Correcting the LogQ Correction: Revisiting Sampled Softmax for Large-Scale Retrieval

The logQ correction for in-batch sampled softmax in two-tower retrieval models overlooks a subtle detail: the positive item in the denominator is always present with probability 1, not Monte Carlo–sampled, so a residual bias remains. We derive a refined correction whose interpretable sample weight reflects the model’s probability of misclassification, yielding consistent improvements over the standard logQ correction on both public and proprietary datasets.