Discrete and Continuous Difference of Submodular Minimization

arXiv — cs.LG•Wednesday, November 5, 2025 at 5:00:00 AM

A recent study published on arXiv investigates the minimization of the difference between two submodular functions in both discrete and continuous domains. The research demonstrates that all functions defined on discrete domains, as well as all smooth functions on continuous domains, can be classified as differences of submodular functions. This classification extends previous understanding by encompassing a broad range of functions within this framework. Furthermore, the findings indicate an equivalence between minimizing these functions in discrete settings and minimizing their differences, suggesting a unified approach to optimization in such contexts. These results contribute to the theoretical foundation of submodular function minimization and may have implications for related machine learning and optimization problems. The study builds on and aligns with ongoing research efforts documented in recent arXiv publications.

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