Increasing Information Extraction in Low-Signal Regimes via Multiple Instance Learning

In this work, we introduce a new information-theoretic perspective on Multiple Instance Learning (MIL) for parameter estimation with i.i.d. data, and show that MIL can outperform single-instance learners in low-signal regimes. Prior work [Nachman and Thaler, 2021] argued that single-instance methods are often sufficient, but this conclusion presumes enough single-instance signal to train near-optimal classifiers. We demonstrate that even state-of-the-art single-instance models can fail to reach optimal classifier performance in challenging low-signal regimes, whereas MIL can mitigate this sub-optimality. As a concrete application, we constrain Wilson coefficients of the Standard Model Effective Field Theory (SMEFT) using kinematic information from subatomic particle collision events at the Large Hadron Collider (LHC). In experiments, we observe that under specific modeling and weak signal conditions, pooling instances can increase the effective Fisher information compared to single-instance approaches.