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Message PassingNeural Network
+are+often+vulnerable+to+attack%252C+we+need+to+know+when+we+can+trust+them.+We+develop+a+computationally+effective+approach+towards+providing+robust+certificates+for+message-passing+neural+networks+(MPNNs)+using+a+Rectified+Linear+Unit+(ReLU)+activation+function.+Because+our+work+builds+on+mixed-integer+optimization%252C+it+encodes+a+wide+variety+of+subproblems%252C+for+example+it+admits+(i)+both+adding+and+removing+edges%252C+(ii)+both+global+and+local+budgets%252C+and+(iii)+both+topological+perturbations+and+feature+modifications.+Our+key+technology%252C+topology-based+bounds+tightening%252C+uses+graph+structure+to+tighten+bounds.+We+also+experiment+with+aggressive+bounds+tightening+to+dynamically+change+the+optimization+constraints+by+tightening+variable+bounds.+To+demonstrate+the+effectiveness+of+these+strategies%252C+we+implement+an+extension+to+the+open-source+branch-and-cut+solver+SCIP.+We+test+on+both+node+and+graph+classification+problems+and+consider+topological+attacks+that+both+add+and+remove+edges.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.ef5fad5d90b3b701bbbeeeb2b4549c25%3frik%3do4uLVf%252buIuM%252fhg%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Message+Passing+Neural+Network&FORM=IRPRST&ck=458BB95FDA6170AEAC50C24D8C074CD7&selectedIndex=33&itb=0)
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