Multiplicative Loss for Enhancing Semantic Segmentation in Medical and Cellular Images

Abstract: We propose two novel loss functions, Multiplicative Loss and Confidence-Adaptive Multiplicative Loss, for semantic segmentation in medical and cellular images. Although Cross Entropy and Dice Loss are widely used, their additive combination is sensitive to hyperparameters and often performs suboptimally, especially with limited data. Medical images suffer from data scarcity due to privacy, ethics, and costly annotations, requiring robust and efficient training objectives. Our Multiplicative Loss combines Cross Entropy and Dice losses multiplicatively, dynamically modulating gradients based on prediction confidence. This reduces penalties for confident correct predictions and amplifies gradients for incorrect overconfident ones, stabilizing optimization. Building on this, Confidence-Adaptive Multiplicative Loss applies a confidence-driven exponential scaling inspired by Focal Loss, integrating predicted probabilities and Dice coefficients to emphasize difficult samples. This enhances learning under extreme data scarcity by strengthening gradients when confidence is low. Experiments on cellular and medical segmentation benchmarks show our framework consistently outperforms tuned additive and existing loss functions, offering a simple, effective, and hyperparameter-free mechanism for robust segmentation under challenging data limitations.