%20and%20Binary%20Programming%20(BP)%20problems%2C%20laying%20the%20groundwork%20for%20GNNs%20to%20approximate%20solutions%20for%20these%20computationally%20challenging%20problems.%20By%20analyzing%20the%20sensitivity%20of%20BP%20problems%2C%20we%20are%20able%20to%20frame%20the%20solution%20of%20BP%20problems%20as%20a%20heterophilic%20node%20classification%20task.%20We%20then%20propose%20Binary-Programming%20GNN%20(BPGNN)%2C%20an%20architecture%20that%20integrates%20graph%20representation%20learning%20techniques%20with%20BP-aware%20features%20to%20approximate%20BP%20solutions%20efficiently.%20Additionally%2C%20we%20introduce%20a%20self-supervised%20data%20generation%20mechanism%2C%20to%20enable%20efficient%20and%20tractable%20training%20data%20acquisition%20even%20for%20large-scale%20BP%20problems.%20Experimental%20evaluations%20of%20BPGNN%20across%20diverse%20BP%20problem%20sizes%20showcase%20its%20superior%20performance%20compared%20to%20exhaustive%20search%20and%20heuristic%20approaches.%20Finally%2C%20we%20discuss%20open%20challenges%20in%20the%20under-explored%20field%20of%20BP%20problems%20with%20GNNs.)
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