We propose a deep product-unit residual neural network (PURe) that integrates product units into residual blocks to improve the expressiveness and parameter efficiency of deep convolutional networks. Unlike standard summation neurons, product units enable multiplicative feature interactions, potentially offering a more powerful representation of complex patterns. PURe replaces conventional convolutional layers with 2D product units in the second layer of each residual block, eliminating nonlinear activation functions to preserve structural information. We validate PURe on three benchmark datasets. On Galaxy10 DECaLS, PURe34 achieves the highest test accuracy of 84.89%, surpassing the much deeper ResNet152, while converging nearly five times faster and demonstrating strong robustness to Poisson noise. On ImageNet, PURe architectures outperform standard ResNet models at similar depths, with PURe34 achieving a top-1 accuracy of 80.27% and top-5 accuracy of 95.78%, surpassing deeper ResNet variants (ResNet50, ResNet101) while utilizing significantly fewer parameters and computational resources. On CIFAR-10, PURe consistently outperforms ResNet variants across varying depths, with PURe272 reaching 95.01% test accuracy, comparable to ResNet1001 but at less than half the model size. These results demonstrate that PURe achieves a favorable balance between accuracy, efficiency, and robustness. Compared to traditional residual networks, PURe not only achieves competitive classification performance with faster convergence and fewer parameters, but also demonstrates greater robustness to noise. Its effectiveness across diverse datasets highlights the potential of product-unit-based architectures for scalable and reliable deep learning in computer vision.

本研究解决了深度卷积网络表达能力和参数效率不足的问题，提出了一种深度乘积单元残差神经网络（PURe），通过在残差块中集成乘积单元，替代传统卷积层。研究表明，PURe在多个基准数据集上的分类性能超越了深层ResNet，同时实现了更快的收敛速度和更强的抗噪声能力，展示了乘积单元架构在计算机视觉中的潜在应用价值。

深度残差学习与乘积单元