. DeepSeek-R1-Distill-Qwen-7B and OLMo-3-7B- Think, respectively. Results for Qwen3-30B-A3B- Instruct, Qwen3-30B-A3B-Thinking, DeepSeek- R1-Distill-Qwen-1.5B, Gemma-3-12B-IT, Phi-4- mini-instruct, and Phi-4-mini-reasoning are pro- vided in Appendix Figures 6, 7, 8, 9, 10, and 11. 4.1 Four Difficulty-Dependent Language-Consistency Cases Output-language consistency does not follow a sin- gle pattern as task difficulty increases. Across mod- els and languages, we identify four representative cases based on how the output language aligns with the input language from low to top difficulty, as il- lustrated in Figure 2. Case 1: Output language remains consistent with the input language. Some models preserve the requested language across all difficulty levels, even as task accuracy decreases. For example, Phi- 4-mini-reasoning maintains approximately 100% answer- and thinking-language consistency for En- glish from low through top difficulty, while accu- racy decreases from 94.0% to 14.0% (Figure 11). Case 2: Output language remains inconsis- tent with the input language. Some models con- sistently reason in a language different from the requested input language. For Arabic, Qwen3- 30B-A3B-Thinking-2507 maintains 0% thinking- language consistency across all difficulty levels, in- dicating that model prefers to use dominant internal reasoning language (English) despite the Arabic in- put. Similar behavior appears for Bengali, French, Swahili, and Telugu (Figure 7). Case 3: Output-language consistency declines gradually. Language consistency may progres- sively decrease as task difficulty increases. For Rus- sian in DeepSeek-R1-Distill-Qwen-7B, thinking- language consistency decreases from 97.1% at low difficulty to 86.7% at top difficulty (Figure 3). Case 4: Output-language consistency de- clines abruptly. In some cases, language con- sistency exhibits a sudden and substantial de- crease between consecutive difficulty levels. For Telugu, DeepSeek-R1-Distill-Qwen-7B decreases from 99.2% at low difficulty to 11.7% at medium difficulty (Figure 3). We formally define and an- alyze this behavior as the language consistency breakdown effect in Section 4.2. 4.2 Language Consistency Breakdown Effect As task difficulty increases, reasoning models of- ten become less consistent in the language used for their thinking traces and final answers. We define the language consistency breakdown effect using a user-defined drop thresholdâ break . Between con- secutive difficulty levelsdandd + 1, a breakdown occurs when âTC d = TC d â TC d+1 â„ â break ,(3) âAC d = AC d â AC d+1 â„ â break .(4) We setâ break = 30percentage points and re- port sensitivity results forâ break â 30, 50, 70 in Appendix C.2. For DeepSeek-R1-Distill-Qwen- 7B, Bengali TC drops from 97.9% to 1.6%, while AC drops from 98.1% to 0.5% between low and medium difficulty. Similar breakdowns occur for Arabic, French, Swahili, and Telugu, whereas Chi- nese and Russian remain comparatively stable. The effect is strongly model-dependent. DeepSeek-R1-Distill-Qwen-1.5B and 7B exhibit AC and TC breakdowns in 5/8 languages, respec- tively. Qwen3-30B-A3B-Thinking-2507 exhibits no breakdown in either metric. Increasing task difficulty generally reduces TC and AC, with some languages exhibiting abrupt breakdowns in one or both. 6 en zh ar bnfr rusw te 0 20 40 60 80 100 Language Code Aggregated Thinking Consistency (%) BaselineGPTQAWQAutoRound Figure 5: Aggregated thinking-language consistency of Baseline and W4A16-quantized DeepSeek-R1-Distill-Qwen- 7B across eight languages. 4.3 Language consistency breakdown breaks monotonic accuracyâdifficulty trend Model accuracy is generally expected to decline monotonically as task difficulty increases. How- ever, language consistency breakdown effect intro- duces non-linear behavior that breaks this expected relationship: accuracy can preserve or improve at a higher difficulty level when TC and AC collapse. For DeepSeek-R1-Distill-Qwen-7B, Bengali ac- curacy increases (Figure 3) from 47.5% at low dif- ficulty to 50.9% at medium difficulty, while TC decreases from 97.9% to 1.6% and AC decreases from 98.1% to 0.5%. Swahili accuracy similarly increases from 4.5% to 35.7%, despite TC and AC collapsing from 89.9% and 85.3% to 1.9% and 1.6%, respectively. Telugu exhibits the same pat- tern, with accuracy increasing from 22.9% to 41.9% while TC and AC decrease sharply. These results show that improved accuracy at a harder difficulty level does not necessarily indicate improved reasoning or answer consistency. Instead, the model may solve more problems by shifting toward a more dominant internal language during thinking or answer generation. The language consistency breakdown breaks the expected monotonic accuracyâdifficulty re- lationship, revealing that accuracy can preserve or increase at a higher difficulty level when lan- guage consistency collapses. 5 Analyses and Discussion In this section, we analyze output-language consis- tency from perspectives of quantization, reasoning versus non-reasoning, and prompt control. 5.1 Impact of Quantization How does quantization affect multilingual reason- ing accuracy and thinking-language consistency? Quantization affects multilingual reasoning un- evenly: final-answer accuracy is generally pre- served or reduced, whereas output-language con- sistency can either improve or degrade depending on the model, language, and quantization method. To the best of our knowledge, this is the first sys- tematic study of how quantization affects thinking- language consistency in multilingual reasoning models. Among the evaluated W4A16 integer methods, AutoRound provides the strongest accuracy preser- vation. For DeepSeek-R1-Distill-Qwen-7B, Au- toRound reduces average accuracy by only0.80 points, compared with2.53for AWQ and3.39 for GPTQ. Similarly, for OLMo-3-7B-Think, Au- toRound yields the smallest degradation at1.14 points, compared with2.33for GPTQ and2.39for AWQ as showed in Table 2. This gives the overall accuracy-preservation order: AutoRound > AWQ â„ GPTQ. This ordering does not extend to output-language consistency, since quantization affects language consistency differently. It can degrade or improve and can be skewed by large gains or drops in a small number of languages. Therefore, we use tolerance- based voting as the main criteria to rank quanti- zation methods for TC and report avg.âTC as a complementary magnitude measure. The tolerance parameterΔdefines the minimum TC difference considered meaningful, preventing very small gaps 7 from being over-interpreted. A method is counted as a co-winner if âTC m â„ max m âČ âM âTC m âČ â Δ, whereM =GPTQ, AWQ, AutoRoundandΔ = 1.0percentage point. Under this criterion, GPTQ receives the better support for preserving or improv- ing TC, while AWQ achieves larger-magnitude im- provements; AutoRound performs comparatively worse as illustrated in Figure 5 and 12.Ap- pendix C.1 reports additional TC voting results for Δâ0.5, 1.0, 2.0. Quantization affects accuracy and language consistency differently: AutoRound best pre- serves final-answer accuracy, while GPTQ and AWQ more often preserve or improve thinking- language consistency. 5.2 Reasoning versus Non-Reasoning How does task difficulty affect language consis- tency in reasoning and non-reasoning models? Reasoning and non-reasoning models exhibit dis- tinct language-consistency behavior as task diffi- culty increases. The evaluated non-reasoning mod- els remain comparatively stable, with no answer- language consistency (AC) breakdown across the eight languages. In contrast, DeepSeek-R1-Distill- Qwen-1.5B and 7B, OLMo-3-7B-Think, and Phi-4- mini-reasoning exhibit AC breakdowns in multiple languages as illustrated in Figure 8, 3, 4, and 11. Language-consistency degradation becomes more pronounced in reasoning models as task difficulty increases. 5.3 Prompt Control Can allowing models to reason in their preferred language improve answer-language consistency? Our main experiments explicitly instruct each model to reason and answer in the target lan- guage. As a prompt control, we relax the reasoning- language constraint and allow the model to select its preferred reasoning language while still requir- ing the final answer in the target language. We evaluate this control on DeepSeek-R1-Distill- Qwen-7B and Phi-4-mini-reasoning. Allowing unrestricted reasoning does not ensure answer- language consistency. DeepSeek-R1-Distill-Qwen- 7B achieves answer-language consistency below Ï cons = 90%at Top difficulty for 6/8 languages. Phi-4-mini-reasoning achieves answer-language consistency below the threshold for 7/8 languages. English remains highly consistent, whereas Ara- bic, Bengali, French, Swahili, and Telugu exhibit substantially lower AC (Table 5). Allowing models to reason in their preferred language does not reliably preserve the re- quested answer language, particularly at higher difficulty levels. 6 Conclusion In this paper, we uncover hidden language- consistency phenomena in reasoning and non- reasoning LLMs, revealing how task difficulty af- fects final-answer accuracy, thinking-language con- sistency (TC), and answer-language consistency (AC). Using PolyMath across eight languages and four difficulty levels, we show that accuracy and language consistency capture distinct aspects of multilingual capability. Our results reveal four difficulty-dependent language-consistency behaviors, ranging from con- sistent TC and AC to gradual degradation and abrupt collapse. Increasing task difficulty gener- ally reduces thinking- and answer-language con- sistency, with some languages exhibiting the lan- guage consistency breakdown effect, where TC or AC drops abruptly. This effect is more prevalent in lower-resource and non-Latin-script languages and is substantially more pronounced in several rea- soning models, while the evaluated non-reasoning models maintain comparatively consistent answer- language consistency.We also uncover non- linear behavior that breaks the expected accuracyâ difficulty relationship: accuracy can improve at a higher difficulty level as TC and AC collapse. Quantization further affects these dimensions unevenly. It can improve or degrade language- consistency independently of task accuracy. Among the evaluated W4A16 integer methods, AutoRound best preserves final-answer accuracy, while AWQ and GPTQ more often preserve or improve thinking-language consistency under tolerance-based voting with Δ = 1.0. Overall, multilingual capability cannot be char- acterized by accuracy alone. Reliable evaluation should jointly consider task difficulty, accuracy, answer- and thinking-language consistency scores. 7 Limitations Model coverage. We evaluate five open rea- soning models and three non-reasoning models across several model families and scales. However, 8 our findings may not generalize to substantially larger models, closed-source systems, or models trained with different reasoning and post-training strategies. Language coverage. We evaluate eight lan- guages from PolyMath, selected to cover different scripts and levels of multilingual representation. The observed language-consistency patterns may differ for other languages, particularly those that are less represented in multilingual model training. Benchmark coverage. Our experiments focus on PolyMath, a multilingual mathematical reason- ing benchmark with four difficulty levels. The observed difficulty-related language-consistency breakdown may differ for other reasoning domains, such as scientific reasoning, coding, or open-ended tasks. Prompt dependence. Our experiments use native-language reasoning and boxed-answer in- structions. Different prompting strategies, such as English reasoning prompts across all languages, free-form responses, or few-shot prompting, may produce different language-consistency behavior. 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Ruochen Zhang, Samuel Cahyawijaya, Jan Chris- tian Blaise Cruz, Genta Winata, and Alham Aji. 2023.Multilingual large language models are not (yet) code-switchers.InProceedingsofthe 2023ConferenceonEmpiricalMethodsinNatural LanguageProcessing, pages 12567â12582, Singa- pore. Association for Computational Linguistics. A Quantization Algorithms In this section, we briefly describe the quantiza- tion methods, evaluated in this study. All quan- tized models are produced usingllm-compressor standard presets to ensure a fair and reproducible comparison across methods. A.1 Integer W4A16 Quantization GPTQ. GPTQ (Frantar et al., 2022) is a post- training quantization method that reduces recon- struction error between full precision and quantized layer outputs of the model. Given input activation Xand weightW, GPTQ tries to calculate quan- tized weight matrix Ë W by solving: arg min Ë W â„ Ë WXâ WXâ„ F . It uses approximate second-order information to reduce quantization error. In this study, GPTQ is evaluated using thellm-compressorW4A16 preset with group size g=128. AWQ. AWQ (Lin et al., 2024) is an activation- aware post-training quantization method that pro- tects salient weight channels by applying channel- wise scale factor before applying quantization. Given activationsX, weightsW, and scaling vec- tor s, AWQ rewrites the linear operation as: Y = (Xs â1 )(sW †), wheresis chosen to reduce quantization error due to activation outliers. We evaluate AWQ using llm-compressorW4A16 preset with group size g=128. Like GPTQ, we use calibration with 128 samples from the Pile (Gao et al., 2020). 11 ModelΔMethodCo-winner RankingMean âTC DeepSeek-R1-Distill-Qwen-1.5B0.5 GPTQ78.90 AWQ23.92 AutoRound42.51 DeepSeek-R1-Distill-Qwen-7B0.5 GPTQ5-5.40 AWQ4-3.83 AutoRound2-6.75 OLMo-3-7B-Think0.5 GPTQ54.28 AWQ72.04 AutoRound1-0.19 DeepSeek-R1-Distill-Qwen-1.5B1.0 GPTQ78.90 AWQ23.92 AutoRound42.51 DeepSeek-R1-Distill-Qwen-7B1.0 GPTQ6-5.40 AWQ5-3.83 AutoRound3-6.75 OLMo-3-7B-Think1.0 GPTQ74.28 AWQ72.04 AutoRound5-0.19 DeepSeek-R1-Distill-Qwen-1.5B2.0 GPTQ78.90 AWQ33.92 AutoRound42.51 DeepSeek-R1-Distill-Qwen-7B2.0 GPTQ6-5.40 AWQ5-3.83 AutoRound4-6.75 OLMo-3-7B-Think2.0 GPTQ84.28 AWQ72.04 AutoRound7-0.19 Table 3: Sensitivity of tolerance-based TC voting toΔ. Methods withinΔTC points of the best signedâTC are considered as co-winners. DeepSeek-R1-Distill-Qwen-1.5B/ 7B and OLMo-3-7B-Think values are recorded for eight languages. AutoRound.AutoRound (Cheng et al., 2024) is a post-training quantization method that uses signed gradient descent to optimize the weight rounding and clipping ranges values. Instead of relying on nearest rounding, it tries to learn the rounding de- cisions that reduce layer-wise reconstruction error with no extra inference time overhead. In our paper, we evaluate AutoRound usingllm-compressor W4A16 preset with group size g=128. B Prompting Strategy. For each problem, the model is instructed to reason in the target language and the target language is again used to place the final-answer inside a boxed expression. These thinking and answer formatting phrases for given target language, are also provided by PolyMath (Wang et al., 2026). The prompting design is given below target_language_question target_language_reasoning target_language_answer_formatting For English, the prompt becomes: target_language_question Use English to think and answer. Note: Please put the final answer in . During post-processing, we split the model re- sponse into corresponding thinking and answer parts using the</think>delimiter if it is available. This way, we record raw response and correspond- ing reasoning and answer parts for the evaluations. C Additional Experiments C.1 Tolerance-Based Voting We repeat tolerance-based voting withΔ â 0.5, 1.0, 2.0 . For each model-language pair, the method with the highest signedâTC is selected as the reference, and all methods withinΔTC points are counted as co-winners. We report co-winner counts and average signed âTC in Table 3. C.2 Breakdown-Threshold Sensitivity Table 4 reports breakdown counts underâ break â 30, 50, 70percentage points. As expected, the number of detected breakdowns generally de- creases as the threshold becomes stricter. However, the main conclusion remains same: DeepSeek rea- soning models exhibit breakdowns in both TC and 12 AC, OLMo-3-7B-Think and Phi-4-mini-reasoning primarily exhibit AC breakdowns, and Qwen3- 30B-A3B-Thinking-2507 and the evaluated non- reasoning models remain comparatively stable. D Hardware and Software Details Our experimental pipeline consists of three stages. quantization, inference, and evaluation. For quantization, we usellm-compressorver- sion 0.9.0.2 andcompressed-tensorsversion 0.13.0. For inference, we usevLLMversion 0.20.1 withtorchversion 2.11.0 andtransformersver- sion 5.7.0. Evaluation is performed using the offi- cial PolyMath scripts, which compute final-answer correctness as well as language consistency scores. All experiments are run on NVIDIA H100 GPUs. E AI Assistance ChatGPT-5.5 was used for grammar refinement and latex coding assistance with table/ figure structure and debugging. The authors take full responsibility for the final published version. 13 â break = 30 â break = 50 â break = 70 ModelTCACTCACTCAC DeepSeek-R1-Distill-Qwen-1.5B5/85/83/84/82/81/8 DeepSeek-R1-Distill-Qwen-7B5/85/85/85/84/85/8 OLMo-3-7B-Think0/86/80/84/80/82/8 Phi-4-mini-reasoning0/84/80/83/80/80/8 Qwen3-30B-A3B-Thinking-25070/80/80/80/80/80/8 Gemma-3-12B-ITâ0/8â0/8â0/8 Phi-4-mini-instructâ0/8â0/8â0/8 Qwen3-30B-A3B-Instruct-2507â0/8â0/8â0/8 Table 4: Sensitivity of language-consistency breakdown counts toâ break â30, 50, 70percentage points. Each value reports the number of languages, out of eight, exhibiting at least one breakdown between consecutive difficulty levels. ModelAvg. Acc. TC belowÏ cons @ Top AC belowÏ cons @ Top DeepSeek-R1-Distill-Qwen-7B35.36/86/8 Phi-4-mini-reasoning32.46/87/8 Table 5: Task accuracy and language-consistency behavior under preferred-language reasoning prompting. Avg. Acc. denotes average PolyMath accuracy across eight languages. TC belowÏ cons @ Top and AC belowÏ cons @ Top count languages with thinking- and answer-language consistency belowÏ cons = 90%at Top difficulty. The threshold Ï cons is an analysis hyperparameter. 14 Qwen3-30B-A3B-Instruct-2507 AccuracyAnswer Consistency (AC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 6: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language consis- tency (AC) of Qwen3-30B-A3B-Instruct-2507 across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. The results show that answer-language consistency is largely preserved across several languages. Qwen3-30B-A3B-Thinking-2507 AccuracyAnswer Consistency (AC)Thinking Consistency (TC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 7: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language consis- tency (AC) of Qwen3-30B-A3B-Thinking-2507 across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. The results show that answer-language consistency is largely preserved, while the model often reasons in English or Chinese for Arabic, Bengali, French, Swahili, and Telugu. 15 DeepSeek-R1-Distill-Qwen-1.5B AccuracyAnswer Consistency (AC)Thinking Consistency (TC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 8: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language consis- tency (AC) of DeepSeek-R1-Distill-Qwen-1.5B across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. The results show that language consistency is preserved for English and Chinese but breaks down for several other languages. Gemma-3-12B-IT AccuracyAnswer Consistency (AC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 9: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language consis- tency (AC) of Gemma-3-12B-IT across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. The results show that answer-language consistency is largely preserved across languages. 16 Phi-4-mini-instruct AccuracyAnswer Consistency (AC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 10: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language consistency (AC) of Phi-4-mini-instruct across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. The results show that answer-language consistency remains stable across most languages but decreases for a few as task difficulty increases. Phi-4-mini-reasoning AccuracyAnswer Consistency (AC)Thinking Consistency (TC) 1234 0 20 40 60 80 100 Difficulty Level Score (%) (a) English 1234 0 20 40 60 80 100 Difficulty Level (b) Chinese 1234 0 20 40 60 80 100 Difficulty Level (c) Arabic 1234 0 20 40 60 80 100 Difficulty Level (d) Bengali 1234 0 20 40 60 80 100 Difficulty Level Score (%) (e) French 1234 0 20 40 60 80 100 Difficulty Level (f) Russian 1234 0 20 40 60 80 100 Difficulty Level (g) Swahili 1234 0 20 40 60 80 100 Difficulty Level (h) Telugu Figure 11: Difficulty-wise final-answer accuracy, thinking-language consistency (TC), and answer-language consistency (AC) of Phi-4-mini-reasoning across eight languages and four PolyMath difficulty levels: 1 = low, 2 = medium, 3 = high, and 4 = top. The results show that thinking- and answer-language consistency are preserved for English and Chinese, while answer-language consistency breaks down for several other languages. 17 ModelMethodW-A-KV BitsAvg. Acc.Avg. TCAccuracy-wise Winner Lang.Accuracy-wise Loss Lang. DeepSeek-R1 Distill-Qwen-7B â36.552.3â GPTQ4-16-1633.146.9âen, zh, ar, bn, sw, te AWQ4-16-1633.948.5bn, swfr, ru AutoRound4-16-1635.745.6en, zh, ar, fr, ru, teâ OLMo-3-7B-Think â42.727.0â GPTQ4-16-1640.431.3enzh, ar, sw, te AWQ4-16-1640.329.1enbn, fr, ru AutoRound4-16-1641.626.8zh, ar, bn, fr, ru, sw, teen Table 6: Summary of accuracy and thinking-language consistency (TC) across eight languages for DeepSeek-R1- Distill-Qwen-7B and OLMo-3-7B-Think. Avg. Acc. and Avg. TC report averages over the eight shown languages. Green/red cells mark the best/worst values among GPTQ, AWQ, and AutoRound within each model. Accuracy-wise winner/loss languages indicate where each method obtains the highest/lowest accuracy within the same model. Full per-language Acc./TC results are reported in Table 7. ModelMethod W-A-KV # Bits enzharbnfrruswteAvg Acc.TCAcc.TCAcc.TCAcc.TCAcc.TCAcc.TCAcc.TCAcc.TCAcc.TC DS-R1 Qwen-7B â49.299.846.092.739.220.236.326.242.037.837.688.916.126.025.331.136.552.3 GPTQ4-16-1644.899.740.394.833.614.532.419.639.831.037.061.414.127.322.631.233.146.9 AWQ4-16-1645.699.742.092.736.315.533.721.839.530.234.886.616.020.423.625.233.948.5 AutoRound4-16-1648.0100.043.391.938.814.532.721.341.826.840.263.515.025.825.524.935.745.6 Olmo-3-7B -Think â57.699.754.011.344.70.532.93.153.90.438.199.422.90.737.61.142.727.0 GPTQ4-16-1657.499.949.344.243.01.330.13.552.90.635.698.220.41.334.41.440.431.3 AWQ4-16-1657.499.751.024.243.81.229.24.351.21.634.198.320.71.035.22.240.329.1 AutoRound4-16-1656.299.851.511.646.00.630.52.754.21.137.596.921.10.735.61.341.626.8 Table 7: Accuracy and thinking-language consistency (TC) results across eight languages and quantization methods. Acc. denotes benchmark accuracy and TC denotes thinking-language consistency scores. The green/red cells mark the best/worst accuracy values respectively within each model-language-quantization group and total average column. ModelMethod W-A-KV # Bits enzharbnfrruswte Avg. â âAcc. âTCâAcc.âTCâAcc. âTCâAcc. âTCâAcc. âTCâAcc. âTCâAcc. âTCâAcc. âTCAcc.TC DS-R1 Qwen-7B GPTQ4-16-16-4.4-0.1-5.7+2.1-5.6-5.7-3.9-6.6-2.2-6.8-0.6-27.5-2.0+1.3-2.7+0.1-3.39-5.40 AWQ4-16-16-3.6-0.1-4.00.0-2.9-4.7-2.6-4.4-2.5-7.6-2.8-2.3-0.1-5.6-1.7-5.9-2.53-3.83 AutoRound4-16-16-1.2+0.2-2.7-0.8-0.4-5.7-3.6-4.9-0.2-11.0+2.6-25.4-1.1-0.2+0.2-6.2-0.80-6.75 Olmo-3-7B -Think GPTQ4-16-16-0.2+0.2-4.7+32.9-1.7+0.8-2.8+0.4-1.0+0.2-2.5-1.2-2.5+0.6-3.2+0.3-2.33+4.28 AWQ4-16-16-0.20.0-3.0+12.9-0.9+0.7-3.7+1.2-2.7+1.2-4.0-1.1-2.2+0.3-2.4+1.1-2.39+2.04 AutoRound4-16-16-1.4+0.1-2.5+0.3+1.3+0.1-2.4-0.4+0.3+0.7-0.6-2.5-1.80.0-2.0+0.2-1.14-0.19 Table 8: Accuracy and Thinking-language Consistency (TC) â scores, relative to Baseline across eight languages. The green/red cells mark the best/worst integer methods by magnitude-basedâTC scores. Yellow cells indicate tolerance-based TC voting co-winners withΔ = 1.0, i.e., methods within one TC point of the bestâTC for each model-language-quantization group are considered as co-winner. Table 3 reports tolerance-based voting results for Δ = 1.0. DS-R1-Qwen-7B denotes DeepSeek-R1-Distill-Qwen-7B. 18 en zh ar bnfr rusw te 0 20 40 60 80 100 Language Code Aggregated Thinking Consistency (%) BaselineGPTQAWQAutoRound Figure 12: Aggregated thinking-language consistency of Baseline and W4A16-quantized OLMo-3-7B-Think across eight languages. Language Consistency for Chinese with DeepSeek-R1-Distill-Qwen-7B at low difficulty Figure 13: Example of output-language consistency: the model receives an Chinese input, reasons and answers in Chinese. 19 Language Inconsistency for Arabic with Qwen3-30B-A3B-Thinking at low difficulty Figure 14: Example of output-language inconsistency: the model receives an Arabic input, reasons in English, and answers in Arabic. 20