Advancing Optimal Subset Oracle via Learning Relaxation of Neural Set Functions

Abstract:Learning neural set functions is pivotal to a wide range of important applications, including compound selection in AI-driven drug discovery and product recommendation. Recent work has introduced optimal subset oracles to implicitly learn set functions under practical weakly supervised settings, where model parameters are optimized through mean-field variational inference. However, these frameworks rely on Monte Carlo sampling to estimate gradients of the evidence lower bound when updating the variational distribution. Repeated sampling across iterations incurs substantial computational overhead, while the resulting stochasticity can destabilize the optimization trajectory. In this work, we reinterpret the evidence lower bound as a continuous relaxation of the set function and learn a surrogate objective that replaces sampling-based ELBO gradient estimation during variational optimization. The learned surrogate provides stable and efficient gradients throughout the continuous domain, thereby reducing computational overhead and accelerating inference. Furthermore, we establish an approximation guarantee for the proposed framework under submodular maximization and characterize its connection to variational free energy. Experiments on a variety of real-world tasks demonstrate consistent improvements over existing baselines.

Machine Learning (cs.LG)

arXiv:2607.11555 [cs.LG]

(or arXiv:2607.11555v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.11555 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.