PU-UNet: Stable Multiplicative Interactions for Medical Image Segmentation

Medical image segmentation models, such as the standard U-Net, typically rely on additive feature transformations. While effective, these models often struggle to explicitly capture complex, higher-order dependencies between image features like texture, shape, and contrast. The authors investigate whether integrating product units—which allow for multiplicative feature interactions—can enhance segmentation performance. Historically, product units have been avoided in deep networks due to numerical instability caused by their logarithmic-exponential formulation. To address this, the authors propose PU-UNet, which stabilizes these units using a combination of smooth positivity mapping and log-domain clipping, and selectively integrates them into the lower-resolution stages of a Residual U-Net.

PU-UNet consistently outperforms a matched Residual U-Net baseline across three diverse medical imaging datasets: ISIC 2018 (skin lesions), Kvasir-SEG (polyps), and BUSI (breast ultrasound). Notably, these performance gains—measured by Dice and IoU scores—are achieved with negligible increases in parameter count, FLOPs, or inference latency. Furthermore, the model demonstrates improved robustness, particularly in the BUSI dataset, where it significantly reduces false-positive rates on normal images. Ablation studies confirm that the model's success is driven by the strategic placement of product units in low-resolution stages and the effectiveness of the proposed stabilization techniques.

This work demonstrates that the historical underutilization of multiplicative interactions in deep learning for medical imaging is largely a technical hurdle rather than a conceptual one. By providing a stable, computationally efficient implementation of product units, the authors offer a practical way to enhance existing segmentation architectures. The ability to improve accuracy without increasing the model's computational footprint makes this approach particularly attractive for clinical settings where efficiency and reliability are paramount.