ABP: Adaptive Bonferroni Pooling for Convolutional Neural Networks

Abstract Pooling is a fundamental operation in convolutional networks, and commonly used strategies such as max or average pooling are fixed and inflexible. They apply the same aggregation everywhere, ignoring the fact that different regions of an image may require different operations to get the required information. More recent methods, including stochastic or attention-based pooling, offer greater flexibility but at the cost of extra parameters and computational overhead. In this paper, we introduce Adaptive Bonferroni Pooling (ABP), a simple but efficient pooling strategy. ABP computes four statistics—the Bonferroni mean, average, maximum, and minimum—within each local patch, and learns how to combine them through a softmax-weighted fusion. The Bonferroni mean, parameterized by learnable exponents, captures interactions among activations, while the adaptive fusion allows the network to decide whether to focus on sharp details, smooth context, or a balance of both. Across five backbone deep learning-based architectures an six benchmark datasets, ABP consistently improves accuracy over standard pooling methods. For example, DenseNet121 with ABP reaches 86.55% on the CIFAR-10 dataset, and ResNet50 attains 99.36% on the MNIST dataset. ABP provides a flexible, interpretable, and computationally light pooling operation, making it a practical replacement for max and average pooling in deep learning models.