基于代数方法视觉推理与渐进矩阵求解研究.pdfVIP

VisualReasoning:AnAlgebraicApproachforSolvingRaven’s

ProgressiveMatrices

1∗2◦∗2◦∗13◦1†

JingyiXuTusharVaidyaYufeiWuSaketChandraZhangshengLaiKaiFongErnestChong

1SingaporeUniversityofTechnologyandDesign

2NanyangTechnologicalUniversity3SingaporePolytechnic

3jingyixu@mymail.sutd.edu.sgtushar.vaidya@ntu.edu.sgyufei002@e.ntu.edu.sg

2laizhangsheng@sp.edu.sg{saketchandra,ernestchong}@sutd.edu.sg

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Weintroducealgebraicmachinereasoning,anewrea-

1

2soningframeworkthatiswell-suitedforreasoning.

Effectively,algebraicmachinereasoningreducesthediffi-

]cultprocessofnovelproblem-solvingtoroutinealgebraic

Vcomputation.Thefundamentalalgebraicobjectsofinterest

Caretheidealsofsomesuitablyinitializedpolynomialring.

s.WeshallexinhowsolvingRaven’sProgressiveMatri-

cces(RPMs)canberealizedascomputationalproblemsin

[

algebra,whichcombinevariouswell-knownalgebraicsub-

1routinesthatinclude:ComputingtheGro¨bnerbasisofanFigure1.AnexampleofRPMinstancefromtheI-RAVENdataset.

Thecorrectanswerismarkedwitharedbox.

videal,checkingforidealcontainment,etc.Crucially,the

0additionalalgebraicstructuresatisfiedbyidealsallowsfor

3moreoperat