Same Answer, Different Reasons: Trace-Level Divergence in Multilingual Large Language Models
Organizations: University of Illinois Urbana-Champaign · Texas A&M University
Abstract
Multilingual large language models are increasingly deployed in settings where visible reasoning traces support verification, education, and safety auditing, yet standard evaluations typically measure only final-answer agreement or holistic response similarity. As a result, they establish outcome consistency without determining whether users across languages receive comparable supporting evidence. We introduce a trace-level divergence framework that compares visible reasoning traces as structured sequences, decomposing agreement into structural similarity, order consistency, and holistic similarity, with pair-specific calibration to enable comparison across languages. Across three reasoning benchmarks, seven languages, and six frontier LLMs, the natural baseline---embedding each whole response and comparing the two by cosine---systematically overstates agreement: -- of examples in the top quartile of holistic similarity are not in the top quartile of structural similarity. This dissociation is stable across sentence encoders and step segmentations, and blind bilingual annotation studies in two English-anchored language pairs show that human judgments align with structural similarity rather than with the holistic baseline. A same-language control shows that the level of divergence is language-specific: two English traces for paraphrases of the same question agree more closely than an English trace and its counterparts in other languages. Our results show that answer-level and holistic evaluations can substantially overestimate the consistency of multilingual explanatory artifacts, motivating trace-level evaluation for reliable multilingual deployment.
Figures & tables
| Dataset | Model | # samples | # pairs | ||||||
|---|---|---|---|---|---|---|---|---|---|
| MMLU-ProX | Claude Opus 4.6 | 500 | 431 | 8,470 | 21 | 0.569 [ 0.007] | 0.414 [ 0.014] | 0.800 [ 0.004] | 0.231 |
| MMLU-ProX | Claude Haiku 4.5 | 500 | 321 | 5,459 | 21 | 0.514 [ 0.009] | 0.393 [ 0.016] | 0.787 [ 0.004] | 0.273 |
| MMLU-ProX | DeepSeek-V3.2 | 500 | 394 | 7,179 | 21 | 0.537 [ 0.007] | 0.356 [ 0.014] | 0.794 [ 0.004] | 0.257 |
| MMLU-ProX | GPT-OSS-120B | 500 | 372 | 6,552 | 21 | 0.542 [ 0.008] | 0.469 [ 0.016] | 0.791 [ 0.004] | 0.249 |
| MMLU-ProX | Qwen3-235B | 500 | 370 | 6,656 | 21 | 0.540 [ 0.006] | 0.348 [ 0.015] | 0.793 [ 0.004] | 0.253 |
| MMLU-ProX | Qwen3-32B | 500 | 295 | 4,714 | 21 | 0.513 [ 0.008] | 0.412 [ 0.015] | 0.791 [ 0.005] | 0.278 |
| Dataset | – | – | – | |
|---|---|---|---|---|
| MMLU-ProX | 8,470 | .29 / .29 | .29 / .29 | .05 / .04 |
| StrategyQA | 9,039 | .30 / .31 | .33 / .33 | .04 / .07 |
| SciBench | 7,062 | .17 / .17 | .29 / .29 | .02 / .03 |
| Dataset | Model | |||
|---|---|---|---|---|
| MMLU-ProX | GPT-OSS | 59 | [ 0.029] | 49 |
| MMLU-ProX | DeepSeek | 68 | [ 0.024] | 56 |
| SciBench | GPT-OSS | 41 | [ 0.048] | 36 |
| SciBench | DeepSeek | 47 | [ 0.037] | 39 |
| StrategyQA | GPT-OSS | 57 | [ 0.029] | 36 |
| StrategyQA | DeepSeek | 65 | [ 0.028] | 56 |
| Quantity | EN–ZH | EN–ES | ||
| [95% CI] | ||||
| .371 | .004 | .44 [.23, .62] | .001 | |
| .421 | .001 | .38 [.16, .57] | .001 | |
| .066 | n.s. | .03 [ .21, .26] | .80 | |
| .391 | .002 | .45 [.24, .63] | .001 | |
| .147 | n.s. | .08 [ .31, .16] | .51 | |
Appendix figures & tables29 assets
Supplementary material from the paper’s appendix.
Appendix
| Dataset | top- | calibrated | ||
|---|---|---|---|---|
| StrategyQA | 9,039 | 2,267 | 0.5554 | 0.0000 |
| SciBench | 7,062 | 1,772 | 0.6552 | 0.0000 |
| MMLU-ProX | 8,470 | 2,125 | 0.5906 | 0.0000 |
| Evaluation | floor range | floor spread | ceiling range | ceiling spread |
|---|---|---|---|---|
| MMLU-ProX , Claude Opus 4.6 | 0.187–0.331 | 0.144 | 0.960–0.980 | 0.020 |
| StrategyQA , Claude Opus 4.6 | 0.157–0.381 | 0.224 | 0.912–0.968 | 0.056 |
| SciBench , Claude Opus 4.6 | 0.292–0.352 | 0.059 | 0.980–0.980 | 0.000 |
| pair | |||||
|---|---|---|---|---|---|
| ar-en | 0.943 | 0.941 | |||
| ar-es | 0.960 | 0.957 | |||
| ar-hi | 0.935 | 0.934 | |||
| ar-ru | 0.943 | 0.935 | |||
| ar-vi | 0.922 | 0.923 | |||
| ar-zh | 0.950 | 0.947 |
| MMLU-ProX | StrategyQA | SciBench | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| pair | pair | pair | |||||||||||||
| es-ru | 408 | 4.2% | 0.610 | 0.451 | 0.819 | es-ru | 430 | 0.625 | 0.462 | 0.836 | en-es | 338 | 0.669 | 0.492 | 0.863 |
| en-es | 411 | 3.8% | 0.604 | 0.449 | 0.859 | ar-hi | 434 | 0.622 | 0.419 | 0.798 | es-ru | 336 | 0.645 | 0.483 | 0.812 |
| ru-vi | 409 | 4.8% | 0.585 | 0.429 | 0.799 | ar-zh | 430 | 0.618 | 0.420 | 0.775 | es-vi | 336 | 0.638 | 0.471 | 0.784 |
| ar-es | 409 | 3.2% | 0.583 | 0.423 | 0.789 | vi-zh | 431 | 0.614 | 0.410 | 0.813 | ru-vi | 334 | 0.625 | 0.464 | 0.778 |
| en-zh | 400 | 6.6% | 0.583 | 0.416 | 0.813 | en-zh | 431 | 0.613 | 0.407 | 0.820 | en-vi | 335 | 0.621 | 0.441 | 0.801 |
| metric | MMLU-ProX / StrategyQA | MMLU-ProX / SciBench | StrategyQA / SciBench |
|---|---|---|---|
| ( ) | ( ) | ( ) | |
| ( ) | ( ) | ( ) | |
| ( ) | ( ) | ( ) |
| Dataset | Model | pairs | top- not top- | top- bottom- | ||
|---|---|---|---|---|---|---|
| MMLU-ProX | Claude Haiku 4.5 | 5,459 | 21 | 0.23 | 66.0% | 13.8% |
| MMLU-ProX | Claude Opus 4.6 | 8,470 | 21 | 0.29 | 59.1% | 12.8% |
| MMLU-ProX | DeepSeek-V3.2 | 7,179 | 21 | 0.30 | 60.6% | 12.9% |
| MMLU-ProX | GPT-OSS-120B | 6,552 | 21 | 0.42 | 53.9% | 7.5% |
| MMLU-ProX | Qwen3-235B | 6,656 | 21 | 0.30 | 60.6% | 13.3% |
| MMLU-ProX | Qwen3-32B | 4,714 | 21 | 0.30 | 59.9% | 14.5% |
| top- not top- | mean | |||||||
|---|---|---|---|---|---|---|---|---|
| Dataset | Model | all | matched | % matched | all | matched | ||
| MMLU-ProX | Claude Haiku 4.5 | 5,459 | 66.0% | 68.1% | 37.9% | 0.520 | 0.540 | |
| MMLU-ProX | Claude Opus 4.6 | 8,470 | 59.1% | 56.2% | 38.0% | 0.572 | 0.595 | |
| MMLU-ProX | DeepSeek-V3.2 | 7,179 | 60.6% | 58.0% | 22.5% | 0.542 | 0.565 | |
| MMLU-ProX | GPT-OSS-120B | 6,552 | 53.9% | 52.7% | 41.0% | 0.548 | 0.563 | |
| MMLU-ProX | Qwen3-235B | 6,656 | 60.6% | 61.5% | 20.2% | 0.544 | 0.566 | |
| Case | Chinese-side perturbation | |||
|---|---|---|---|---|
| base (aligned reasoning) | 0.851 | 0.827 | 0.960 | Same five reasoning moves in the same order, translated directly. |
| reversed order steps | 0.834 | 0.857 | 0.964 | Same five moves but in reversed order. |
| step merge (coarser steps) | 0.826 | 0.723 | 0.891 | The first two premises are merged, and feasibility plus conclusion are expressed in fewer coarser steps. |
| step skip (missing steps) | 0.848 | 0.746 | 0.884 | One intermediate historical comparison is omitted while the final answer is preserved. |
| abstraction (semantic drift) | 0.779 | 0.366 | 0.643 | The trace keeps the broad topic but replaces concrete date comparisons with higher-level historical claims. |
| granularity mismatch (uneven split) | 0.825 | 0.631 | 0.839 | The same content is split into uneven step units across the two traces. |
| scheme | Spearman | Pearson | mean |
|---|---|---|---|
| power | |||
| power | |||
| power | |||
| power | |||
| power | |||
| softmax |
| English trace | Spanish trace |
|---|---|
| Step 1. Consider the physical properties of sandals. Sandals are open-toed, minimally insulated footwear that leave significant portions of the feet exposed to the environment. | Step 1. Analicemos la pregunta desde el punto de vista de la seguridad y la salud. Usar sandalias en la nieve implica exponer los pies a temperaturas muy bajas, humedad y superficies resbaladizas. |
| Step 2. Consider the conditions associated with snow. Snow implies temperatures at or below 0 ∘ C, along with wet conditions from snow and slush. | Step 2. Riesgos principales de usar sandalias en la nieve: hipotermia localizada y congelación; resbalones y caídas; entumecimiento; enfermedades. |
| Step 3. Evaluate the risks. Exposed feet in snow can rapidly lose heat, leading to frostbite; sandals also lack traction suitable for icy or snowy surfaces. | Step 3. Comparación con el calzado adecuado: las botas de invierno aíslan, mantienen los pies secos y proporcionan tracción; las sandalias carecen de estas características. |
| Step 4. Consider any mitigating factors. Thick socks with sandals might marginally delay heat loss but do not adequately protect against the hazards. | Step 4. Conclusión: no, no es seguro usar sandalias en la nieve. Se recomienda calzado cerrado, impermeable y con buena tracción. |
| Step 5. Wearing sandals in snow is not safe due to frostbite, hypothermia of the feet, loss of sensation, and increased likelihood of slipping. |
| Hindi trace (translated) | Russian trace (translated) |
|---|---|
| Step 1. Find the initial volume: since compression reduces volume, . | Step 1. List the given data: , bar, , and the process is isothermal. |
| Step 2. Apply Boyle’s law for an isothermal ideal-gas process: . | Step 2. Recover the initial volume: . |
| Step 3. Compute in bar: bar. | Step 3. Apply Boyle’s law and compute in bar: bar. |
| Step 4. Convert bar to atm: atm. | Step 4. Convert pressure units: bar, so atm. |
| Step 5. Express with appropriate significant figures: atm. | Step 5. Round to three significant figures: atm. |
| English trace | Chinese trace (translated) |
|---|---|
| Step 1. Define dormancy as suspended growth and metabolic activity that lets seeds survive unfavorable conditions until germination is suitable. | Step 1. Define dormancy as a special physiological state in which a seed may not germinate even when water, temperature, and oxygen are externally suitable. |
| Step 2. Evaluate the options: reject answers that describe flavor, spontaneous germination, active growth, or a single cue such as light or water. | Step 2. Explain dormancy termination: it typically depends on combinations of temperature, light, water, oxygen, scarification, and species-specific cues. |
| Step 3. Continue eliminating options A–I because each is either harmful, too narrow, or contrary to seed biology. | Step 3. Exclude A–I one by one: each either misunderstands dormancy or treats germination as controlled by a single oversimplified condition. |
| Step 4. Select option J as the comprehensive answer: dormancy is a resting state and germination requires precise environmental combinations. | Step 4. Select option J : it captures both the survival role of dormancy and the need for precise environmental signals. |
| English trace | Spanish trace |
|---|---|
| Step 1. Identify the FCO as a department of the UK government responsible for British foreign affairs. | Step 1. Identifica la FCO como un ministerio del gobierno del Reino Unido responsable de la política exterior y la Commonwealth. |
| Step 2. Define a European political agency as an EU or pan-European institution such as the European Commission or Europol. | Step 2. Determina que una agencia política europea sería una agencia de la Unión Europea o de una organización paneuropea. |
| Step 3. Compare the FCO against that definition and conclude it is a national British institution, not an EU or pan-European agency. | Step 3. Aunque el Reino Unido está geográficamente en Europa, la FCO es un ministerio nacional británico, no una institución supranacional europea. |
| Final. No. | Final. No. |
| English trace | Hindi trace (translated) |
|---|---|
| Step 1. Treat “Hooke Sea” as a fictional or hypothetical sea named after Robert Hooke. | Step 1. Treat Hooke Sea as a fictional sea related to Hooke’s law. |
| Step 2. In the absence of special constraints, assume it is a body of water similar to ordinary seas. | Step 2. Since the sea is fictional, there are no real people there to rescue. |
| Step 3. Lifeboats are designed to rescue people in seas or oceans if they can navigate the conditions. | Step 3. A lifeboat is for rescuing real people, but a fictional sea contains no real rescue target. |
| Final. Yes. | Final. No. |
| English trace | Spanish trace | Chinese trace (translated) |
|---|---|---|
| Rate assumption. Uses 20-payment life \26.47$24.44$1{,}000$ , then tries nearby textbook rates. | Rate assumption. Starts with \25.04$22.86$1{,}000$ , then tries alternate rates. | Rate assumption. Starts with \26.40$24.26$ , then switches to a much wider “common textbook” rate gap. |
| Calculation. Computes differences around \30.45$30.60$ and maps this to option A . | Calculation. Computes \32.70$32.10$32.55$ candidate that maps to option D . | Calculation. Reverse-engineers option I : \31.55/15=$2.1033$1{,}000$2.10$ rate gap. |
| Final. Selects A . | Final. Selects D . | Final. Selects I . |
| Study | Metric | sample sd | pool sd | ratio |
|---|---|---|---|---|
| EN–ZH | 0.103 | 0.102 | 1.02 | |
| EN–ZH | 0.048 | 0.053 | 0.90 | |
| EN–ES | 0.109 | 0.105 | 1.04 | |
| EN–ES | 0.042 | 0.047 | 0.89 |
| Dataset | Quantity | LaBSE | BGE-M3 | MiniLM |
|---|---|---|---|---|
| StrategyQA | 0.220 | 0.232 | 0.111 | |
| Mismatch | 55.5% | 50.1% | 58.7% | |
| — | 0.803 | 0.696 | ||
| — | 0.876 | 0.795 | ||
| MMLU-ProX | 0.231 | 0.244 | 0.134 | |
| Mismatch | 59.1% | 52.2% | 57.9% |
| Dataset | Model | 95% CI | Rank | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| MMLU-ProX | GPT-OSS-120B | 59 | [ , ] | 8.32 | 49 | 0.599 | 0.500 | 1/22 | ||
| MMLU-ProX | DeepSeek-V3.2 | 68 | [ , ] | 5.79 | 56 | 0.416 | 0.389 | 1/22 | ||
| SciBench | GPT-OSS-120B | 41 | [ , ] | 5.76 | 36 | 0.441 | 0.353 | 1/22 | ||
| SciBench | DeepSeek-V3.2 | 47 | [ , ] | 4.50 | 39 | 0.404 | 0.357 | 1/22 | ||
| StrategyQA | GPT-OSS-120B | 57 | [ , ] | 2.80 | 36 | 0.438 | 0.401 | 4/22 | ||
| StrategyQA | DeepSeek-V3.2 | 65 | [ , ] | 7.31 | 56 | 0.335 | 0.267 | 1/22 |
| Dataset | Model | Floor | en-anch. floors | Bias | Share | Corrected | Thr. |
|---|---|---|---|---|---|---|---|
| MMLU-ProX | GPT-OSS-120B | 0.209 | 0.191–0.253 | 3% | 0.030 | ||
| MMLU-ProX | DeepSeek-V3.2 | 0.195 | 0.203–0.259 | 20% | 0.030 | ||
| SciBench | GPT-OSS-120B | 0.373 | 0.368–0.397 | 9% | 0.015 | ||
| SciBench | DeepSeek-V3.2 | 0.317 | 0.327–0.358 | 29% | 0.015 | ||
| StrategyQA | GPT-OSS-120B | 0.200 | 0.182–0.268 | 13% | — | ||
| StrategyQA | DeepSeek-V3.2 | 0.174 | 0.164–0.229 | 1% | — |
| Top- not top- | Mean | Mean | |||||
|---|---|---|---|---|---|---|---|
| Dataset | Model | within | cross-lingual | within | cross | within | cross |
| MMLU-ProX | GPT-OSS-120B | 43.8% | 54.8% | 0.658 | 0.534 | 0.922 | 0.804 |
| MMLU-ProX | DeepSeek-V3.2 | 52.9% | 64.6% | 0.609 | 0.543 | 0.923 | 0.813 |
| SciBench | GPT-OSS-120B | 45.5% | 63.8% | 0.695 | 0.562 | 0.929 | 0.814 |
| SciBench | DeepSeek-V3.2 | 41.7% | 62.4% | 0.591 | 0.509 | 0.917 | 0.811 |
| StrategyQA | GPT-OSS-120B | 60.0% | 50.5% | 0.615 | 0.575 | 0.911 | 0.803 |
| q1 | q2 | q3 | q4 | q5 | |
|---|---|---|---|---|---|
| All | 0.556 | 0.561 | 0.551 | 0.531 | 0.492 |
| StrategyQA | 0.589 | 0.575 | 0.526 | 0.487 | 0.483 |
| SciBench | 0.546 | 0.583 | 0.600 | 0.588 | 0.494 |
| MMLU-ProX | 0.539 | 0.529 | 0.528 | 0.515 | 0.497 |
| first | middle | last | last middle | 95% CI | ||
|---|---|---|---|---|---|---|
| All | all | 0.563 | 0.546 | 0.504 | [ , ] | |
| eq. | 0.591 | 0.573 | 0.515 | [ , ] | ||
| StrategyQA | all | 0.596 | 0.534 | 0.494 | [ , ] | |
| eq. | 0.622 | 0.549 | 0.498 | [ , ] | ||
| SciBench | all | 0.536 | 0.580 | 0.513 | [ , ] | |
| eq. | 0.558 | 0.618 | 0.541 | [ , ] |
| mean position | share at first step | |||||
|---|---|---|---|---|---|---|
| threshold | 0.4 | 0.5 | 0.6 | 0.4 | 0.5 | 0.6 |
| SciBench | 0.315 | 0.207 | 0.129 | 0.445 | 0.573 | 0.698 |
| MMLU-ProX | 0.383 | 0.253 | 0.141 | 0.274 | 0.451 | 0.654 |
| StrategyQA | 0.495 | 0.368 | 0.230 | 0.234 | 0.348 | 0.532 |
| q1 | q2 | q3 | q4 | q5 | q1 q5 [95% CI] | |
|---|---|---|---|---|---|---|
| es | 0.592 | 0.590 | 0.580 | 0.559 | 0.520 | [ , ] |
| zh | 0.563 | 0.574 | 0.565 | 0.548 | 0.510 | [ , ] |
| ar | 0.554 | 0.561 | 0.553 | 0.533 | 0.494 | [ , ] |
| ru | 0.552 | 0.557 | 0.547 | 0.523 | 0.483 | [ , ] |
| vi | 0.550 | 0.549 | 0.536 | 0.512 | 0.472 | [ , ] |
| hi | 0.525 | 0.534 | 0.527 | 0.508 | 0.474 | [ , ] |
| Group | median | median | |
|---|---|---|---|
| Both correct (reference) | 11,176 | 0.570 | 0.837 |
| Both wrong, same answer | 225 | 0.511 | 0.834 |
| Both wrong, different answers | 137 | 0.528 | 0.816 |
| Exactly one correct | 1,318 | 0.512 | 0.814 |
| Contrast | |||
|---|---|---|---|
| Same wrong answer | [ , ] | [ , ] | [ , ] |
| matched on | [ , ] | [ , ] | [ , ] |
| matched on dataset, | [ , ] | [ , ] | [ , ] |
| Exactly one correct |
| Ranking | found at 25% budget |
|---|---|
| structural | [ , ] |
| holistic | [ , ] |
| random | |
| paired difference | points [ , ] |
Multilingual Language Model Evaluation
Multilingual Language Model Evaluation measures how reliably language models perform across languages, scripts, dialects, and cultural contexts.
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