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Mathematical Reasoning on MGSM (test)

88Accuracy (ZH)self-cons
5.21626.70848.269.692Oct 16, 2025Nov 22, 2025Dec 30, 2025Feb 6, 2026Mar 16, 2026Apr 23, 2026May 31, 2026

Evaluation results

MethodLinks
self-consBackbone=Qwen-2.5 14B IT, Strategy=cross-lingual self-consistency2026.0588————88.4—88.487.865.689.282.280.849.681.676.944.6
DARE MergingSetting=Ability Transfer, SFT=false2026.0186————91.288.6——————————
LIDRBackbone=Qwen-2.5 14B IT, Strategy=DPO2026.0586————87.6—66.881.25471.265.251.650.869.865.738.6
Task ArithmeticSetting=Ability Transfer, SFT=false2026.0185.6————89.687.6——————————
S1Backbone=Qwen-2.5 14B IT, Strategy=test-time scaling2026.0585.2————90.4—89.286.860.486.480.480.8547675.640.4
ACTSetting=Ability Transfer (transfer-only), SFT=false2026.0184.8————9087.4——————————
TIES MergingSetting=Ability Transfer, SFT=false2026.0184.4————92.488.4——————————
Qwen2.5-7B Math InstructSetting=Multi-lingual LLM Baseline2026.0184————92.488.2——————————
trans-testBackbone=Qwen-2.5 14B IT, Strategy=translate-test2026.0582.3————84.2—49.270.433.46657.353.241.470.257.626.2
Qwen-2.5 14B ITBackbone=Qwen-2.5 14B IT, Strategy=native-cot2026.0580.8————84.2—4475.237.661.648.847.240.46655.221.8
Task ArithmeticSetting=With supervised fine-tuning, SFT=true2026.0179.6————88.484——————————
ACTSetting=With supervised fine-tuning, SFT=true2026.0179.6————90.485——————————
TIES MergingSetting=With supervised fine-tuning, SFT=true2026.0175.6————88.482——————————
SFTSetting=With supervised fine-tuning, SFT=true2026.0174.8————87.681.2——————————
DARE MergingSetting=With supervised fine-tuning, SFT=true2026.0174.8————88.881.8——————————
Qwen2.5-7B InstructSetting=Multi-lingual LLM Baseline2026.0174————8278——————————
XBridge_LLMBase Model=Qwen2.5-7B-Instruct, reasoning_output=English (LLM)2026.0371.6————83.6—7477.263.274.472.865.267.668.471.8—
XBridge_DecBase Model=Qwen2.5-7B-Instruct, reasoning_output=multilingual (external decoder)2026.0370.4————83.2—72.47660.872.465.659.266.86469.08—
LiRA-LARGEPARAMS=15.9B, YEAR=OURS2025.1070.3————79.2—73.97569.669.369.869.161.972.571.1—
MindMergerBase Model=Qwen2.5-7B-Instruct2026.0370————83.6—77.276.460.471.673.664.865.266.470.92—
LayerAlignBase Model=Qwen2.5-7B-Instruct2026.0368.8————83.2—74.478.465.675.27462.866.865.671.48—
self-consBackbone=Llama3 8B-IT2026.0568.4————82.4—69.674.864.476.47257.259.241.665.5—
QWEN3-8BPARAMS=8B, YEAR=20252025.1067.9————78.9—72.575.166.47169.364.559.169.369.4—
SFTBase Model=Qwen2.5-7B-Instruct2026.0367.6————66.4—6059.649.66458.454.448.462.859.12—
Translate-TestBase Model=Qwen2.5-7B-Instruct2026.0362.8————74.4—63.262.443.267.660.459.658.44459.6—
S1Backbone=Qwen-2.5 7B IT, Strategy=test-time scaling2026.0560.4————88.2—72.466.45063.67063.28.864.455.915.6
LIDRBackbone=Qwen-2.5 7B IT, Strategy=DPO2026.0560————79.6—55.260.451.268.866.460.425.25654.617.2
self-consBackbone=Qwen-2.5 7B IT, Strategy=cross-lingual self-consistency2026.0559.6————81.8—7672.454.875.271.655.617.673.259.324
MAPO-13BBackbone=Llama2-13B2026.0559.6————71.6—59.362.844.859.263.65655.247.658—
LIDRBackbone=Llama3 8B-IT2026.0559.2————72—626447.25760.847.632.853.655.6—
LoRAFlowBase LLM=LLaMA-3-8B, Paradigm=Supervised2025.1256.8——62.1———60.469.2————————
XBridge_LLMBase Model=LLaMA3-8B, reasoning_output=English (LLM)2026.0356.4————65.2—60.46247.259.26250.849.654.456.72—
LIDRBackbone=Qwen-2.5 1.5B IT, Strategy=DPO2026.0555.6————57.6—55.654.418525439.68.437.239.96.4
XBridge_DecBase Model=LLaMA3-8B, reasoning_output=multilingual (external decoder)2026.0355.2————62.8—58.461.24656.857.246.449.651.254.48—
MULTIREASON-LORAPARAMS=7B, YEAR=20222025.1054.8————64.8—62.459.629.659.658.4522835.250.4—
MINDMERGER-HARDPARAMS=10.7B, YEAR=20242025.1054.4————71.2—60.4624660.45652.448.43654.7—
self-consBackbone=Qwen-2.5 1.5B IT, Strategy=cross-lingual self-consistency2026.0554————50.3—55.263.221.253.656.4365.24840.97.2
MAPOBackbone=Llama3 8B-IT2026.0554————71.6—6262.838.450.859.238.430.847.251.5—
MINDMERGER-SOFTPARAMS=10.7B, YEAR=20242025.1053.6————66.8—60.858.450.461.257.654.457.252.857.3—
MetaMathOctopus-13BBackbone=Llama2-13B2026.0553.1————66.8—59.161.141.660.160.857.350.952.151.5—
XBridge_LLMBase Model=MetaMath-7B, reasoning_output=English (LLM)2026.0352.8————67.2—57.660.848.454.857.247.246.445.653.8—
LayerAlignBase Model=LLaMA3-8B2026.0352.8————62.4—56.860.4505657.65047.648.854.24—
trans-testBackbone=Qwen-2.5 7B IT, Strategy=translate-test2026.0552.6————78.6—39.250.333.467.654.443.611.460.246.418.6
XBridge_DecBase Model=MetaMath-7B, reasoning_output=multilingual (external decoder)2026.0352————66.8—566047.252.851.644.845.644.452.12—
LayerAlignBase Model=MetaMath-7B2026.0351.2————62.8—56.459.240.454.852.451.653.247.252.92—
MathOctopus-13BBackbone=Llama2-13B2026.0551.2————51.6—47.653.24249.249.639.6464647.6—
MindMergerBase Model=LLaMA3-8B2026.0350.8————60—55.256.849.654.855.6504846.452.72—
Translate-TestBase Model=Aya-23-8B2026.0350.8————57.2—50.448.4345045.642.843.633.245.6—
qa-FLoRABase LLM=LLaMA-3-8B, Paradigm=Data & Training free2025.1250.4——58.3———58.466————————
S1Backbone=Qwen-2.5 1.5B IT, Strategy=test-time scaling2026.0550.4————54.1—5057.217.247.652.832.8640.737.64.4
Llama3 8B-ITBackbone=Llama3 8B-IT2026.0549.6————73.2—58.864.442.458.857.240.831.635.651.2—
SFTBase Model=LLaMA3-8B2026.0349.2————54—45.254.838.846.444.438.840.84445.64—
Qwen-2.5 7B ITBackbone=Qwen-2.5 7B IT, Strategy=native-cot2026.0549.2————78.6—37.440.23060.448.249.819.854.844.218.2
MindMergerBase Model=MetaMath-7B2026.0348.8————67.2—57.659.243.657.26045.649.242.453.08—
Llama2-13BBackbone=Llama2-13B2026.0548.8————53.2—47.64835.244.448.443.242.846.845.8—
QALIGNPARAMS=7B, YEAR=20242025.1048.4————68—52.459.639.654.856.8444440.449.6—
Translate-TestBase Model=LLaMA3-8B2026.0348————62—57.254.840.45654.851.646.835.250.68—
TRANSLATE-ENPARAMS=3.3B, YEAR=20232025.1046.8————65.5—47.659.648.460.456.449.237.637.650.6—
Translate-TestBase Model=MetaMath-7B2026.0346————53.2—49.247.634.849.240.845.243.232.444.16—
LayerAlignBase Model=Aya-23-8B2026.0346————49.2—46.848.841.645.248.44441.237.644.88—
XBridge_LLMBase Model=Aya-23-8B, reasoning_output=English (LLM)2026.0346————56.8—49.253.244.449.25047.244.837.647.84—
LANGBRIDGEPARAMS=7B, YEAR=20242025.1045.2————63.2—52.45842.856.450.84043.250.450.2—
MathOctopus-7BBackbone=Llama2-7B2026.0545.2————54.8—48.445.233.243.63835.638.436.441.9—
XBridge_DecBase Model=Aya-23-8B, reasoning_output=multilingual (external decoder)2026.0344————56.8—49.253.244.846.446.446.444.83446.6—
INCLINE-7BBackbone=Llama2-7B2026.0542.8————46.8—3845.248.451.237.644.838.843.243.7—
SFTBase Model=Aya-23-8B2026.0342————50.8—46.447.633.652.843.646.438.839.244.12—
MULTIREASON-SFTPARAMS=7B, YEAR=20242025.1042————52—45.24833.245.244.842424043.4—
Qwen-2.5 1.5B ITBackbone=Qwen-2.5 1.5B IT, Strategy=native-cot2026.0541.2————52.4—46.548.81241.248.131.62.834.633.14.4
Avg [0.5, 0.5]Base LLM=LLaMA-3-8B, Paradigm=Static fusion2025.1240.8——45.1———45.249.2————————
trans-testBackbone=Qwen-2.5 1.5B IT, Strategy=translate-test2026.0540.8————52.4—38.85014.444.242.123.68.436.833.412.4
MindMergerBase Model=Aya-23-8B2026.0340.4————48—484840.849.64642.442.433.643.92—
MONOREASONPARAMS=7B, YEAR=20242025.1038.4————68.8—5257.26.855.254.436.46.87.238.3—
SFTBase Model=MetaMath-7B2026.0336————48—39.639.63040.439.232.435.232.837.32—
Centroid sim.Base LLM=LLaMA-3-8B, Paradigm=Training free2025.1234.4——40.5———41.645.6————————
LoRAFlowBase LLM=LLaMA-2-7B, Paradigm=Supervised2025.1233.2——37.6———37.642————————
Llama2-7BBackbone=Llama2-7B2026.0531.6————52—33.639.218.83836.427.223.621.632.2—
qa-FLoRABase LLM=LLaMA-2-7B, Paradigm=Data & Training free2025.1221.6——26.5———21.636.4————————
LoRAHubBase LLM=LLaMA-2-7B, Paradigm=Supervised2025.1220.8——28.7———28.436.8————————
Avg [0.5, 0.5]Base LLM=LLaMA-2-7B, Paradigm=Static fusion2025.1212.8——13.9———10.418.4————————
Centroid sim.Base LLM=LLaMA-2-7B, Paradigm=Training free2025.128.4——10.1———4.417.6————————
CLPBackbone=Llama2-7B, Training Mode=Non-Fine-Tuned2025.02———48.3—————————————
CodeLlama-7B (+ SC)Backbone=CodeLlama-7B, Training Mode=Fine-tuned, Setting=Cross-lingual, Test-time Scaling=Self-Consistency (SC)2025.02———46.7—————————————
CodeLlama-7B (+ SC)Backbone=CodeLlama-7B, Training Mode=Fine-tuned, Setting=Multilingual, Strategy=PoT Parallel + SC2025.02———62.8—————————————
CodeLlama-7B (+ Soft-SC (ICE-Score))Backbone=CodeLlama-7B, Training Mode=Fine-tuned, Setting=Cross-lingual, Test-time Scaling=Soft-SC, Scoring=ICE-Score2025.02———61.1—————————————
CodeLlama-7B (+ Soft-SC (ICE-Score))Backbone=CodeLlama-7B, Training Mode=Fine-tuned, Setting=Multilingual, Strategy=PoT Parallel + Soft-SC, Scoring=ICE-Score2025.02———75.6—————————————
CodeLlama-7B (PoT Parallel)Backbone=CodeLlama-7B, Training Mode=Fine-tuned, Setting=Multilingual, Strategy=PoT Parallel2025.02———49—————————————
CodeLlama-7B (Without Comments)Backbone=CodeLlama-7B, Training Mode=Fine-tuned, Setting=Cross-lingual, Prompting=Without Comments2025.02———38.6—————————————
Cross-PALBackbone=Llama2-7B, Training Mode=Non-Fine-Tuned2025.02———49.9—————————————
Flan-PaLMPrompting=8-shot Chain-of-thought2023.05—72———————————————
Flan-PaLM 2Prompting=8-shot Chain-of-thought, Self-consistency=True, Config=In-language exemplars2023.05—75.985.8——————————————
IFalpha=0.5, Merge Strategy=TIES-merging, Use DARE=false2024.10———7—————————————
Llama2-7B (+ SC)Backbone=Llama2-7B, Training Mode=Fine-tuned, Setting=Multilingual, Strategy=PoT Parallel + SC2025.02———57.2—————————————
Llama2-7B (+ Soft-SC (ICE-Score))Backbone=Llama2-7B, Training Mode=Fine-tuned, Setting=Cross-lingual, Test-time Scaling=Soft-SC, Scoring=ICE-Score2025.02———56.6—————————————
Llama2-7B (+ Soft-SC (ICE-Score))Backbone=Llama2-7B, Training Mode=Fine-tuned, Setting=Multilingual, Strategy=PoT Parallel + Soft-SC, Scoring=ICE-Score2025.02———71.2—————————————
Llama2-7B (PoT Parallel)Backbone=Llama2-7B, Training Mode=Fine-tuned, Setting=Multilingual, Strategy=PoT Parallel2025.02———44.6—————————————
Llama2-7B (Without Comments)Backbone=Llama2-7B, Training Mode=Fine-tuned, Setting=Cross-lingual, Prompting=Without Comments2025.02———39.2—————————————
MERGEPRINTalpha=0.7, Merge Strategy=Task Arithmetic, Use DARE=true2024.10———42—————————————
MERGEPRINTalpha=0.9, Merge Strategy=TIES-merging, Use DARE=false2024.10———3—————————————
PaLMPrompting=8-shot Chain-of-thought, Self-consistency=True2023.05—45.957.9——————————————
PaLM 2Prompting=8-shot Chain-of-thought, Self-consistency=True, Config=In-language exemplars2023.05—72.287——————————————