PU-UNet: Stable Multiplicative Interactions for Medical Image Segmentation

2026-06-18

AI Summary

This work addresses the limitations of existing medical image segmentation methods, which predominantly rely on additive feature transformations and struggle to explicitly model high-order feature interactions, while multiplicative operations are often avoided due to numerical instability in dense prediction tasks. To overcome this, the authors propose PU-UNet, which integrates numerically stable product-unit residual blocks into the low-resolution stages of a U-Net architecture. Stability is achieved through smooth positivity mapping and logarithmic-domain clipping, enabling explicit multiplicative feature interaction without additional computational overhead. Evaluated on ISIC 2018, Kvasir-SEG, and BUSI datasets, PU-UNet achieves Dice scores of 0.942, 0.959, and 0.925, respectively, and notably reduces the image-level false positive rate to zero for normal samples in the BUSI dataset.

Abstract

Many dense prediction networks rely on additive feature transformations and model higher-order feature interactions only implicitly. Product units provide an explicit mechanism for multiplicative feature modeling, but their logarithmic--exponential formulation can cause numerical instability, which has limited their use in deep dense prediction networks. In this work, we propose Product-Unit U-Net (PU-UNet), a residual U-Net that integrates stable product-unit residual blocks into rich low-resolution stages for medical image segmentation. The proposed formulation combines smooth positivity mapping with log-domain clipping, enabling stable multiplicative feature learning with negligible computational overhead. On ISIC 2018, Kvasir-SEG, and BUSI, PU-UNet achieves Dice scores of 0.942, 0.959, and up to 0.925, respectively. Compared with a matched Residual U-Net baseline, PU-UNet consistently improves Dice and IoU while keeping parameters, FLOPs, and inference latency nearly unchanged, and reduces the image-level false-positive rate on normal BUSI cases from 0.077 to zero. Ablation studies suggest that the gains are associated with product-unit interactions, are strongest under low-resolution placement, and benefit from the proposed stabilization design. These results suggest that stable product-unit residual learning can be an effective way to enhance U-Net-style segmentation networks with explicit multiplicative interactions.

Problem

• multiplicative interactions
• numerical instability
• medical image segmentation
• product units
• dense prediction

Innovation

• Product-Unit
• Multiplicative Interactions
• Stable Training
• Medical Image Segmentation
• U-Net