Existing MIPL algorithms often overlook the margins for attention scores andpredicted probabilities, leading tosuboptimal generalization performance.

Problem(7)isNP-complete. Weshow that there exists apolynomial time reduction from the set cover problem to(7). We construct theM matrix according to the sets A1,...,Am (thei-thcolumnof M isthenonzeropatternof Ai).

Whenlabelsaresemantically complex and multi-modal, it is more natural to assign a label to multiple semantic clusters. In product categorization, for instance, the tag "belt" can be related to a vehicle belt (under "vehicle accessories" category),oraman'sbelt(under "clothing" category).