What Does Post-Training Change in Multilingual Reasoning?

Hongyang Li; Xiao Li; Caesar Wu; Grégoire Danoy; Pascal Bouvry

cs.CLSep 29, 2026

What Does Post-Training Change in Multilingual Reasoning?

Authors: Hongyang Li, Xiao Li, Caesar Wu, Grégoire Danoy, Pascal Bouvry

Organizations: University of Luxembourg · Seafill Open-Source Community

Abstract

Open-source reasoning models provide unequal access to reasoning capability across languages. When a model can solve a problem but cannot deliver a complete solution in the user's language, language becomes an access barrier rather than merely a source of performance variation. We audit Qwen3 checkpoints on competition-mathematics tasks in eleven languages. Across the ten non-English languages, only 15.4-17.9% of problems receive a correct, terminating solution with visible reasoning in the requested language in any of 16 samples, compared with 92.9% in English. To identify the source of this disparity, we evaluate thirteen endpoints from one model family, spanning released checkpoints, multilingual supervised fine-tuning (SFT) at two scales, controlled SFT ablations, and three reinforcement-learning (RL) reward formulations. We jointly track correctness, language adherence, termination, and delivery efficiency. The dominant bottleneck shifts across post-training stages. Released models often reason in English. Multilingual SFT restores target-language reasoning, but accuracy declines across multilingual, English-only, and single-language SFT runs, showing that this cost is not specific to multilingual mixing; non-English reasoning traces additionally become prone to non-terminating loops. RL restores termination in both arms at no cost in accuracy, but only the arm whose reward includes a language term delivers: rewarding correctness alone returns the model to English. Together, these stages establish a constructive post-training path from English-pivoted capability to multilingual reasoning that is reliably delivered.

Figures & tables

stage	intervention	endpoint	$C@1$	$L$	$1{-}T$	$J@1$	$J@16$	eff. vs En	dominant residual
I	released	Qwen3-8B	$78.1\%$	$26.9\%$	$5.8\%$	$19.6\%$	$30.6\%$	$27\%$	language selection
II	multilingual SFT	+ SFT (8B)	$66.0\%$	$99.7\%$	$18.2\%$	$65.1\%$	$86.3\%$	$78\%$	termination
I	released	Qwen3-4B	$76.2\%$	$39.8\%$	$4.7\%$	$28.6\%$	$35.7\%$	$47\%$	language selection
II	multilingual SFT	+ SFT	$61.4\%$	$99.4\%$	$21.1\%$	$60.2\%$	$84.6\%$	$73\%$	termination
III	correctness-only RL	RL: correctness only	$60.5\%$	$8.7\%$	$0.3\%$	$5.0\%$	$15.4\%$	$9\%$	returns to English
III	target-language RL	RL: additive $\rightarrow$ gated	$60.1\%$	$99.8\%$	$0.5\%$	$60.0\%$	$81.7\%$	$102\%$	answer correctness

Table 1: One protocol exposes a staged repair. The upper block reports the released and multilingual-SFT Qwen3-8B endpoints; the lower block reports the full Qwen3-4B lineage. Stage III has a correctness-only control and a target-language procedure whose gated phase continues its additive phase.

C@1

L

1-T

, and

J@1

are sample-level rates, and

J@16

is pass@16, averaged over the five primary non-English languages. Green indicates delivery and red non-termination. Eff. vs En is relative adjusted delivery efficiency, with

100\%

denoting parity; at the released checkpoints that mean is carried by Chinese and Russian alone, because the other three languages deliver nothing. Dominant residual identifies the remaining bottleneck.

run	initialized from	examples	batch	epochs (cfg.)	evaluated at
supervised
multilingual 4B	Qwen3-4B	43,218	16	5	epoch 2, step 5,402
multilingual 8B	Qwen3-8B	56,307	16	2	epoch 1, step 3,519
English-only	Qwen3-4B	9,800	4	3	epoch 1, step 2,450
specialist zh	Qwen3-4B	9,334	4	3	epoch 1
specialist es	Qwen3-4B	9,491	4	3	epoch 1

Table 2: Complete training ledger. The Qwen3-8B chain changes both model scale and corpus; the English-only and specialist controls differ in batch size and data volume; and the gated PPO run continues the additive run rather than restarting from the supervised checkpoint. Reward curves and held-out losses for these runs appear in Figure 2 .

stage	adjusted	raw	adjusted	raw	token yield
	all attempts		$J$ -only
Qwen3-4B	$47\%$	$41\%$	–	–	$34\%$
+ SFT	$73\%$	$62\%$	$110\%$	$94\%$	$67\%$
RL: correctness only	$9\%$	$9\%$	–	–	$6\%$
RL: gated	$102\%$	$87\%$	$117\%$	$100\%$	$88\%$
Qwen3-8B	$27\%$	$26\%$	–	–	$23\%$

Table 3: Delivery efficiency under four accounting conventions. Efficiency is joint successes per 1,000 generated tokens. Every entry is a percentage of the same endpoint’s English value, so

100\%

means parity with English; the four efficiency columns average the five primary non-English languages, and the yield column pools them. The conventions differ in which tokens are counted. Adjusted first divides each trace by its language’s encoding factor—the same text costs between

1.003

times (Chinese) and

1.314

times (Russian) as many tokens as in English, purely because of how the tokenizer segments the script—so an adjusted column asks whether the model produced more reasoning , while a raw column counts the tokens a user is actually billed for. All attempts charges every generated token, including those spent on responses that never delivered;

J

-only charges only the tokens inside delivered solutions. The two are linked by token yield : the share of a language’s generated tokens that ends up inside a delivered solution, here the non-English share as a percentage of the endpoint’s English share. All-attempt efficiency is

J

-only efficiency times yield, and the identity holds in these ratios exactly as it does in the underlying absolute shares. Absolute per-language yields are in Appendix C (Table S17 ).

J

-only is undefined, and omitted, where a language delivers nothing.

Qwen3-4B (released)
what the prompt supplies	zh	es	fr	ar	ru
$X$ problem, asks $X$	$99.6\%$	$0.1\%$	$0.0\%$	$0.0\%$	$99.2\%$
English problem, asks $X$	$0.0\%$	$0.0\%$	$0.0\%$	$0.0\%$	$4.2\%$
$+$ multilingual SFT
$X$ problem, asks $X$	$99.9\%$	$99.6\%$	$99.0\%$	$98.4\%$	$99.9\%$
English problem, asks $X$	$0.0\%$	$2.5\%$	$0.8\%$	$0.0\%$	$94.2\%$

Table 4: The problem language is a stronger cue than the requested reasoning language. Entries report target-language adherence for Qwen3-4B endpoints, where X is the language of the column (Chinese, Spanish, French, Arabic, or Russian). “X problem, asks X” uses the main 70-problem evaluation; “English problem, asks X” uses the separate 30-problem probe. Each cell contains 1,120 and 120 samples, respectively.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

checkpoint	language	$C$ @16 [95% CI]	$J$ @16 [95% CI]	$L$	$1{-}T$	cap only	looping	tokens
Qwen3-4B	English	$92.9\%$ [85.7, 98.6]	$92.9\%$ [85.7, 98.6]	$100.0\%$	$6.8\%$	$6.7\%$	$0.1\%$	9,568
	Chinese	$91.4\%$ [84.3, 97.1]	$91.4\%$ [84.3, 97.1]	$99.6\%$	$3.4\%$	$2.5\%$	$0.9\%$	8,127
	Spanish	$91.4\%$ [84.3, 97.1]	$1.4\%$ [0.0, 4.3]	$0.1\%$	$4.7\%$	$4.4\%$	$0.4\%$	7,928
	French	$92.9\%$ [85.7, 98.6]	$0.0\%$ [0.0, 0.0]	$0.0\%$	$2.7\%$	$2.7\%$	$0.0\%$	7,158
	Arabic	$91.4\%$ [84.3, 97.1]	$0.0\%$ [0.0, 0.0]	$0.0\%$	$3.8\%$	$3.5\%$	$0.4\%$	7,613
	Russian	$85.7\%$ [77.1, 92.9]	$85.7\%$ [77.1, 92.9]	$99.2\%$	$8.8\%$	$3.1\%$	$5.6\%$	8,380

Appendix

Table S1: Accuracy and joint delivery with 95% problem-clustered bootstrap intervals. The two termination columns are budget exhaustion without repetition and detected looping; a trace can satisfy both conditions. “tokens” is the mean over all attempts.

		outcome			two instruments for $L$
model	lang	$C@16$	$J@16$	gap	langid- $L$	judge-en	judge-tgt	judge-frac
Qwen3-4B	is	$78.6\%$	$0.0\%$	$78.6\%$	$0.0\%$	$84.4\%$	$0.0\%$	$2.0\%$
	sv	$92.9\%$	$0.0\%$	$92.9\%$	$0.0\%$	$96.9\%$	$0.0\%$	$0.5\%$
	sw	$54.3\%$	$0.0\%$	$54.3\%$	$0.0\%$	$78.1\%$	$0.0\%$	$1.9\%$
	ta	$80.0\%$	$0.0\%$	$80.0\%$	$0.0\%$	$93.8\%$	$0.0\%$	$0.8\%$
	ur	$84.3\%$	$0.0\%$	$84.3\%$	$0.0\%$	$90.6\%$	$0.0\%$	$1.0\%$

Appendix

Table S2: Robustness audit over five additional languages, none of which appears in any corpus we construct; gap is

C@16-J@16

. The right-hand block reports two independently constructed instruments for

L

. langid-

L

is the automatic per-response criterion, with the langid candidate set extended to all eleven evaluation languages so that these five can be detected at all. judge-en and judge-tgt are the shares of sampled traces a blind LLM judge labels as reasoning in English and in the target language, and judge-frac is its estimate of how much of the trace is written in the target language. The two instruments agree in all ten cells, and judge-en is a positive identification of English rather than a failure to identify the target language, so the absent target-language reasoning is a property of the models and not an artifact of either instrument.

instructed language	$n$	$L$	target frac.	$C$
en	120	$100.0\%$	$91.3\%$	$56.7\%$
zh	120	$0.0\%$	$5.7\%$	$59.2\%$
es	120	$2.5\%$	$3.6\%$	$59.2\%$
fr	120	$0.8\%$	$1.7\%$	$56.7\%$
ar	120	$0.0\%$	$0.3\%$	$54.2\%$
ru	120	$94.2\%$	$86.7\%$	$46.7\%$

Appendix

Table S3: English problem text with an instruction to reason in the listed language, multilingual SFT on Qwen3-4B.

L

measures the language of the visible solution trace; “target frac.” is its mean instructed-language fraction.

		mechanical fidelity				blind
language	translator	boxed	digits	L a T e X	trunc.	faithfulness
Chinese	Qwen3-14B	$100.0\%$	$99.7\%$	$100.0\%$	$0.0\%$	$4.90$
	Hunyuan-MT-7B	$97.0\%$	$93.9\%$	$100.0\%$	$0.4\%$	$3.04$
Spanish	Qwen3-14B	$100.0\%$	$100.0\%$	$100.0\%$	$0.0\%$	$4.88$
	Hunyuan-MT-7B	$96.6\%$	$91.8\%$	$100.0\%$	$0.0\%$	$3.12$
French	Qwen3-14B	$100.0\%$	$99.9\%$	$100.0\%$	$0.0\%$	$4.96$

Appendix

Table S4: Pre-registered translator comparison, per language. Mechanical columns are over 2,515 aligned chunks per arm; faithfulness is a blind judge score over 250 randomized pairs. The pre-specified number-recall pass mark was

.98

language	coherence	fidelity	reaches \boxed	math kept	no major leak
Chinese	$4.90$	$4.62$	$99.6\%$	$100.0\%$	$96.0\%$
Spanish	$4.78$	$4.40$	$99.6\%$	$100.0\%$	$94.0\%$
French	$4.81$	$4.32$	$99.6\%$	$100.0\%$	$95.6\%$
Arabic	$4.47$	$3.54$	$99.6\%$	$99.6\%$	$84.0\%$
Russian	$4.76$	$4.40$	$100.0\%$	$98.8\%$	$94.4\%$
English (untranslated)	$4.88$	—	$100.0\%$	$100.0\%$	—

Appendix

Table S5: Audit of the 4B multilingual corpus, 250 sampled traces per language. Coherence and target-language fidelity are independent judge scores on a five-point scale; the last column is the share of traces free of moderate or severe English residue. The English row is the untranslated source, i.e. the floor these scores are read against.

Hyperparameter	Value
Framework	verl SFT trainer, FSDP
Base models	Qwen3-4B, Qwen3-8B (released, post-trained)
Chat template	Qwen3, thinking enabled
Sequence cutoff length	32,768 (Arabic specialist: 24,576)
Padding	no_padding
Truncation	left

Appendix

Table S6: Key training hyperparameters used in supervised fine-tuning.

Hyperparameter	Value
Framework	verl, FSDP
Algorithm	PPO, GAE advantages
Initialized from	multilingual SFT on Qwen3-4B / additive @ step 200 (gated)
Training dataset	DAPO-Math-17K, localized (16,754 prompts; 16,751 after the over-length filter)
Max prompt length	2048
Max response length	16384 / 8192 (gated)

Appendix

Table S7: Key training hyperparameters used in reinforcement learning. Values separated by a slash differ between the correctness-only and additive runs on one side and the gated continuation on the other.

comparison	$\Delta J@1\,(\mathrm{NE})$	$\Delta C_{\mathrm{en}}$	$\Delta{(1-T)}_{\mathrm{NE}}$
Qwen3-4B $\to$ SFT	$+31.6\%$	$-8.8\%$	$+16.4\%$
Qwen3-8B $\to$ SFT	$+45.5\%$	$-6.8\%$	$+12.4\%$
Qwen3-4B $\to$ English-only	$-5.7\%$	$-9.2\%$	$+4.0\%$
mixed $-$ spec. (own)	$[-0.03,+0.03]$	–	–
mixed $-$ spec. (en)	–	$[+0.01,+0.05]$	–

Appendix

Table S8: Compact SFT control summary. NE denotes the five primary non-English languages. The mixed–specialist rows compare the Qwen3-4B multilingual SFT endpoint with the five Qwen3-4B single-language specialists, paired on each specialist’s own language or on English.

edge	lang	$\Delta J@1$	$\Delta C$	$\Delta$ term. fail.
Qwen3-4B $\to$ multilingual SFT	en	$-8.7\%$	$-8.8\%$	$-3.6\%$
	zh	$-16.5\%^{*}$	$-16.6\%^{*}$	$+17.4\%^{*}$
	es	$+64.5\%^{*}$	$-14.8\%^{*}$	$+7.6\%^{*}$
	fr	$+64.5\%^{*}$	$-13.9\%^{*}$	$+10.3\%^{*}$
	ar	$+53.6\%^{*}$	$-22.1\%^{*}$	$+27.9\%^{*}$
	ru	$-7.9\%^{*}$	$-6.2\%^{*}$	$+18.8\%^{*}$

Appendix

Table S9: Per-language paired deltas for the three SFT-side comparisons ( ∗ : significant after Holm correction). The English-default languages drive the delivery gains, while correctness declines in English as well as the target languages.

Qwen3-4B $\rightarrow$ multilingual SFT-4B
	English	Chinese	Spanish	French	Arabic	Russian
looping	$+0.002$	$+0.175$ ∗	$+0.062$ ∗	$+0.088$ ∗	$+0.259$ ∗	$+0.173$ ∗
ran out of room	$-0.037$	$-0.001$	$+0.013$	$+0.014$	$+0.020$	$+0.014$
Qwen3-8B $\rightarrow$ multilingual SFT-8B
looping	$+0.004$	$+0.121$ ∗	$+0.047$ ∗	$+0.082$ ∗	$+0.258$ ∗	$+0.141$ ∗
ran out of room	$-0.067$	$-0.011$	$+0.002$	$+0.004$	$-0.016$	$-0.011$

Appendix

Table S10: Paired changes in termination failures. Asterisks mark Holm-corrected significance within each five-language comparison family.

	English	Chinese	Spanish	French	Arabic	Russian	non-English
Qwen3-4B	$92.9\%$	$91.4\%$	$1.4\%$	$0.0\%$	$0.0\%$	$85.7\%$	$\mathbf{35.7\%}$
+ SFT	$94.3\%$	$85.7\%$	$87.1\%$	$87.1\%$	$80.0\%$	$82.9\%$	$\mathbf{84.6\%}$
RL: gated	$85.7\%$	$81.4\%$	$80.0\%$	$87.1\%$	$80.0\%$	$80.0\%$	$\mathbf{81.7\%}$
Qwen3-8B	$92.9\%$	$91.4\%$	$0.0\%$	$0.0\%$	$0.0\%$	$61.4\%$	$\mathbf{30.6\%}$
+ SFT (8B)	$94.3\%$	$85.7\%$	$88.6\%$	$84.3\%$	$85.7\%$	$87.1\%$	$\mathbf{86.3\%}$

Appendix

Table S11:

J@16

through the main lineage. The upper block is Qwen3-4B (released,

+

six-language SFT,

+

correctness-gated RL) and the lower block Qwen3-8B (released,

+

SFT); no RL was run at 8B. The non-English column averages the five primary non-English languages.

diagnostic	additive endpoint	gated continuation	scope
task–language component	$.7C_{\rm tr}{+}.3\ell_{\rm tr}$	$C_{\rm tr}(.7{+}.3\ell_{\rm tr})$	training configuration
positive reward mass on wrong	$63.1\%$	$0.0\%$	recorded rollouts
correct and target-language	$20.5\%$	$43.8\%$	late training rollouts
mean response tokens	1960	1983	late training rollouts
AIME accuracy	$5.0\%$	$17.2\%$	monitored development

Appendix

Table S12: Reward-accounting diagnostics from recorded PPO rollouts of the two Qwen3-4B correctness–language phases—the additive phase, and the gated phase continuing it from step 200—of one procedure initialized from the Qwen3-4B multilingual SFT checkpoint. These values describe training dynamics, not held-out capability.

	en	zh	es	fr	ar	ru
en	—	$.92$	$.97$	$.97$	$.93$	$.86$
zh	$.92$	—	$.90$	$.92$	$.87$	$.87$
es	$.97$	$.90$	—	$.99$	$.91$	$.88$
fr	$.97$	$.92$	$.99$	—	$.91$	$.88$
ar	$.93$	$.87$	$.91$	$.91$	—	$.82$
ru	$.86$	$.87$	$.88$	$.88$	$.82$	—

Appendix

Table S13: Pearson correlation of problem-level correctness between language versions of the same 70 items, measured on the released Qwen3-4B. High values mean the translation preserved which problems are difficult.

endpoint	RL corpus	$J@16$ (70)	$J@16$ (56)	change	excess over SFT
Qwen3-4B	no	$35.7\%$	$34.3\%$	$-1.4\%$	—
+ SFT	no	$84.6\%$	$82.1\%$	$-2.4\%$	—
RL: correctness only	yes	$15.4\%$	$15.0\%$	$-0.4\%$	$+2.0\%$
RL: additive	yes	$83.4\%$	$80.4\%$	$-3.1\%$	$-0.6\%$
RL: gated	yes	$81.7\%$	$78.2\%$	$-3.5\%$	$-1.1\%$

Appendix

Table S14:

J@16

on all 70 evaluation problems and on the 56 that do not appear in the RL training corpus, averaged over the five primary non-English languages. “Excess over SFT” is the endpoint’s signed change minus the supervised parent’s signed change; a negative value would indicate a memorization advantage.

endpoint	en	zh	es	fr	ar	ru
Qwen3-4B	$92.9\%$ ( $0.0\%$ )	$91.4\%$ ( $0.0\%$ )	$1.4\%$ ( $90.0\%$ )	$0.0\%$ ( $92.9\%$ )	$0.0\%$ ( $91.4\%$ )	$85.7\%$ ( $0.0\%$ )
Qwen3-8B	$92.9\%$ ( $0.0\%$ )	$91.4\%$ ( $0.0\%$ )	$0.0\%$ ( $94.3\%$ )	$0.0\%$ ( $92.9\%$ )	$0.0\%$ ( $92.9\%$ )	$61.4\%$ ( $30.0\%$ )
multilingual SFT	$94.3\%$ ( $0.0\%$ )	$85.7\%$ ( $0.0\%$ )	$87.1\%$ ( $0.0\%$ )	$87.1\%$ ( $0.0\%$ )	$80.0\%$ ( $1.4\%$ )	$82.9\%$ ( $1.4\%$ )
multilingual SFT (8B)	$94.3\%$ ( $0.0\%$ )	$85.7\%$ ( $0.0\%$ )	$88.6\%$ ( $0.0\%$ )	$84.3\%$ ( $0.0\%$ )	$85.7\%$ ( $0.0\%$ )	$87.1\%$ ( $2.9\%$ )
English-only SFT	$90.0\%$ ( $0.0\%$ )	$84.3\%$ ( $0.0\%$ )	$0.0\%$ ( $85.7\%$ )	$0.0\%$ ( $87.1\%$ )	$0.0\%$ ( $85.7\%$ )	$78.6\%$ ( $0.0\%$ )
specialist zh	$88.6\%$ ( $0.0\%$ )	$84.3\%$ ( $0.0\%$ )	–	–	–	–

Appendix

Table S15:

J@16

for all endpoints, with

C@16-J@16

in parentheses. Every endpoint is a Qwen3-4B derivative except the two rows named Qwen3-8B and multilingual SFT (8B); “multilingual SFT” is the six-language Qwen3-4B checkpoint from which the correctness-only and additive runs start. The additive and gated rows complete the endpoint ledger and are not a matched reward-form comparison.

stage	tokens charged	zh	es	fr	ar	ru
Qwen3-4B	all attempts	$109$ (108)	$0$ (0)	$0$ (0)	$0$ (0)	$128$ (98)
	$J$ -only	$131$ (131)	$\dagger$	–	–	$169$ (128)
+ SFT	all attempts	$64$ (63)	$84$ (71)	$83$ (69)	$59$ (48)	$77$ (59)
	$J$ -only	$121$ (120)	$104$ (88)	$103$ (86)	$113$ (92)	$108$ (82)
RL: correctness only	all attempts	$44$ (44)	$0$ (0)	$0$ (0)	$0$ (0)	$1$ (1)
	$J$ -only	$134$ (134)	–	–	–	$\dagger$

Appendix

Table S16: Delivery efficiency by language, as a percentage of the same endpoint’s English efficiency. Each cell is encoding-adjusted, with the raw-token value in parentheses.

\dagger

marks a

J

-only cell with fewer than 20 delivered samples out of 1,120, which is too thin to report; – marks zero delivered samples. Chinese is nearly unaffected by the adjustment because its encoding factor is

1.003

, whereas Russian is affected most at

1.314

stage	en	zh	es	fr	ar	ru
Qwen3-4B	$59.7$	$49.4$	$0.1$	$0.0$	$0.0$	$45.7$
+ SFT	$45.9$	$24.2$	$37.0$	$37.0$	$24.0$	$32.9$
RL: correctness only	$37.1$	$12.1$	$0.0$	$0.0$	$0.0$	$0.5$
RL: additive	$35.6$	$31.4$	$35.4$	$34.3$	$32.8$	$35.4$
RL: gated	$39.8$	$32.4$	$36.7$	$37.6$	$31.0$	$36.8$
Qwen3-8B	$61.5$	$50.8$	$0.0$	$0.0$	$0.0$	$15.6$

Appendix

Table S17: Token yield: the percentage of generated tokens that sit inside a delivered solution, by language and stage, in raw tokens. This quantity is dimensionless and tokenizer-independent, and it is the factor that separates the two conventions in the main paper’s efficiency table.

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