We investigate whether performing reasoning in a continuous latent space leads to more robust multilingual capabilities. We compare Continuous Chain-of-Thought (using the CODI framework) against standard supervised fine-tuning across five typologically diverse languages: English, Chinese, German, French, and Urdu. Our experiments on GSM8k and CommonsenseQA demonstrate that continuous reasoning significantly outperforms explicit reasoning on low-resource languages, particularly in zero-shot settings where the target language was not seen during training. Additionally, this approach achieves extreme efficiency, compressing reasoning traces by approximately 29× to 50×. These findings indicate that continuous latent representations naturally exhibit greater language invariance, offering a scalable solution for cross-lingual reasoning.
Figures & tables
Test Language
GSM8K-AUG-NL
CommonsenseQA
CODI
CoT-SFT
CODI
CoT-SFT
German
31.79
36.09
58.48
38.41
French
32.35
38.21
57.66
46.03
Chinese
30.46
27.37
57.58
48.40
English
46.08
55.04
71.42
63.23
Urdu
9.58
5.38
32.57
21.87
Table 1: Accuracy (%) on GSM8K-AUG-NL and CommonsenseQA (test splits) comparing CODI vs. CoT-SFT when trained on English.
Figure 1: Performance of LLaMA3.2-1B-Instruct trained on multi-lingual GSM8k-Aug-NL data. Both models perform similarly, with CoT-SFT performing better for high-resource languages and CODI performing better for low-resource languages. Moreover, CODI performs significantly better than CoT-SFT on Urdu when it is Out-of-distribution (OOD) (i.e., when Urdu was not part of the fine-tuning data).
Dataset
CoT-SFT (Avg Tokens)
CODI (Latent Tokens)
Compression Ratio
GSM8K-Aug-NL
∼ 176
6
∼ 29 ×
CommonsenseQA
∼ 299
6
∼ 50 ×
Table 2: Efficiency comparison between explicit and continuous reasoning. Average CoT lengths are calculated across all 5 test languages using the Multi-Lingual-with-Urdu training setup (see Tables 8 & 9 in the appendix).
Figure 3: Performance on a low-resource language (Urdu). The latent reasoning approach works significantly better than CoT-SFT in all cases.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Training Dataset
Train Setup
Test Language
Accuracy (%)
CODI
COT-SFT
GSM8K-Aug-NL
Multi-Lingual
German
44.76
43.20
French
45.19
45.07
Chinese
43.75
35.60
English
46.47
51.20
Urdu
12.28
6.84
Appendix
Table 3: Accuracy (%) on GSM8K-Aug-NL (test split): CODI vs. COT-SFT across training setups.
Training Dataset
Train Setup
Test Language
Accuracy (%)
CODI
COT-SFT
CommonSenseQA
Multi-Lingual
German
58.72
49.71
French
57.65
49.39
Chinese
57.66
51.52
English
71.42
62.49
Urdu
35.95
23.01
Appendix
Table 4: Accuracy (%) on CommonSenseQA (test split) across test languages for different training setups (CODI vs. COT-SFT).
Test Language
Base Accuracy (%)
German
26.84
French
25.32
Chinese
23.50
English
36.01
Urdu
7.66
Appendix
Table 5: Base model accuracy (%) on GSM8K-Aug-NL by test language (independent of fine-tuning setup).
Test Language
Base Accuracy (%)
German
33.09
French
39.89
Chinese
41.28
English
44.49
Urdu
26.54
Appendix
Table 6: Base model accuracy (%) on CommonSenseQA (test split) by test language (independent of fine-tuning setup).
Hyperparameter
Value
Shared Parameters (CODI & CoT-SFT)
Learning Rate
8×10−4
LR Scheduler
Cosine
Warmup Ratio
0.03
Weight Decay
0.1
Max Gradient Norm
2.0
Appendix
Table 7: Training hyperparameters for CODI and CoT-SFT. All parameters are kept constant across both GSM8k-Aug-NL and CommonsenseQA datasets to ensure fair comparison.
Training Dataset
Train Setup
Test Language
Avg CoT Length (tokens)
GSM8K_AUG_NL
English
German
172.2
French
161.6
Chinese
171.4
English
155.4
Urdu
512.0
Multi-Lingual
German
239.6
Appendix
Table 8: Average Chain-of-Thought (CoT) length (tokens) on GSM8K_AUG_NL across training setups and test languages (CoT-SFT).
Training Dataset
Train Setup
Test Language
Avg CoT Length (tokens)
CommonsenseQA
English
German
455.1
French
329.1
Chinese
203.8
English
205.5
Urdu
512.0
Multi-Lingual
German
296.8
Appendix
Table 9: Average Chain-of-Thought (CoT) length (tokens) on CommonsenseQA across training setups and test languages (CoT-SFT).
Cross-lingual chain-of-thought (XCoT) with self-consistency markedly enhances multilingual reasoning, yet existing methods remain costly due to extensive sampling of full trajectories across languages. Moreover, multilingual LLM representations vary strongly by language, hindering direct feature comparisons and effective pruning. Motivated by this, we introduce UL-XCoT, the first efficient unified logic cross-lingual reasoning framework that minimizes redundancy in token usage and latency, yielding the greatest efficiency under limited sampling budgets during inference. Specifically, UL-XCoT (1) achieves less languages by selecting, per query, a small candidate language set in a language-invariant unified logic space, (2) enables less tokens by monitoring logic-space trajectory dynamics during decoding to prune low-quality reasoning paths, and (3) aggregates the remaining high-quality trajectories via voting. Experiments on PolyMath across 18 languages and MMLU-ProX-Lite across 29 languages with DeepSeek-R1-DistillQwen-7B demonstrate that UL-XCoT achieves competitive accuracy while sharply cutting over 50% decoding token cost versus prior sampling baselines. UL-XCoT also delivers more stable gains on low-resource languages, underscoring consistently superior robustness where standard XCoT self-consistency method fails.
Chenyuan Zhang, Qiguang Chen, Xie Chen +6
Harbin Institute of Technology, Shenzhen · Shanghai Innovation Institute · Central South University +3
Despite expanding their multilingual coverage, the advanced reasoning capabilities of LLMs remain largely confined to a few high-resource languages like English. To address this, we propose an unsupervised Reinforcement Learning (RL) approach to enhance multilingual reasoning by enforcing cross-lingual self-consistency: the principle that a model should produce the same final answer for equivalent problems in different languages. Existing methods are limited by the scarcity of multilingual reasoning data and show weak generalization to unseen languages. Our approach requires neither gold answers nor parallel data, and it achieves average gains of up to 21.7% on MGSM across 10 languages. In addition, our method demonstrates strong generalization, with an 18.2% mean improvement on MGSM languages unseen during training, and up to 6.2% gain on 3 out-of-distribution benchmarks. These results show the potential of consistency-based methods to improve the multilingual capabilities of LLMs without requiring supervised data.
Ahmed Elhady, Eneko Agirre, Mikel Artetxe
HiTZ Center, University of the Basque Country (UPV/EHU) · Reka AI
As LLMs reduce English-centric bias, a surprising trend emerges: non-English responses sometimes outperform English on reasoning tasks. We hypothesize that language functions as a latent variable that structurally modulates the model's internal inference pathways, rather than merely serving as an output medium. To test this, we conducted a Polyglot Thinking Experiment, in which models were prompted to solve identical problems under language-constrained and language-unconstrained conditions. Results show that non-English responses often achieve higher accuracy, and the best performance frequently occur when language is unconstrained, suggesting that multilinguality broadens the model's latent reasoning space. Based on this insight, we propose polyGRPO (Polyglot Group Relative Policy Optimization), an RL framework that treats language variation as an implicit exploration signal. It generates polyglot preference data online under language-constrained and unconstrained conditions, optimizing the policy with respect to both answer accuracy and reasoning structure. Trained on only 18.1K multilingual math problems without chain-of-thought annotations, polyGRPO improves the base model (Qwen2.5-7B-Instruct) by 6.72% absolute accuracy on four English reasoning testset and 6.89% in their multilingual benchmark. Remarkably, it is the only method that surpasses the base LLM on English commonsense reasoning task (4.9%), despite being trained solely on math data-highlighting its strong cross-task generalization. Further analysis reveals that treating language as a latent variable expands the model's latent reasoning space, yielding consistent and generalizable improvements in reasoning performance.