Distribution-Aware Energy Minimization: Physical-Inspired Efficient Active Learning and Quantum Potentials

Abstract

Active learning aims to maximize model performance with minimal annotation costs by selecting the most informative samples from large unlabeled pools, which often face a budget dilemma: uncertainty-based methods induce redundancy under low budgets, while representativeness-based methods struggle to mine challenging samples under high budgets. Although some heuristic parameter interpolation schemes attempt to bridge this gap, such strategies suffer from a misalignment between theoretical assumptions and real-world distributions, failing to achieve a good exploration-exploitation balance across all scenarios. In this paper, we propose a general active learning framework based on Distribution-Aware Energy Minimization, which reformulates sample selection as minimizing the energy function for the distributional discrepancy between the selected subset and the global uncertainty field. This physical-inspired perspective naturally derives a Hamiltonian comprising attractive terms and repulsive terms, mathematically achieving an intrinsic and dynamic balance between uncertainty and representativeness. Furthermore, we transform the optimization objective to the ground-state search of an Ising Model, enabling efficient solutions via Coherent Ising Machine. Extensive numerical experiments show that our method outperforms prior state-of-the-art methods across multi-budget regimes on several benchmark datasets. Validation on a real quantum hardware also demonstrates the potential for quantum computer in future large-scale selection tasks.