| | -Bench: | | Graduate-level | | | Multi-disciplinary | | | Benchmarks | | | for | | | --- | ------- | --- | -------------- | --- | ------- | ------------------ | --------- | --- | ---------- | --- | --- | --- | --- | | | | LLM | & MLLM | | Complex | | Reasoning | | Evaluation | | | | | Meng-HaoGuo1 JiajunXu*1 YiZhang*1 JiaxiSong*1 HaoyangPeng*1 Yi-XuanDeng*1 XinzhiDong*1 KiyohiroNakayama2 ZhengyangGeng3 ChenWang4 BolinNi5 Guo-WeiYang6 YongmingRao†5 HouwenPeng†5 HanHu5 GordonWetzstein2 Shi-MinHu†(cid:66)1 5202 yaM 4 ]VC.sc[ 1v81020.5052:viXra Abstract Reasoningstandsasacornerstoneofintelligence, 92.3 90.0 M M L U - B e n c h - T | | | | | | | | | 88.0 | | | | M M M U | - B e n c h - M | | --- | --- | --- | --- | --- | --- | --- | --- | ---- | --- | --- | --- | ------- | --------------- | enablingthesynthesisofexistingknowledgeto 78.2 | solve complex | | problems. | Despite | remarkable | | | | | | | | | | | ------------- | --- | --------- | ------- | ---------- | --- | --- | --- | ---- | --- | --- | --- | ---- | --- | | | | | | | | | | 69.0 | | | | 69.1 | | progress,existingreasoningbenchmarksoftenfail 61.2 )%( ycaruccA | torigorouslyevaluatethenuancedreasoningcapa- | | | | | | | | | 53.6 | | | 53.2 | | | -------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | ---- | --- | --- | ---- | --- | bilitiesrequiredforcomplex,real-worldproblem- | solving, | particularly | | in multi-disciplinary | | and | | | | | | | | | | -------- | ------------ | --- | --------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | 33.4 | multimodal | contexts. | | In this paper, | | we intro- | | | | | | | | | | ---------- | --------- | --- | -------------- | --- | --------- | --- | --- | --- | --- | --- | --- | --- | --- | duceagraduate-level,multi-disciplinary,English- Chinesebenchmark,dubbedasReasoningBench | (R-Bench), | for | assessing | the reasoning | | capabil- | | | | | | | | | | ---------- | --- | --------- | ------------- | --- | -------- | --- | --- | --- | --- | --- | --- | --- | --- | R- ityofbothlanguageandmultimodalmodels. o1-20241217 GPT-4o DeepSeek-R1 o1-20241217 GPT-4o Benchspans1,094questionsacross108subjects forlanguagemodelevaluationand665questions | | | | | | | | Figure1.Top-1 | accuracy | comparison | | of different | models | on | | --- | --- | --- | --- | --- | --- | --- | ------------- | -------- | ---------- | --- | ------------ | ------ | --- | across 83 subjects for multimodal model test- MMLU,MMMU,andR-Bench. R-Benchposesagreaterchal- | ing in both | English | | and Chinese. | These | ques- | | lengetocurrentmodels. | | | | | | | | ----------- | ------- | --- | ------------ | ----- | ----- | --- | --------------------- | --- | --- | --- | --- | --- | --- | tionsaremeticulouslycuratedtoensurerigorous difficultycalibration,subjectbalance,andcross- linguisticalignment,enablingtheassessmentto Reasoning,thesystematicprocessofsynthesizingknowl- be an Olympiad-level multi-disciplinary bench- edgetosolvenovelproblems,liesattheheartofintelligence. mark. Weevaluatewidelyusedmodels,includ- Yet,asfoundationmodelsgrowincreasinglysophisticated, | ingOpenAIo1,GPT-4o,DeepSeek-R1,etc. | | | | | | Ex- | | | | | | | | | ----------------------------------- | --- | --- | --- | --- | --- | --- | ------------------- | --- | ---- | ------------------ | --- | ------ | ----- | | | | | | | | | existing benchmarks | | fail | to comprehensively | | assess | their | perimentalresultsindicatethatadvancedmodels complex reasoning capabilities. As shown in the above performpoorlyoncomplexreasoning,especially quote,beforeequippingfoundationmodelswithreasoning multimodalreasoning. Eventhetop-performing skills,weshouldfirstdefinegoalsforthembyestablishing modelOpenAIo1achievesonly53.2%accuracy areliableevaluationtoassesstheirreasoningcapabilities. | onourmultimodalevaluation. | | | Dataandcodeare | | | | | | | | | | | | -------------------------- | --- | --- | -------------- | --- | --- | --- | --------------------------- | --- | --- | --- | ------------------- | --- | --- | | | | | | | | | Asnotedin(Kahneman,2011)and | | | | (Weietal.,2022),re- | | | madepubliclyavailableathere. | | | | | | | | alizing system-I, | | a.k.a., quick | and | intuitive | thinking | and | | --- | --- | --- | --- | --- | --- | --- | ----------------- | --- | ------------- | --- | --------- | -------- | --- | system-II,a.k.a.,slowanddeliberatereasoningraisesdis- | | | | | | | | tinctrequirementsonfoundationmodels. | | | | | Similarly,assess- | | | --- | --- | --- | --- | --- | --- | --- | ------------------------------------ | --- | --- | --- | --- | ----------------- | --- | 1.Introduction | | | | | | | | ing quick | thinking | and complex | | reasoning | requires | sub- | | --- | --- | --- | --- | --- | --- | --- | --------- | -------- | ----------- | --- | --------- | -------- | ---- | “Settinggoalsisthefirststepinturningtheinvisi- stantiallydifferentassessmentmethods. Ontheonehand, evaluatingsystem-Ineedstoevaluatetheknowledgeand | bleintothevisible.” | | | —TonyRobbins | | | | | | | | | | | | ------------------- | --- | --- | ------------ | --- | --- | --- | ------------- | --- | -------- | ---------- | ------- | ----- | ------- | | | | | | | | | memory, which | | requires | collecting | various | daily | conver- | *Secondauthorslistedrandomly,†Jointprojectlead,1Tsinghua | | | | | | | | sations and | knowledge-based | | questions | | e.g., concept | and | | --------- | --- | --- | --------- | --- | --- | --- | ----------- | --------------- | --- | --------- | --- | ------------- | --- | | 2Stanford | | | 3Carnegie | | | | | | | | | | | University, University, Mellon University, common sense questions. On the other hand, evaluating 4UniversityofPennsylvania,5TencentHunyuanX,6Fitten.Corre- | | | | | | | | system-IIrequiresevaluatingcomplexreasoningskills. | | | | | | It | | --- | --- | --- | --- | --- | --- | --- | -------------------------------------------------- | --- | --- | --- | --- | --- | --- | spondenceto:Shi-MinHu. requiresgatheringadiverserangeofreasoningquestions, suchasanalyticalanddeductiveones,whichismorechal- 1 R-Bench | | | | | | | benchmarksasexamples. | | MMLU(Hendrycksetal.,2021) | | | | ------------ | ------- | ------------------ | --- | --- | --------------- | --------------------- | --- | ------------------------- | --- | --- | | Table1.Comp. | denotes | comprehensiveness. | | o1 | saturation rep- | | | | | | isacomprehensivebenchmarkformulti-disciplineunder- | resentso1(OpenAI,2024b)performanceonthisbenchmark. | | | | | It | | | | | | | -------------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | standing,whichhasservedasacriticalguideforthedevelop- reflectsthechallengethatthebenchmarkposestoadvancedmod- mentoffoundationmodelsinrecentyears.However,consid- els. eringthecurrentlevelofmodelintelligence,thisbenchmark | Name | | Comp. | o1Saturation | | Language | | | | | | | ---- | --- | ----- | ------------ | --- | -------- | --- | --- | --- | --- | --- | isclosetosaturation(e.g.,o1(OpenAI,2024b)hasachieved | | | ✓ | | | | 92.3%accuracyonit). | | Besides,itdosenottakemultimodal- | | | | ---- | --- | --- | ----- | --- | --- | ------------------- | --- | -------------------------------- | --- | --- | | MMLU | | | 0.923 | | en | | | | | | AIME@2024 ✗ 0.744 en ityandmultilingualismintoconsideration,whichisalsocrit- R-Bench-T ✓ 0.690 en&zh icalforanidealreasoningtest. MMMU(Yueetal.,2024a) | | | | | | | isaholisticevaluationformultimodalreasoningtests. | | | | With | | --- | --- | --- | --- | --- | --- | ------------------------------------------------- | --- | --- | --- | ---- | ✓ | MMMU | | | 0.782 | | en | | | | | | | ---- | --- | --- | ----- | --- | --- | --- | --- | --- | --- | --- | thelaunchofo1(OpenAI,2024b),thisbenchmarkisalso | R-Bench-M | | ✓ | 0.532 | | en&zh | | | | | | | --------- | --- | --- | ----- | --- | ----- | ----------------------------------------- | --- | --------------------------------- | --- | ------ | | | | | | | | closetosaturation. | | Also,itcannotbeusedtoevaluatelan- | | | | | | | | | | guagemodelsandignoresmultilingualtesting. | | | | Weshow | thecomparisonofMMLU,MMMU,andR-BenchinFig.1 lengingtocollectandfilterthantheformer.Inthispaper,we | | | | | | | andTab.1. | Frontiermath(Glazeretal.,2024)collectssome | | | | | --- | --- | --- | --- | --- | --- | --------- | ------------------------------------------ | --- | --- | --- | focusonbuildingareliablecomplexreasoningbenchmark | | | | | | | challenging | problems | specifically | designed | for advanced | | -------------- | -------- | ------ | ------ | --- | ---------- | ------------ | --------- | ------------ | -------- | -------------- | | for both large | language | models | (LLMs) | and | multimodal | | | | | | | | | | | | | mathematical | reasoning | evaluation, | which | indicates that | largelanguagemodels(MLLMs). currentmodelsstillexhibitweaknessesinmathematicalrea- Howcanwedesignanidealassessmentforcomplexreason- soning. However,itfallsshortincomprehensivenessand ing? Webelievefollowingfourpropertiesarecritical. multilingualtesting. ThisalsoappliestoOmni-Math(Gao | | | | | | | et al., 2024) | and AIME | (OpenAI, | 2024b), | both of which | | --- | --- | --- | --- | --- | --- | ------------- | -------- | -------- | ------- | ------------- | • Comprehensiveness. Evaluating the intelligence of serveasbenchmarksfocusedonemployingmathematical olympiadchallenges. foundationmodelsisakintoevaluatinghumanintel- | ligence. | Wecannotfocusonjustoneaspect,suchas | | | | | | | | | | | -------- | ----------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | Inthispaper,ourgoalistobuildabenchmarkR-Benchthat mathematics. Acomprehensiveevaluationisessential. alignswiththefourpropertiesweproposedforevaluating | | | | | | | the reasoning | abilities | of intelligent | models. | To achieve | | ------------- | --- | ------------ | ---------- | ------ | ------- | ------------- | --------- | -------------- | ------- | ---------- | | • Difficulty. | | A meaningful | evaluation | should | exhibit | | | | | | that,wefollowmorethan100collegecoursesfrom19de- thecapabilitytoeffectivelydiscriminatebetweenthe performanceofdifferentmodelsandprovidevaluable partmentsatTsinghuaUniversityandcollectchallenging problemsfromtheirexams,textbooks,quizzes,homework, | insightsforguidingmodelimprovement. | | | | | Atpresent, | | | | | | | ----------------------------------- | --- | --- | --- | --- | ---------- | --- | --- | --- | --- | --- | etc. Aftermultipleroundsofrigorousscreeningbyexperts foundationmodelsaredevelopingrapidly,andsome andmodels,wefinallyselect1,094questionsspanning108 simplebenchmarkshavebeensaturatedandcannotpro- subjectsforlanguagemodelsreasoningtest,and665ques- videguidanceanddiscriminationforadvancedmodels. tionscovering83subjectsformultimodalmodelsreasoning • Multimodality. Weliveinamultimodalworld,con- test. Wewillpresentthedetailedscreeningprocessinthe stantlyprocessingvariousvisualandlinguisticsignals. Sec2. AfterbuildingtheR-Benchbenchmark,wetestthe Therefore,anidealbenchmarkshouldbedesignedto reasoningcapabilitiesofvariouspowerfulproprietarymod- assessbothLLMsandMLLMs. elssuchaso1(OpenAI,2024b),GPT-4o(OpenAI,2024a), Gemini(Teametal.,2023),Claude(Anthropic,2024a),and | • Multilingualism. | | We | believe | that performing | com- | | | | | | | ------------------ | --- | --- | ------- | --------------- | ---- | --- | --- | --- | --- | --- | open-sourcedmodelssuchasLlama3(Touvronetal.,2023), plexreasoningismorechallengingthanunderstanding Qwen2.5(Yangetal.,2024),etc. Fromexperiments,our | multiplelanguages. | | Amodelwithrobustcomplexrea- | | | | | | | | | | ------------------ | --- | --------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | observationsandfindingsaresummarizedasfollows: soningskillsshouldbecapableofsolvingreasoning | problemsacrossdifferentlanguages. | | | | Thisislikefora | | | | | | | | --------------------------------- | --- | --- | --- | -------------- | --- | --- | --- | --- | --- | --- | • Withtheemergenceofadvancedmodelslikeo1,exist- humanexpert,heorshewillnotlosetheabilitytoad- ingmultidisciplinaryevaluationshavenearlyreached | dressproblemsduetolanguagechanges. | | | | | Thus,assess- | | | | | | | ---------------------------------- | --- | --- | --- | --- | ------------ | ----------- | ------------------------------------ | --- | --- | --- | | | | | | | | saturation. | Besides,solelyrelyingonmathproblems, | | | | ingmodelperformanceonequallydifficultquestions e.g.,mathematicalolympiadproblems,maybringbias | across | languages | is essential. | It | will provide | insight | | | | | | | ------ | --------- | ------------- | --- | ------------ | ------- | ------------------ | --- | --------------------------- | --- | --- | | | | | | | | inmodelevaluation. | | Therefore,thecommunityneeds | | | intowhetherthemodelhasgenuinelylearnedtoreason | | | | | | | challenging | | multi-disciplinary | benchmarks | to guide | | --- | --- | --- | --- | --- | --- | ----------- | --- | ------------------ | ---------- | -------- | orismerelyoverfittingtoaspecificlanguage. foundationalmodelsinenhancingtheirreasoningabil- ities,andthegoalofR-Benchistoaddressit. Whiletherehavebeenattemptstocreateanidealreasoning benchmark,tothebestofourknowledge,existingbench- • We illustrate from three dimensions — expert scor- marks cannot incorporate all four of these key properties ing,modelscoring,andmodelthinkingtime—that simultaneously. Here,wetakesomewidelyusedreasoning R-Bench is a more complex benchmark with higher 2 R-Bench requirementsformodelreasoningcomparedtoexisting multidisciplinarybenchmarksMMLUandMMMU. Step1: Step2:Experts collectand | • Multimodalcomplexreasoningremainschallenging. | | | | | | | Define a list | | | | | | ----------------------------------------------- | --- | --- | --- | --- | --- | --- | -------------- | --- | --- | --- | --- | selectreasoningquestions | Despiterapidadvances,modelslagbehindtext-based | | | | | | | of collected | | | | | | ---------------------------------------------- | --- | --- | --- | --- | --- | --- | ------------- | --- | --- | --- | --- | KQ disciplines | reasoning. | Forinstance,GPT-4oscores53.6%ontext | | | | | | | | | | | | ---------- | ----------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | RQ butonly33.7%inmultimodalreasoningonR-Bench. | • ChainofThought(CoT)canenhancereasoningabili- | | | | | | Step3: | | | | | | | ---------------------------------------------- | --- | --- | --- | --- | --- | ------ | --- | --- | --- | ---- | ---- | | tiesinmostchatmodels,suchasGPT-4o.However,for | | | | | | | | | | Some | Some | Digitize the questions | | | | | | | | | | text-only | | multimodal | | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---------- | --- | ---------- | reasoningmodelslikeo1-mini,CoTdoesnothavethe | | | | | | | | | | questions | | questions | | ----------- | --- | ------------------------------- | --- | --- | --- | --- | --- | --- | --------- | --- | --------- | | sameeffect. | | Thismaybebecausereasoningmodels | | | | | | | | | | inherentlybuildCoT,makingexplicitCoTineffective. • ModelsmaintainhighconsistencyinansweringChi- neseandEnglishquestionsofequaldifficulty,exceed- Step4:o1 model rescreen | | | | | | | Step5:The third round | | | based on reasoning difficulty | | | | --- | --- | --- | --- | --- | --- | ---------------------- | --- | --- | ----------------------------- | --- | --- | ing70%formostmodels,demonstratingstrongcross- screensfor completeness, | lingualreasoningcapabilities. | | | | | | | | | | <2000 | | | ----------------------------- | --- | --- | --- | --- | --- | ------------- | --------- | --- | --- | ----- | --- | | | | | | | | repetitionand | ambiguity | | | | | AQ | • Foundation | models | perform | differently | across | disci- | | | | | | | | ------------ | ---------- | ------- | ---------------- | ----------- | ------ | --- | --- | --- | --- | --- | ----- | | plines. | Specifical | ly , G | P T -4o achieves | 30.4%–68.3% | | | | | | | | | | | ℛ -B e | nc h- T | | | | | CQ | | | >2000 | accuracyacrossvariousfields. 2.R-Bench !-Bench | | | | | | | | | | Step6: | Constructing | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | ------ | ------------- | --- | optionsandtranslations Inthissection,wewillthoroughlyintroducetheconstruc- | tionprocessofR-Bench. | | | | | | ℛ-Bench | | ℛ-Bench | | | | | --------------------- | --- | ---------------------------- | --- | --- | --- | ------- | --- | ------- | --- | --- | --- | | | | Theentireprocessinvolvesmul- | | | | -T | | -T(zh) | | | | tiplestepssuchasdatacollection,filteringandimproving. | | | | | | | ℛ-Bench | | ℛ-Bench | | | | | --- | --- | --- | --- | --- | --- | ------- | --- | ------- | --- | --- | --- | TheoverallpipelineisillustratedinFig.2. | | | | | | | -M | | -M(zh) | | | | | --- | --- | --- | --- | --- | --- | --- | --- | ------ | --- | --- | --- | 2.1.Datacollection Before gathering reasoning questions, we conducted an Figure2.PipelineofbuildingR-Bench. Theprocessisdivided intosixsteps,whicharedetailedinSec.2.Thefunnelrepresents | investigation | of the | curriculum | systems | of graduate | and | | | | | | | | ------------- | ------ | ---------- | ------- | ----------- | --- | --- | --- | --- | --- | --- | --- | screening.WealwaysRfiBlteenrcohuttheblueballandpreservethebrown undergraduatestudentsacross19diffeCrentdepDartmentsat -TC TsinghuaUniversity. Basedonoursurvey,weobtaineda one. InStep2,KQandRQdenoteknowledge-basedquestions | | | | B | | E | andreasoning-basedquestions,respectively. | | | | InStep4,<2000 | | | --- | --- | --- | --- | --- | --- | ----------------------------------------- | --- | --- | --- | ------------- | --- | collectionlistcoveringover100coursesacross19depart- indicatesthatthereasoningtokensofo1arelessthan2000.Finally, | ments,whichisshowninFig.2Step1. | | | | | | RBench | | RBench | | | | | ------------------------------- | --- | --- | --- | --- | --- | ------------- | ------------------------------------------- | ------ | --- | --- | --- | | | | | A | | | inStep5,-AMQE | andCQ-rMeCpresentambiguousquestionsandclear | | | | | F After acquiring a collection list, we recruit senior under- questions,respectively. -Tindicatestext-onlytestingforLLMs. graduatesandgraduatestudentsfromdifferentdepartments -Mmeansmultimodaltesting.zhrepresentstheChineseversion. | asexpertstoprovidereasoningquestion-answerpairs. | | | | | We | | | | | | | | ------------------------------------------------ | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | recruitatotalof51experts,withatleasttwoparticipants | from each | department, | to | help us collect | and filter | ques- | | | | | | | | ---------------------------------- | ------------- | --- | --------------- | --------------- | --------- | ---------- | --------- | ------ | ---------------- | ------- | ------------ | | | | | | | | After the | two steps | above, | we collected | a total | of 10,270 | | tions. Duringthecollectionprocess, | | | | wemainlyfocuson | | | | | | | | | | | | | | | questions. | Among | them, | 7,163 questions, | | which do not | | controlling | the following | | key aspects: | 1) The | questions | | | | | | | includeimages,aredesignatedfortestinglanguagemodels, should align with the collection list we provide. 2) The whiletheremaining3,107questions,containingimages,are professionalexpertiseshouldfilterout“knowledge-based” allocatedfortestingmultimodalmodels. | questions—those | | that rely | solely on memory | rather | than | | | | | | | | --------------- | ---------------------------------- | --------- | ---------------- | ------ | -------- | --- | --- | --- | --- | --- | --- | | reasoning, | suchasconcept-definitionquestions. | | | | Simulta- | | | | | | | 2.2.Datadigitization | neously, | experts should | retain | reasoning-based | | questions | | | | | | | | -------- | -------------- | ------ | --------------- | --- | --------- | --- | --- | --- | --- | --- | --- | andensuretheypresentasufficientdegreeofdifficulty. 3) Afterinitiallycollectingthequestions,wefindthatthecol- Allquestionsshouldhavecorrespondinganswersthatcan lectedquestionsareinamessyformat,includingpictures, beautomaticallyverified. Inthiscollectingprocess,weex- screenshots, text, etc. In addition, the summary question cludeproof-basedquestions,ascurrentautomatedmethods filesprovidedbydifferentexpertsarealsodifferent,includ- cannotverifythecorrectnessofproofs. Theprocessabove ingpdf,word,excel,etc. Therefore,weneedtoorganize | isshowninFig.2Step2. | | | | | | anddigitizethisdata. | | | | | | | -------------------- | --- | --- | --- | --- | --- | -------------------- | --- | --- | --- | --- | --- | 3 R-Bench Examples for language models reasoning ability test | | | Major: computerscience; | | | | Major:math; | | | | | | --- | --- | ----------------------- | --- | --- | --- | ---------------------------------- | --- | --- | --- | --- | | | | Subject:data structure. | | | | Subject:complex variable function. | | | | | In the undirected graph G=(V,E) where V={1,2,3,4,5,6,7} and E={(1,2), (1,3), (2,3), English Chinese (4,5), (3,6), (4,7), (5,7)}, how many different Consider the polynomial p ( z ) = z 5 + z 3 + 5 z 2 + 2 . p(z)=z5+z3+5z2+2。 | | s p a n n | i n g f o r e s ts d o e s th e gr | a p h G c o n t a in ? | | | | 考虑多项式 | | | | | --- | ---------- | ------------------------------------------ | ----------------------------- | --------- | ----------------------------- | ----------------------------------- | ----------------------------- | --- | --- | --- | | | | | | H o w m | a n y z e r o p o in t s ( | c o u n ti n g m u ltiplicities) | 在环域 1<|z|<2 中p 有多少个零点(计入重数)? | | | | | | N o t e : | I f t h e e d g e s e ts o f t w o | s p a nn in g f o re s ts | do e s p | h a v e i n th e a n n u | l u s 1 < |z | < 2 ? | | | | | are different, they are considered different | | spanning forests. | | | A:5 B:3 | | | A:5 B:3 | | | | | --- | ------------------ | --- | --- | --------- | --- | --- | --------- | --- | --- | --- | C:2 D:其他答案都不正确 C:2 D:All other answers are incorrect | | A:14 B:9 C:10 D:12 E:11 | | | E:4 F :6 | | | E:4 F :6 | | | | | --- | ------------------------------- | --- | --- | ---------- | --- | --- | ---------- | --- | --- | --- | F:All other answers are incorrect Examples for multimodal models reasoning ability test Major:mechanical engineering; Subject:theoretical mechanics. | | | English | | | | | Chinese | | | | | --- | --- | ------- | --- | --- | --- | --- | ------- | --- | --- | --- | Thewidthofthebrickclampis25cm,and | | thecurvedrodsAGBandGCEDarehinged | | | | | 砖夹的宽度为 | 25 cm , 曲杆 AGB | | | | | --- | --------------------------------------- | ----------------------------- | --- | --- | --- | ----------------- | -------------- | --- | --- | --- | | | | | | | | 与 在 | 点铰接，尺寸如图 | | | | | | atpointG,withdimensionsasshowninthe | | | | | GCED | G | | | | | | figure.Supposetheweightofthebrickis | | | | | 所示。设砖重 | Q=120N 提起砖的力 | | | | | | Q=120NandtheforcePthatliftsthebrick | | | | | P 作用在砖夹的中心线上，砖夹与砖 | | | | | | | | | | | | 间的摩擦系数 | f=0.5, 若想把砖夹起， | | | | | | actsalong | thecenterlineofthebrickclamp. | | | | | | | | | | | Thecoefficientoffrictionbetweenthebrick | | | | | 试求距离b的最大值？ | | | | | clampandthebrickisf=0.5.Determinethe A : 9 cm B : 11 cm C : 15 cm maximumvalueofdistancebrequiredtolift | | thebrickusingtheclamp. | | | | | D:20 cm E : 25 cm | | | | | | --- | ---------------------- | --- | --- | --- | --- | ------------------------ | --- | --- | --- | --- | F: 其他答案都不正确 | | | A : 9 cm B : 11 cm | C : 15 cm | | | | | | | | | --- | --- | -------------------------- | --------- | --- | --- | --- | --- | --- | --- | --- | D : 20 cm E : 25 cm F : All other answers are incorrect Figure3.SomeexamplesinR-Bench.TheseexamplesshowthatR-Benchismultidisciplinary,multimodal,andmultilingual.Asshown inthefigure,theproblemsinR-Bencharecomplexandcannotbesolvedbyquickthinking,whichshowsthatR-Benchfocusesondeep reasoningproblemsratherthanknowledgeproblems,suchasconceptualproblems. | To | do so, | we recruit a data | annotation | team of | about 20 | 2.3.Datafiltering | | | | | | ------- | ------ | -------------------- | --------------- | ------- | ----------- | ----------------- | --- | --- | --- | --- | | people. | | They are responsible | for organizing, | | digitizing, | | | | | | AsshowninFig.2,thefunnelsinsteps2,4,and5represent checking,andcompilingallthequestionsintoExcelsheets. threedifferentroundsofdatafiltering.Thesethreeroundsof Thequestionsusedforlanguagemodelsareorganizedin screeningrepresentexpertscreening,model-basedfiltering, thefollowingformat: andmanualreview. | “Department | | - Subject - | Question (text) | - Answer | (text) | - | | | | | | ---------------------------------------------- | --- | ----------- | --------------- | -------- | --------- | --- | --- | --- | --- | --- | | OriginalQuestion(text,screenshots,photos,etc.) | | | | | -Original | | | | | | Answer(text,screenshots,photos,etc.)”. Expert-screening. AsmentionedinSec.2.1,werecruit expertsfromdifferentdepartmentstoprovidequestionsfor Asforquestionsdesignedformultimodalmodels,theyare | | | | | | | us. They primarily | rely on their | professional | knowledge | | | --- | --- | --- | --- | --- | --- | ------------------ | ------------- | ------------ | --------- | --- | organizedintothefollowingformat: tofilterout“knowledge-based”questionswhileretaining “reasoning-based”questions. | “Department | | - Subject - | Question (text) | - Answer | (text) | - | | | | | | ----------- | --- | ----------- | --------------- | -------- | ------ | --- | --- | --- | --- | --- | QuestionImages-OriginalQuestion(text,screenshots,pho- tosetc.) -OriginalAnswer(text,screenshots,photosetc.)”. | | | | | | | Model-screening. | OpenAI | o1 (OpenAI, | 2024b) | is a | | --- | --- | --- | --- | --- | --- | ---------------- | ------ | ----------- | ------ | ---- | Inthisprocess,weutilizetoolssuchasGPT-4oandMathpix widely used reasoning model. When we call its API, it | | | | | | | returns the | number of reasoning | tokens, | which, | to some | | --- | --- | --- | --- | --- | --- | ----------- | ------------------- | ------- | ------ | ------- | forOCRprocessing,followedbymanualproofreadingto ensureitiscorrect. Afterthedatateamorganizesthedata, extent,reflectsthedifficultyofthequestion. Inthisround weperformadouble-checkontheOCRresults. ofscreening,wemainlyfocusonthedifficultyofreasoning. Wefilteroutthequestionswithlessthan2,000reasoning tokenstoensurethatourR-Benchisabenchmarkforrea- soningevaluation. 4 R-Bench Inorganic Chemistry Analytical Mechanics | | | | | | | C h | e m i c a l T h e r m o d y n a m i c s | | | | | | F u n d a m e n t a l P | h ysics | | | --------------- | --- | --- | ------------ | --- | --- | ----- | ----------------------------------------- | --- | --- | --- | --- | --- | --------------------------- | ------- | --- | | C h e m i s t | ry | | | | | P h | y s i c a l C h e m i s t r y | | | | | | | | | | M a t h | | | 3.7%3.7%3.4% | | | | | | | | | | E l e c t r o m a g n e t | i s m | | 4.4% C h e m i c a l R e a c t i o n K i n e t i c s 4.1%3.9%3.8% E l e c t r o d y n a m i c s | P h y s ic s | | | | 2.9% | | C o | m p u t a t i o n a l C h e m i s t r y | | | | | | | | | | -------------- | --- | --- | --- | ---- | --- | ----- | ----------------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | C o m p u t e r S. 4.7% 2.3% O rg a n i c C h e m i s t r y 4.7% 3.8% O p t i c s | E l e c t ro n | ic E. | | | | 2.3 % | | | | | | 3.5% | | | | | | ---------------- | ------ | ---- | --- | --- | ----- | ------------------ | ---- | --- | ---- | --- | ---- | ---- | --- | --- | --- | | | | 4.8% | | | 2 .1% | Quantum Chemistry | | | 4.8% | | | | | | | | A e r o s pa | c e | | | | | | | | | | | 3.2% | | | | | Automation | | | | | 2 % | | | | | | | | | | | | | | | | | 1 .6% | | | 5% | | | | 2.7% | | | | | Statistics | | 5.4% | | | | | | | | | | 2.6% | | | | | Mechanical E. | | | | | | | 4.6% | | | | | | | | | Materials | | | | | | | | | 5.9% | | | | | 3.8% | | | | ---------------- | --- | ---- | --- | --- | --- | ----- | ---- | ---- | --- | --- | --- | --- | ------- | --- | --- | | B i o l o g y | | 7.3% | | | | | | | | | | | | | | | C i v i l E . | | | | | | 14.7% | 4.4% | | | | | | 9% 1.5% | | | 1.5% | Vehicle E. | | | | | | | | 6.6% | | | | | | | | | ----------------- | ------ | ---- | --- | --- | --- | ---- | ---- | ---- | ---- | --- | ----- | --- | ---- | --- | --- | | Physics E. | | | | | | | 2% | | | | | | 1.4% | | | | C h e m i ca | l E. | 8.1% | | | | | | | | | | | | | | | | | | | | | 1.8% | 1% | | | | | | 0.9% | | | | Ec o n o m | i c s | | | | | | | | | | 10.2% | | | | | | Microelectronics | | | | | | | 0.5% | | 7.5% | | | | | | | 17.2% | Environment | | | 9.4% | | | | 0.5% | | | | | | | | | | ------------- | --- | ------------------------ | ---- | --- | --- | --- | ---- | --- | ------------------------ | --- | ---- | --- | --- | --- | --- | | Architecture | | | | | | | | | 9.2% | | 9.8% | | | | | | | | (a)StatisticsofR-Bench-T | | | | | | | (b)StatisticsofR-Bench-M | | | | | | | Figure4.AccordingtostatisticsonR-Bench,thebenchmarkspans19departments,includingmathematics,physics,biology,computer science,andchemistry,coveringover100subjectssuchasInorganicChemistry,ChemicalReactionKinetics,andElectromagnetism.It features1,094questionsdesignedfortestinglanguagemodelsand665questionsspecificallytailoredforevaluatingmultimodalreasoning capabilities.Foradetailedlistofsubjects,pleaserefertotheappendix. 2.5.OverviewofR-Bench | Manualreview. | | Ourmanualreviewfocusesonwhether | | | | | | | | | | | | | | | ------------- | --- | ------------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | thequestionconditionsarecomplete,whetherthequestions | | | | | | | | After | completing | the | aforementioned | | steps, | we develop | | | | -------------------------------------------------- | --- | --- | --- | --- | --- | --- | -------- | ---------- | --------------- | -------------- | ----------------- | ------ | ------------ | --- | --- | | arerepeated,whetherthequestionsareambiguous,andthe | | | | | | | R-Bench, | | | | | | | | | | | | | | | | | | a | graduate-level, | | multi-discipline, | | multilingual | | | balanceofsubjects. benchmarkdesignedtoevaluatecomplexreasoningcapa- Checking for completeness, repetition, and ambiguity re- bilitiesforbothlanguageandmultimodalmodels. Fig.3 quire multiple rounds of thorough review by different in- illustrates several examples from R-Bench, clearly high- dividuals to eliminate ambiguities, along with the use of lightingitsabovedistinctivefeatures. | duplicationdetectiontoolstoavoidrepetition. | | | | | | Asforthe | | | | | | | | | | | ------------------------------------------- | --- | --------- | ------- | --------- | ------- | -------- | ------- | --- | ---------- | --- | --------- | --------------- | --- | --- | --- | | | | | | | | | R-Bench | can | be divided | | into four | sub-benchmarks: | | R- | 1 | | balance check, | | to reduce | testing | bias from | subject | imbal- | | | | | | | | | | Bench-TandR-Bench-T(zh)forlanguagemodelevaluation, | ance, we | limit | the number | of questions | | per | subject | to a | | | | | | | | | | -------- | ----- | ---------- | ------------ | --- | --- | ------- | --------- | --- | ------------- | --- | --- | -------------- | --- | ----- | --- | | | | | | | | | R-Bench-M | | R-Bench-M(zh) | | | | | | | | | | | | | | | | | and | | | for multimodal | | model | | maximumof50byfilteringoutexcess. | | | | | | | | evaluation. | Here,R-Bench-TdenotesR-Benchusingtext- | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | -------------- | -------------------------------------- | ---------- | --- | ------- | ----------- | ------- | --- | --- | | | | | | | | | only questions | | in English | | for LLM | evaluation, | whereas | | | 2.4.Conductingoptionsandtranslations R-Bench-T(zh)representsR-Benchusingtext-onlyques- | | | | | | | | tionsinChineseforLLMevaluation. | | | | | Likewise,theother | | | | | -------- | --------- | ------- | ----- | --------- | ------------- | --- | ------------------------------- | --- | --- | --- | --- | ----------------- | --- | --- | --- | | In order | to enable | answers | to be | evaluated | automatically | | | | | | | | | | | and accurately, we convert all questions such as analyti- twonotationsfollowthesamenamingconvention. cal,fill-in-the-blank,andmultiple-choicequestionsintothe WeconductstatisticalanalysisonR-Benchwiththeresults single-choicequestionformat. WeuseGPT-4otoconstruct ItpresentstheR-Bench-Tstatisticsfor presentedinFig.4. | 5 options | for each | question | and | add an | option | “All | other | | | | | | | | | | --------- | -------- | -------- | --- | ------ | ------ | ---- | ----- | --- | --- | --- | --- | --- | --- | --- | --- | text-onlyquestionsusedinevaluatingthereasoningcapabil- answersareincorrect”,whichequipseachquestionwith6 R-Bench-Tspans18departments, itiesoflanguagemodels. | candidate | answers. | Then, | we check | the | options | multiple | | | | | | | | | | | --------------------------------------------- | -------- | ----- | -------- | --- | ------- | -------- | --------------------- | ---------- | ------------ | -------- | ---------- | ------- | -------------- | --- | --- | | | | | | | | | includingmathematics, | | | biology, | chemistry, | | computersci- | | | | timestoensurethecorrectnessofourconstruction. | | | | | | Further- | | | | | | | | | | | | | | | | | | ence, | electronic | engineering, | | and | others. | It encompasses | | | more,wemanuallyadjusttheoptionstoensureasufficient over108subjects,suchascalculus,numbertheory,analytic numericalgapbetweenthem,therebyavoidingerrorscaused | | | | | | | | geometry, | ordinary | | differential | equations, | | and functional | | | | --- | --- | --- | --- | --- | --- | --- | --------- | -------- | --- | ------------ | ---------- | --- | -------------- | --- | --- | bynumericalapproximations. analysis,andcomprisesatotalof1,094questions. Fig.4 alsopresentsthestatisticsofR-Bench-M,whichevaluates Besides,inordertoenableR-Benchtoacquirethemulti- | | | | | | | | thereasoningcapabilitiesofmultimodalmodels. | | | | | | R-Bench- | | | | --- | --- | --- | --- | --- | --- | --- | ------------------------------------------- | --- | --- | --- | --- | --- | -------- | --- | --- | lingualproperty,wemanuallyconstructedEnglish-Chinese translationsforeachquestion. Duringthetranslationpro- Mincorporatesadiversesetofquestiontypesrequiringboth cess,weutilizetoolslikeGPT-4o. Eachquestionismeticu- textualandvisualinputs. Itcovers18departments,suchas physics,biology,architecture,andeconomics,andincludes louslyreviewedandrefinedbythreeexpertsfluentinboth EnglishandChinesetoensurecorrectnessandclarity. 83 subjects, such as thermodynamics, molecular biology, structuraldesign,andmicroeconomics,includingatotalof | | | | | | | | 665questions. | | ItisworthnotingthatweprovideEnglish | | | | | | | | --- | --- | --- | --- | --- | --- | --- | ------------- | --- | ----------------------------------- | --- | --- | --- | --- | --- | --- | andChineseversionsforallquestions. 5 R-Bench Table2.Comparisonofreasoningrequirementsforproblemsin Table4.Theaveragethinkingtimeofo1on30randomlyselected R-Bench-TandMMLUviaexpertando1voting. samplesfromdifferentbenchmarks.TTdenotesthinkingtime. | | | R-Bench-Twin | | MMLUwin | Tie | | MMLU | | R-Bench-T | MMMU | | R-Bench-M | | | --- | --- | ------------ | --- | ------- | --- | --- | ---- | --- | --------- | ---- | --- | --------- | --- | Expertvoting 85.94% 10.62% 3.44% TT 13.5s 98.2s(7.3×) 20.3s 91.7s(4.5×) | o1voting | | 76.67% | | 20.00% | 3.33% | | | | | | | | | | -------- | --- | ------ | --- | ------ | ----- | --- | --- | --- | --- | --- | --- | --- | --- | Table3.Comparisonofreasoningrequirementsforproblemsin R-Bench-MandMMMUviaexpertando1voting. 3.2.Evaluatingreasoningcapabilityofdifferentmodels R-Bench-Mwin | | | | | MMMUwin | Tie | | | | | | | | | | --- | --- | --- | --- | ------- | --- | --- | --- | --- | --- | --- | --- | --- | --- | WeemployR-Bench-Ttoassessthereasoningcapabilities | Expertvoting | | 76.88% | | 15.94% | 7.19% | | | | | | | | | | ------------ | --- | ------ | --- | ------ | ----- | --- | --- | --- | --- | --- | --- | --- | --- | ofvariousLLMssuchaso1(OpenAI,2024b),GPT-4o(Ope- | o1voting | | 83.33% | | 13.33% | 3.33% | | | | | | | | | | -------- | --- | ------ | --- | ------ | ----- | --- | --- | --- | --- | --- | --- | --- | --- | nAI,2024a),DeepSeek-R1(AI,2025),Gemini(Teametal., 2024),Claude3.5(Anthropic,2024b),Qwen2.5(Yangetal., | | | | | | | 2024), | Llama3 | (Dubey | et | al., 2024), | etc, | in both | English | | --- | --- | --- | --- | --- | --- | ------------------- | ------ | ------ | --------------------------------- | ----------- | ---- | ------- | ------- | | | | | | | | andChinesesettings. | | | TheevaluationinvolvesutilizingAPI | | | | | 3.Experiments | | | | | | | callsanddeployingopen-sourcemodelslocally. | | | | | | | ForAPI | | --- | --- | --- | --- | --- | --- | ------------------------------------------ | --- | --- | --- | --- | --- | --- | ------ | calls,weutilizetheofficialinterfaceswithdefaulthyperpa- AfterdevelopingR-Bench,weutilizeittoassessthecom- rameters. Foropen-sourcemodels,wedeploytheirweights plexreasoningcapabilitiesofvariousLLMsandMLLMs, | | | | | | | locally | usingvLLM | | (Kwon | et al.,2023), | | settingthe | tem- | | --- | --- | --- | --- | --- | --- | ------- | --------- | --- | ----- | ------------- | --- | ---------- | ---- | includingbothopen-sourcemodelssuchasLlamaandclose- sourcemodelssuchasGPT-4o. Firstly,weaimtodemon- perature to 0 while keeping all other parameters at their stratethatR-Benchisabenchmarkforcomplexreasoning default values. The evaluation was conducted using the | | | | | | | toolsprovidedbyOpenCompass(Contributors,2023). | | | | | | | In | | --- | --- | --- | --- | --- | --- | ---------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | throughexpertscoring(userstudy)ando1modelscoring. | | | | | | | alltests,theCoTpromptisusedbydefault. | | | | | | Fordetailson | | | --- | --- | --- | --- | --- | --- | ------------------------------------- | --- | --- | --- | --- | --- | ------------ | --- | Then,weevaluatethereasoningcapabilitiesofmodelswith | | | | | | | thespecificprompts, | | | pleaserefertoourappendix. | | | | Inthe | | --------------------------------------------- | --- | --- | --- | --- | --- | ------------------- | --- | --- | ------------------------- | --- | --- | --- | ----- | | andwithoutCoTpromptingunderazero-shotsetting. | | | | | Fi- | | | | | | | | | resultsshowninTab.5,wefoundthatmodelsdesignedfor nally,weanalyzetheexperimentsandsummarizeobserva- | | | | | | | reasoning | | tasks, | such as o1, | outperform | | chat models | like | | --- | --- | --- | --- | --- | --- | --------- | --- | ------ | ----------- | ---------- | --- | ----------- | ---- | tionsandfindingsfromtheexperimentalprocess. | | | | | | | GPT-4o | in | complex | reasoning. | Besides, | | there | remains a | | --- | --- | --- | --- | --- | --- | ------ | --- | ------- | ---------- | -------- | --- | ----- | --------- | significantgapincomplexreasoningbetweenopen-source 3.1.Reasoningcomparisonwithotherbenchmarks modelsandcommercialmodels. ToillustratethatR-Benchisabenchmarkdesignedtoeval- R-Bench-M | | | | | | | Moreover, | | we utilize | | | to evaluate | the | reason- | | -------------- | -------- | --- | --------- | ------------ | ------ | --------- | --- | ---------- | --- | --- | ----------- | --- | ------- | | uate reasoning | ability, | | we employ | two methods: | expert | | | | | | | | | ingcapabilitiesofvariousMLLMs,includingo1(OpenAI, scoringandreasoningmodelscoring. 2024b),GPT-4o(OpenAI,2024a),Claude3.5(Anthropic, Weconductedexpertscoringthroughuserstudies.Tobespe- 2024b), Qwen2.5-VL (Yang et al., 2024), and InternVL cific,werandomlyselected30questionsfromR-Bench-T 2.5(Chenetal.,2024),etc,acrossbothEnglishandChinese andanother30questionsfromMMLUandpresentedthem languages. TheevaluationalsoinvolvesutilizingAPIcalls to experts for pairwise comparisons to determine which anddeployingopen-sourcemodelslocally. ForAPIcalls, questionrequiredmorereasoningskillstosolve. Wecon- weutilizetheofficialinterfaceswithdefaulthyperparam- structed similar experiments using the same settings be- eters. For open-source models, we deploy their weights tweenR-Bench-MandMMMU. locallyusingVLMEvalKit(Duanetal.,2024),settingthe temperatureto0whilekeepingallotherparametersattheir Forreasoningmodelscoring,weadoptedtwoapproaches. | | | | | | | defaultvalues. | | Inalltests,theCoTpromptisusedbyde- | | | | | | | ------------ | --- | ---- | ------ | ------------------ | ----- | -------------- | --- | ---------------------------------- | --- | --- | --- | --- | --- | | On one hand, | we | used | the o1 | model to determine | which | | | | | | | | | fault. Fordetailsonthespecificprompts,pleaserefertoour questionrequiredmorereasoningabilitybasedonthenum- | | | | | | | appendix. | | We draw | three | conclusions | from | the | results in | | --- | --- | --- | --- | --- | --- | --------- | --- | ------- | ----- | ----------- | ---- | --- | ---------- | berofreasoningtokens(reasoningtime);ontheotherhand, Tab.6. First,wefoundthatmodelsperformworseinmulti- weaskedtheo1modeltodirectlycomparethetwoquestions modalcomplexreasoningcomparedtoreasoninginapurely anddeterminewhichonerequiredmorereasoning. | | | | | | | linguistic | | environment. | Second, | | the reasoning | | model o1 | | --- | --- | --- | --- | --- | --- | ---------- | --- | ------------ | ------- | --- | ------------- | --- | -------- | TheresultsareshowninTab.2,3and4. Theresultsindicate stilldemonstratesoutstandingperformanceinmultimodal thatbotho1’sjudgmentandtheexperts’judgmentconsider complexreasoningevaluation. Third,thegapbetweenopen- R-Bench to require significantly higher reasoning ability sourceandclosed-sourcemodelsisevenmorepronounced | comparedtoMMLUandMMMU. | | | | | | inmultimodalcomplexreasoning. | | | | | | | | | ---------------------- | --- | --- | --- | --- | --- | ----------------------------- | --- | --- | --- | --- | --- | --- | --- | 6 R-Bench Table5.PerformancecomparisonofvariousmodelsonR-Bench- Table6.PerformancecomparisonofvariousmodelsonR-Bench- Tinzero-shotsettingswithCoT.Thetableisdividedbyamiddle Minzero-shotsettingswithCoT.Thetableisdividedbyamiddle line:API-basedmodelsarelistedabovetheline,whileopen-source line:API-basedmodelsarelistedabovetheline,whileopen-source modelsareshownbelow.‘zh’indicatestheChineseversion.The modelsareshownbelow.’zh’indicatestheChineseversion.The valuesinthetablerepresenttheTop-1accuracy,in%. valuesinthetablerepresenttheTop-1accuracy,in%. | | R-Bench-T | R-Bench-T(zh) | | | R-Bench-M | R-Bench-M(zh) | | ----------- | --------- | ------------- | ----------- | --- | --------- | ------------- | | ModelName | | | ModelName | | | | | o1-20241217 | 69.0 | 70.1 | o1-20241217 | | 53.2 | 55.0 | Gemini-2.0-flash-thinking 68.4 67.5 Claude3.5-sonnet@1022 39.7 38.3 Doubao1.5pro-20250121 62.0 63.4 Doubao1.5pro-20250121 37.9 42.4 | o1-preview@20240912 | 62.3 | 62.6 | GPT-4o-20241120 | | 33.4 | 33.2 | | --------------------- | ---- | ---- | ---------------------- | --- | ---- | ---- | | o1-mini@20240912 | 64.0 | 59.9 | Gemini-1.5-Pro | | 35.5 | 35.9 | | Doubao-pro-20241215 | 60.7 | 60.8 | | | | | | | | | Qwen2-VL-72B | | 25.1 | 25.7 | | Claude3.5-sonnet@0620 | 57.5 | 57.0 | | | | | | | | | Qwen2-VL-7B | | 19.6 | 22.3 | | GPT-4o-20241120 | 53.6 | 51.6 | | | | | | | | | LLaVA-OneVision-7B | | 23.8 | 23.5 | | MiniMax-Text-01 | 53.8 | 53.6 | | | | | | | | | DeepSeek-VL2 | | 21.8 | 24.4 | | GLM-Zero-Preview | 53.6 | 48.6 | | | | | | | | | Llama3.2V-11B-Instruct | | 20.0 | 18.6 | | ERNIE-4.0-8K-Latest | 39.7 | 50.1 | | | | | | | | | InternVL-2.5-8B | | 15.9 | 17.1 | | Deepseek-R1 | 61.2 | 59.3 | | | | | | Deepseek-V3 | 59.6 | 56.6 | | | | | | Qwen3-235B-A22B | 58.0 | 58.4 | | | | | Table7.AssessingtheperformanceimpactofCoTacrossdifferent | Qwen3-32B | 52.3 | 54.3 | modelsonR-Bench-T. | | | | | ---------------------- | ---- | ---- | --------------------- | --- | ------- | --------- | | Qwen2.5-72B-Instruct | 53.7 | 52.0 | | | | | | Llama-3.3-70B-Instruct | 49.5 | 47.6 | ModelName | | wCoT(%) | w/oCoT(%) | | Qwen2.5-32B-Instruct | 50.8 | 49.9 | | | | | | | | | o1-mini@20240912 | | 64.0 | 64.0 | | Gemma-2-27b-it | 36.0 | 38.9 | | | | | | | | | GPT-4o-20241120 | | 53.6 | 51.5 | | Phi-4-14B | 55.3 | 47.3 | LLAMA3.3-70B-Instruct | | 49.5 | 47.4 | | Phi-3-14B | 29.5 | 24.4 | | | | | | | | | Qwen2.5-32B-Instruct | | 50.8 | 44.6 | | Qwen3-8B | 47.5 | 45.9 | | | | | | | | | Qwen2.5-7B-Instruct | | 43.6 | 42.6 | | InternLM3-8B-Instruct | 41.1 | 45.8 | | | | | | Qwen2.5-7B-Instruct | 43.6 | 44.5 | | | | | GLM-4-9b-chat 25.6 32.4 focused modelssuch as o1-mini. We conjecture thatthis | Llama-3.1-8B-Instruct | 26.1 | 23.6 | | | | | | --------------------- | ---- | ---- | --- | --- | --- | --- | discrepancyarisesbecausereasoningmodelsinherentlyuti- | Llama-3.2-3B-Instruct | 24.2 | 24.0 | | | | | | --------------------- | ---- | ---- | --- | --- | --- | --- | lizeCoT-likemechanisms,leadingtotheexplicitaddition ofCoTredundantandineffective. 3.3.Observationsandfindings | | | | Consistency | between | English and | Chinese questions. | | --- | --- | --- | ----------- | ------- | ----------- | ------------------ | Multimodalreasoningremainschallengingforcurrent AsshowninFig.5,wetestedtheconsistencyofthesame questionacrossdifferentlanguagesonR-Bench-T.Itcanbe models. Wecomparedtheperformanceofthesamemodel onR-Bench-TandR-Bench-M.Forexample,o1achieved observedthatmostmodels,suchaso1,Doubao1.5pro,and 69.0%onR-Bench-Tbutonly53.2%onR-Bench-M.The GPT-4o,exhibitacertaindegreeofconsistencyacrossdif- samesituationalsooccursinothermodels,suchasGPT-4o. ferentlanguages.Thissuggeststhatfoundationmodelshave Itindicatesthatthemodel’scapabilityinlanguagereasoning alreadydemonstratedacertainlevelofintelligence,enabling significantlysurpassesitsabilityinmultimodalreasoning. themtoperformreasoningonproblemsofthesamediffi- Therefore,akeyfocusofresearchintherecentfuturewill cultyindifferentlinguisticenvironments. However,these behowtotransferlinguisticintelligencetothemultimodal modelsarenotperfectandstillrequirefurtherimprovement domain. inthisaspect. Thisconsistencyreflectstheextenttowhich | | | | themodeloverfitsdifferentlanguages. | | | Therefore,wehope | | --- | --- | --- | ----------------------------------- | --- | --- | ---------------- | futuremodelswillfocusmoreonlearninghowtoreason | TheeffectofCoT. InTab.7,wetestedtheeffectofCoT | | | | | | | | ---------------------------------------------- | --- | --- | --- | --- | --- | --- | onfivemodels. Asseeninthetable,mostmodelsbenefit ratherthanmerelyfittingtospecificlanguages. | fromCoT,butithasnoimpactono1-mini. | | Theresultsindi- | | | | | | ---------------------------------- | --- | --------------- | --- | --- | --- | --- | catethatCoTenhancestheperformanceofchatmodelslike Modelsshowsignificantperformancevariationacross GPT-4o. However,ithasnonotableimpactonreasoning- disciplines. Fig.6showstheperformanceofGPT-4oin 7 R-Bench leveragedacrossdiversefieldssuchaswriting,coding,edu- cation,healthcare,finance,andmore,servingasasource Consistency of English and Chinese questions with the same difficulty 86.7% | | | | | | | forprovidingintelligence. | | | Now, | foundationmodelshave | | | | | --- | -------- | --- | --- | --- | --- | ------------------------- | --- | --- | ---- | -------------------- | --- | --- | --- | | | 80 78.5% | | | | | | | | | | | | | 75.2% 73.5% 73.4% 73.3% becomeanessentialpartofourdailyworkandlife. | | | | 72.4% 70.5% | 69.3% 69.2% | | | | | | | | | | | --- | --- | --- | ----------- | ----------- | ----------------- | ------------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | | | | | | | 68.3% 68.0% 66.9% | | | | | | | | | | | 60 | | | | | Tobuildahigh-qualityfoundationmodel,webelievethat | | | | | | | | ycnetsisnoC fivekeyaspectsareessential: pre-training(Vaswanietal., 2017;Raffeletal.,2020;Sunetal.,2023;Radfordetal., 40 2021;2018),supervisedfine-tuning(Ouyangetal.,2022; | | | | | | | Liu et al., | 2024b; | Pareja | et | al., 2024; | Li | et al., | 2024; | | --- | --- | --- | --- | --- | --- | ----------- | ------ | ------ | --- | ---------- | --- | ------- | ----- | 20 | | | | | | | Zhu et al., | 2023; | Taori | et al., | 2023), | preference | optimiza- | | | --- | --- | --- | --- | --- | --- | ----------- | ----- | ----- | ------- | ------ | ---------- | --------- | --- | tion(Rafailovetal.,2024;Schulmanetal.,2017;Lightman | | 0 7 5 | 2 c t 0 | 0 c t i t | c t uc t -8B-Instruct | B .5-7B-Instruct | | | | | | | | | | --- | ----- | ------- | --------- | --------------------- | ---------------- | --- | --- | --- | --- | --- | --- | --- | --- | 4 1 2 1 4 1 2 1 4 0 9 1 s t r u onnet@ 0 6 2 4 1 1 2 -32B-Inst ru -2 7 b - s tr u s tr 4 -1 4 et al., 2023; Pal et al., 2024; Azar et al., 2024),test-time | | 20 2 -2 0 2 @2 | 0 2 B -I n | 20 2 a -2 70B - In | B - In | Ph i- | | | | | | | | | | --- | -------------- | ---------- | ------------------ | ------- | ----- | --- | --- | --- | --- | --- | --- | --- | --- | | | o1- -p ro w | -7 2 s 4o- | m m - | .1 -8 3 | | | | | | | | | | a o e v ie n 2 . 5 3 . 5 - G P T - n 2 . 5 G e a- 3 . 3 a - 3 rn L M e n 2 enhancement(Brownetal.,2020;Weietal.,2022;OpenAI, | | D o u b 1 -p r | Q w e au d e | Q w e la m L la m | nt e | Q w | | | | | | | | | | --- | -------------- | ------------ | ----------------- | ---- | --- | ------------------------------------------------ | --- | ------- | ------- | ----- | ---------- | ----- | ---- | | | o | C l | L | I | | 2024b;DeepSeek,2024;Dongetal.,2022),andtrustwor- | | | | | | | | | | | | | | | thy evaluation | | (Chiang | et al., | 2024; | Li et al., | 2023; | Chen | Figure5.Theperformanceofdifferentmodelsonquestionsofthe | | | | | | | et al., 2021; | Jain | et al., | 2024; | Yu et | al., 2023). | Reliable | | | --- | --- | --- | --- | --- | --- | ------------- | ---- | ------- | ----- | ----- | ----------- | -------- | --- | samedifficultyinChineseandEnglish. evaluationplaysacrucialroleinrevealingmodels’weak- nessesandshortcomings,guidingfurtheroptimizationand improvement,whichisalsothefocusofthispaper. Accuracy of Different Departments 70 68.3%68.0% Average: 53.6% 4.2.Evaluationforfoundationmodels 62.5% | | | 61.0% | | | | Evaluatingtheintelligenceoffoundationmodelsisamul- | | | | | | | | | --- | --- | ----- | --- | --- | --- | -------------------------------------------------- | --- | --- | --- | --- | --- | --- | --- | | | 60 | 58.4% | | | | | | | | | | | | 55.9%55.8%55.3%54.5%54.2% tifacetedandcomplexchallenge,akintoassessinghuman 53.6% )%( ycaruccA 51.0% intelligence. Researchers have introduced various evalu- | | 50 | | 48.0% | | | | | | | | | | | | --- | --- | --- | ----- | --- | --- | ----------------- | --- | ------- | ----------- | --- | ---- | ------------- | --- | | | | | | | | ation benchmarks, | | broadly | categorized | | into | fast-thinking | | 44.9% | | | | | | | assessments | ( | a.k.a., system-I | | evaluation | | (Chiang | et al., | | --- | --- | --- | --- | ---------- | --- | ------------ | --- | ---------------- | ----- | ---------- | ---------- | ------- | ------- | | | 40 | | | 39.0%38.9% | | | | | | | | | | | | | | | | | 2024; Dubois | | et al., 2024; | Zheng | et | al., 2023; | Lin | et al., | 34.4%33.3% 2021;2024;Luetal.,2022;Yuetal.,2023;Lietal.,2023), 30.4% 30 whichrequiresthefoundationmodelstomemorizeexten- siveknowledgeandretrieveefficiently,andslow-thinking | | Biolog y s E . tronic E | . erospac e hemistry Ma th utomation | s ic s on ic s hanical E. Statist ic s emica l E . | puter S. Materials Civil E | . e E . ironme nt conomics | | | | | | | | | | --- | ------------------------ | ------------------------------------ | -------------------------------------------------- | -------------------------- | --------------------------- | --- | --- | --- | --- | --- | --- | --- | --- | hysic Ph y lectr ehicl assessments(a.k.a.,system-IIevaluation(Hendrycksetal., | | P E l ec | A C A | o e e c C h C om | | V E n v E | | | | | | | | | | --- | -------- | ----- | ---------------- | --- | --------- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | M i cr M | | | | | | | | | | | 2021;Yueetal.,2024a;Luetal.,2023;Wangetal.,2024a; Liuetal.,2024c;Chenetal.,2021;Jimenezetal.,2023), R-Bench-T | Figure6.GPT-4o | | on | across | different | departments, | | | | | | | | | | -------------- | --- | --- | ------ | --------- | ------------ | --- | --- | --- | --- | --- | --- | --- | --- | whichemphasizesthecomplexreasoningskillsoffounda- whichshowslargevariationamongdifferentdisciplines.. R-Benchfocusesonthelatter. tionmodels. MMLU(Hendrycksetal.,2021)isthepioneerinreasoning different areas of the R-Bench-T benchmark. From the evaluation,whichproposesamulti-disciplineunderstanding test. Afterthat,lotsofmulti-disciplinebenchmarks(Rein figure,itcanbeobservedthattheperformancevariessig- nificantlyacrossdifferentdomains,witharangereaching etal.,2023;Wangetal.,2024b;Yueetal.,2024b)atthe 37.9%. This suggests that if we want to improve the rea- undergraduateorgraduatelevelareproposedforreasoning | | | | | | | assessment. | However,withtherapiddevelopmentofintelli- | | | | | | | | --- | --- | --- | --- | --- | --- | ----------- | ----------------------------------------- | --- | --- | --- | --- | --- | --- | soningabilityofmodels,weshouldtakeacomprehensive approachratherthanfocusingsolelyonimprovementsina gentmodels(OpenAI,2024b),thesebenchmarksareclose | | | | | | | tosaturation. | Besides,severalstudies(Glazeretal.,2024; | | | | | | | | --- | --- | --- | --- | --- | --- | ------------- | ---------------------------------------- | --- | --- | --- | --- | --- | --- | singlesubject,suchasmathematics. Gaoetal.,2024;Luetal.,2023;Wangetal.,2024a)assess reasoningabilitythroughcomplexmathematicalproblems 4.RelatedWork | | | | | | | such as | mathematical | | olympiad | challenges, | | which | bring | | --- | --- | --- | --- | --- | --- | ------- | ------------ | --- | -------- | ----------- | --- | ----- | ----- | 4.1.Foundationmodels challengesandguidancetocurrentfoundationmodels.How- ever,onlyguidingthemodeltoimproveitsmathematical WiththeemergenceofChatGPT(OpenAI,2022),founda- | | | | | | | reasoning | skills | appears | to be | limited. | In this | paper, | our | | --- | --- | --- | --- | --- | --- | --------- | ------ | ------- | ----- | -------- | ------- | ------ | --- | tionmodels(Ouyangetal.,2022;Touvronetal.,2023;Yang targetistobuildareliablebenchmarkforLLMandMLLM etal.,2024;Jiangetal.,2023;Teametal.,2024;Zengetal., reasoning evaluation, which matches the comprehensive- | 2022; | Bi et | al., 2024; | Liu et al., 2024a; | Cai | et al., 2024; | | | | | | | | | | ----- | ----- | ---------- | ------------------ | --- | ------------- | --- | --- | --- | --- | --- | --- | --- | --- | nessofMMLU(Hendrycksetal.,2021)whileachieving Anthropic,2024a;Wuetal.,2024)areincreasinglybeing 8 R-Bench thedifficultyofmathematicalolympiadquestions. 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Ad- | | | | | | | | | -------------- | ------------- | ----------- | ---------- | --- | --- | --- | --- | --- | --- | --- | vances in Neural Information Processing Systems, 36: Here, wepresentourquestionandtheoutputoftheOpe- 46595–46623,2023. | | | | | nAI’so1modelintheboxbelow. | | | | Themodelcarriedouta | | | | --- | --- | --- | --- | -------------------------- | --- | --- | --- | ------------------- | --- | --- | step-by-stepanddetailedreasoningbasedonthequestion | Zhu, D., | Chen, J., Shen, | X., Li, X., | and Elhoseiny, M. | | | | | | | | | -------- | --------------- | ----------- | ----------------- | --- | --- | --- | --- | --- | --- | --- | andfinallyarrivedatthecorrectanswer. | Minigpt-4: | Enhancing | vision-language | understanding | | | | | | | | | ------------- | -------------- | --------------- | -------------- | --- | --- | --- | --- | --- | --- | --- | | with advanced | large language | models. | arXiv preprint | | | | | | | | Questionandtheresponsebyo1 arXiv:2304.10592,2023. | | | | | Answer | the | following | single choice | question. | | The | | --- | --- | --- | --- | ------ | --- | --------- | ------------- | --------- | --- | --- | lastlineofyourresponseshouldbeofthefollowing | | | | | format: | ’ANSWER: | | $LETTER’ | (without | quotes) | | | --- | --- | --- | --- | ----------------------------------------- | ----------- | ---------- | --------------- | -------- | ---------- | ------ | | | | | | where | LETTER | is one | of Options(e.g. | | | one of | | | | | | ABCDEF). | | Think step | by step | before | answering. | | | | | | | Question: | | A sudden | environmental | change | | causes | | | | | | arecessivealleletobecomecompletelylethal. | | | | | | How | | | | | | many | generations | will | it take | for its | frequency | to | | | | | | decrease | from | 10−2 to | 10−3? | | | | A. 950 B. 850 | | | | | C. | All other | answers are | incorrect | | | | | --- | --- | --- | --- | --- | --------- | ----------- | --------- | --- | --- | --- | D. 900 E. 800 F. 920 Answer: | | | | | ### | Response | by o1 | | | | | | --- | --- | --- | --- | ---------------------------------- | ----------- | ------- | --------- | -------------- | --------- | --- | | | | | | To | solve this, | use the | fact that | for a fully | recessive | | | | | | | lethalallele(withinitialfrequencyq | | | | ),itsfrequency | | | 0 | | | | | in the | next | generation | is given | by: | | | | --- | --- | --- | --- | ------ | ---- | ---------- | -------- | --- | --- | --- | q | | | | | | | q | = n | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | n+1 1+q n 1 | | | | | Define | R n | = . Then | from the | recurrence | | above: | | --- | --- | --- | --- | ------ | --- | -------- | -------- | ---------- | --- | ------ | qn 1 | | | | | | | R | = | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | n+1 | q | | | | n+1 1+q n = q n 1 | | | | | | | | = +1 | | | | | --- | --- | --- | --- | --- | --- | --- | ---- | --- | --- | --- | q n | | | | | | | | =R +1 | | | | | --- | --- | --- | --- | --- | --- | --- | ----- | --- | --- | --- | n | | | | | Thus,R | =R | +n. SinceR | | = 1 andwewantq | | | | --- | --- | --- | --- | ----------- | ------- | ----------- | --------- | -------------- | --- | --- | | | | | | | n | 0 | 0 | q0 | | n | | | | | | to decrease | | from 0.01 | to 0.001: | | | | | | | | | • | R = | 1 =100. | | | | | | | | | | | 0 | 0.01 | | | | | | | | | | • | We need | 1 =1000, | so R | =1000. | | | | | | | | | | qn | | n | | | | | | | | • | Hence | 1000=100+n, | giving | n=900. | | | | | | | | ANSWER: | | D | | | | | A.2.CoTPrompt Here,wepresenttheformatofourCoTpromptinfollowing box. Aswecansee,ourCoTpromptmainlyuses“Think stepbystep”,whichshowsthatevenasimplepromptstill 12 R-Bench hasapositiveeffectonmostchatmodels. SystemPromptforR-Bench Answer the following single-choice question. The lastlineofyourresponseshouldbeofthefollowing format: ’ANSWER: $LETTER’ (without quotes) where LETTER is one of the Options (e.g. one of ABCDEF). Think step by step before answering. Question: {Question Input} A. {OptionA} B. {OptionB} C. {OptionC} D. {OptionD} E. {OptionE} F. {OptionF} Answer: ### Example: Answer the following single choice question. The lastlineofyourresponseshouldbeofthefollowing format: ‘ANSWER: $LETTER’ (without quotes) where LETTER is one of Options(e.g. one of ABCDEF). Think step by step before answering. Question: ConsideraCMOSinverterdrivingawire of length L. In the initial design, the on-resistance oftheinverterisequaltothetotalresistanceofthe wire, the source-drain capacitance of the inverter is equal to the total capacitance of the wire, and the total delay of the inverter and wire is tp. Now, the devices are scaled down using Constant Field Scaling, while the wire is ideally scaled down. Assumingthewirecanbemodeledusingalumped parameter model, answer the following questions in a first-order approximation: (1) Assuming the wire is a local wire, and the scaling factors for both process and supply voltage are 2, express the total delay after scaling in terms of tp. (2) Now assume the wire is global, and the length of the wire increases inversely with the process scaling, with scaling factors for both process and supply voltage being 2, express the total delay after scaling in terms of tp. A. (1) 1/3tp (2) 35/6tp B. (1) 1/2tp (2) 38/6tp C. All other answers are incorrect D. (1) 3/4tp (2) 36/6tp E. (1) 5/6tp (2) 39/6tp F. (1) 2/3tp (2) 37/6tp Answer: A.3.Specificsubjectdistribution WepresentthespecificsubjectdistributionsofR-Bench-T andR-Bench-MinTable8andTable8,respectively. Itcan beobservedthatR-Benchhasabroadcoverage,makingit difficulttoimproveperformanceonR-Benchbyoverfitting tospecificsubjects. 13 R-Bench DistributionofCoursesbyDisciplineinR-Bench-T Table8: | Discipline | SpecificSubject | Count | | ------------------- | ------------------------------- | ----- | | | FluidMechanics | 33 | | CivilEngineering | StructuralMechanics | 2 | | | Surveying | 1 | | | PrinciplesofProcessTransport | 3 | | ChemicalEngineering | PrinciplesofChemicalEngineering | 15 | | | AnalyticalChemistry | 7 | | | AdvancedMathematicalEconomics | 1 | | | Econometrics | 3 | | | IntermediateFinancialTheory | 1 | | Economics | FinancialEngineering | 1 | | | GameTheoryandMechanismDesign | 5 | | | IntermediateMicroeconomics | 2 | | | PrinciplesofAccounting | 2 | | | TimeSeriesAnalysis | 8 | | | SoilScience | 1 | | | Genetics | 16 | Biology | | Physiology | 1 | | ------- | ----------------------------------- | --- | | | Biochemistry | 15 | | | Heredity | 8 | | | MathematicalMethodsinPhysics | 10 | | | Electromagnetics | 11 | | | Optics | 23 | | | QuantumMechanics | 8 | | Physics | AnalyticalMechanics | 6 | | | Electrodynamics | 5 | | | ThermodynamicsandStatisticalPhysics | 6 | | | GeneralRelativity | 2 | | | BasicPhysics | 29 | | | GroupTheory | 3 | | | MechanicsofMaterials | 1 | | | StructuralMechanicsofAircraft | 3 | | | TheoreticalMechanics | 2 | Aerospace | | FluidMechanicsandAerodynamics | 15 | | --- | ----------------------------------------- | --- | | | OptimalControl | 29 | | | PropulsionPrinciplesandThermalFluidBasics | 9 | | | DigitalLarge-ScaleIntegratedCircuits | 20 | Microelectronics | | AnalogCircuits | 2 | | ---------- | ------------------------------- | --- | | | SignalsandSystems | 20 | | Automation | OperationsResearch | 15 | | | AutomaticControlTheory | 17 | | | CommunicationandNetwork | 15 | | | PrinciplesofAnalogCircuits | 4 | | | ElectromagneticFieldsandWaves | 8 | | | FundamentalsofSolidStatePhysics | 12 | ElectronicEngineering | | DigitalSignalProcessing | 8 | | --- | ----------------------- | --- | | | StochasticProcesses | 3 | Continuedonnextpage 14 R-Bench Table8–Continuedfrompreviouspage | Discipline | SpecificSubject | Count | | ---------- | ---------------------------------------------------------- | ----- | | | SolidStatePhysics | 4 | | | AppliedStochasticProcesses | 26 | | | FluidMechanics | 11 | | | PrinciplesandInterfaceTechnologyofSingle-ChipMicrocomputer | 4 | | | MechanicalDesign | 1 | | | TheoryofMachines | 4 | | | ElectromechanicalTransmissionandControl | 4 | MechanicalEngineering | | ElectricalandelectronicTechnology | 2 | | --------------- | ------------------------------------ | --- | | | MechanicalVibration | 3 | | | HydraulicandPneumaticTransmission | 1 | | | EngineeringThermodynamics | 8 | | | MechanicsofMaterials | 9 | | | TheoreticalMechanics | 1 | | | DataStructure | 24 | | | CombinatorialMathematics | 3 | | | NumericalAnalysis | 5 | | | Cryptography | 17 | | ComputerScience | Automata | 8 | | | PrinciplesofComputerOrganization | 2 | | | CompilationPrinciples | 5 | | | ComputerNetwork | 11 | | | OperatingSystem | 11 | | | ComputerArchitecture | 3 | | | InorganicChemistry | 50 | | | ChemicalThermodynamics | 48 | | | ChemicalReactionKinetics | 20 | | | IntroductiontoComputationalChemistry | 11 | Chemistry | | QuantumChemistry | 5 | | --- | ---------------------------- | --- | | | PhysicalChemistry | 22 | | | OrganicChemistry | 5 | | | ComplexAnalysis | 26 | | | AnalyticGeometry | 26 | | | AdvancedCalculus | 9 | | | NumberTheory | 22 | | | MatrixAnalysis | 36 | | | PartialDifferentialEquations | 29 | Mathematics | | MathematicalAnalysis | 9 | | --- | ----------------------------------- | --- | | | StochasticDifferentialEquations | 8 | | | FunctionalAnalysis | 14 | | | OrdinaryDifferentialEquations | 3 | | | DifferentialGeometry | 3 | | | Topology | 3 | | | ThermodynamicsandStatisticalPhysics | 5 | PhysicsEngineering | | NuclearRadiationPhysicsandDetection | 20 | | --- | ----------------------------------- | --- | | | QuantumandStatistics | 14 | | | PhysicalPropertiesofMaterials | 1 | Materials | | FundamentalsofMaterialsScience | 23 | | --- | ------------------------------ | --- | Continuedonnextpage 15 R-Bench Table8–Continuedfrompreviouspage | Discipline | SpecificSubject | Count | | ------------------ | ------------------------------------ | ----- | | | MaterialsAnalysisandCharacterization | 3 | | | FiniteElementAnalysisBasics | 1 | | | PrinciplesofAutomotivePowerSystem | 11 | | | AutomotiveElectronicsandControl | 1 | | VehicleEngineering | FundamentalsofControlEngineering | 3 | | | TheoryofAutomobile | 3 | | | AutomobileConstruction | 1 | | | DiscreteMathematics | 12 | | | ProbabilityTheory | 42 | | | IntroductiontoBayesianStatistics | 6 | Statistics | | ReliabilityDataandSurvivalAnalysis | 1 | | ----------- | --------------------------------------------------------- | --- | | | StatisticalInference | 2 | | | PrinciplesofEnvironmentalEngineeringScienceandEngineering | 5 | | Environment | WaterTreatmentEngineering | 12 | | | EnvironmentalChemistry | 1 | 16 R-Bench DistributionofCoursesbyDisciplineinR-Bench-M Table9: | Discipline | SpecificSubject | Count | | ---------- | ----------------------------- | ----- | | | MaterialsMechanics | 26 | | | FluidMechanicsandAerodynamics | 2 | | | TheoreticalMechanics | 16 | Aerospace | | AircraftStructuralMechanics | 2 | | --- | ------------------------------------ | --- | | | PropulsionPrinciplesandThermalFluids | 2 | | | OptimalControl | 2 | | | DigitalVLSI | 11 | | | AnalogCircuits | 19 | IntegratedCircuits | | DigitalElectronicsFundamentals | 8 | | ------------------- | ------------------------------ | --- | | | AnalogElectronicsFundamentals | 6 | | | TransportProcessPrinciples | 2 | | ChemicalEngineering | ChemicalPrinciples | 11 | | | PhysicalChemistry | 12 | | | ChemicalThermodynamics | 1 | | | ChemicalReactionKinetics | 10 | | Chemistry | InorganicChemistry | 1 | | | OrganicChemistry | 17 | | | PhysicalChemistry | 2 | | | DataStructures | 4 | | | Combinatorics | 1 | | | DiscreteMathematics | 12 | | | TheoryofAutomata | 7 | | ComputerScience | OperatingSystems | 6 | | | Compilers | 4 | | | ComputerArchitecture | 3 | | | Cryptography | 1 | | | ComputerNetworks | 1 | | | AnalyticalMechanics | 25 | | | Optics | 6 | | Physics | Electrodynamics | 9 | | | Electromagnetism | 10 | | | BasicPhysics | 10 | | | AnalogCircuitPrinciples | 17 | | | SignalsandSystems | 3 | | | DigitalSignalProcessing | 1 | ElectricalEngineering | | CommunicationandNetworks | 4 | | ----------- | ----------------------------- | --- | | | ElectromagneticFieldsandWaves | 1 | | | SolidStatePhysics | 1 | | | ComplexAnalysis | 8 | | | AnalyticGeometry | 2 | | | ProbabilityTheory | 5 | | | StochasticProcesses | 3 | | Mathematics | Analysis | 1 | | | ProbabilityandStatistics | 1 | | | MathematicalAnalysis | 5 | | | Statistics | 6 | Continuedonnextpage 17 R-Bench Table9–Continuedfrompreviouspage | Discipline | SpecificSubject | Count | | ---------- | -------------------------------------------- | ----- | | | Topology | 1 | | | WaterTreatmentEngineering | 4 | | | EnvironmentalScienceandEngineeringPrinciples | 9 | | | EnvironmentalMonitoring | 6 | EnvironmentalEngineering | | WaterPollutionControlProject | 4 | | --- | ------------------------------ | --- | | | EnvironmentalChemistry | 1 | | | SolidWasteTreatmentandDisposal | 2 | | | Genetics | 13 | Biology | | Biochemistry | 4 | | --- | ------------------------------ | --- | | | MaterialsMechanics | 37 | | | QuantumandStatisticalMechanics | 5 | MaterialScience | | MaterialAnalysisandCharacterization | 1 | | --------- | --------------------------------------- | --- | | | BasicMaterialScience | 18 | | | OperationsResearch | 2 | | | PrinciplesofAccounting | 3 | | Economics | FinancialEngineering | 2 | | | IntermediateFinancialTheories | 3 | | | GameTheoryandMechanismDesign | 8 | | | ElectricalandElectronicsTechnology | 5 | | | MechanicalDesign | 24 | | | ElectromechanicalTransmissionandControl | 1 | | | HydraulicandPneumaticTransmission | 9 | MechanicalEngineering | | MechanicalVibrations | 7 | | ------------------ | ------------------------------- | --- | | | FluidMechanics | 7 | | | PrinciplesofMechanics | 1 | | | TheoreticalMechanics | 11 | | CivilEngineering | StructuralMechanics | 33 | | EngineeringPhysics | EngineeringMechanics | 23 | | Automation | AutomaticControlTheory | 25 | | | FluidMechanics | 34 | | | EngineeringControlBasics | 8 | | | FiniteElementAnalysisBasics | 5 | | VehicleEngineering | AutomotiveElectronicsandControl | 5 | | | AutomobileConstruction | 5 | | | AdvancedHeatTransfer | 9 | | | AutomotivePowerSystemPrinciples | 2 | | Architecture | StructuralEngineering | 21 | 18