Quantum Probabilistic Label Refining: Enhancing Label Quality for Robust Image Classification

Abstract

Learning with softmax cross-entropy on one-hot labels often leads to overconfident predictions and poor robustness under noise or perturbations. Label smoothing mitigates this by redistributing some confidence uniformly, but treats all samples equally, ignoring intra-class variability. We propose a hybrid quantum-classical framework that leverages quantum non-determinism to refine data labels into probabilistic ones, offering more nuanced, human-like uncertainty representations than label smoothing or Bayesian approaches. A variational quantum circuit (VQC) encodes inputs into multi-qubit quantum states, using entanglement and superposition to capture subtle feature correlations. Measurement via the Born rule extracts probabilistic soft labels that reflect input-specific uncertainty. These labels are then used to train a classical convolutional neural network (CNN) with soft-target cross-entropy loss. On MNIST and Fashion-MNIST, our method improves robustness, achieving up to 50% higher accuracy under noise while maintaining competitive accuracy on clean data. It also enhances model calibration and interpretability, as CNN outputs better reflect quantum-derived uncertainty. This work introduces Quantum Probabilistic Label Refining, bridging quantum measurement and classical deep learning for robust training via refined, correlation-aware labels without architectural changes or adversarial techniques.