LDS3Pool: Pooling with Quasi-Random Spatial Sampling via Low-Discrepancy Sequences and Hilbert Ordering

Yuening Ma, Liang Guo () and Min Li
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Yuening Ma: School of Mathematics and Statistics, Shandong University, Wen Hua Xi Road 180, Weihai 264209, China
Liang Guo: School of Mathematics and Statistics, Shandong University, Wen Hua Xi Road 180, Weihai 264209, China
Min Li: School of Mathematics and Statistics, Shandong University, Wen Hua Xi Road 180, Weihai 264209, China

Mathematics, 2025, vol. 13, issue 18, 1-30

Abstract: Feature map pooling in convolutional neural networks (CNNs) serves the dual purpose of reducing spatial dimensions and enhancing feature invariance. Current pooling approaches face a fundamental trade-off: deterministic methods (e.g., MaxPool and AvgPool) lack regularization benefits, while stochastic approaches introduce beneficial randomness but can suffer from sampling biases and may require careful hyperparameter tuning (e.g., S3Pool). To address these limitations, this paper introduces LDS3Pool, a novel pooling method that leverages low-discrepancy sequences (LDSs) for quasi-random spatial sampling. LDS3Pool first linearizes 2D feature maps to 1D sequences using Hilbert space-filling curves to preserve spatial locality, then applies LDS-based sampling to achieve quasi-random downsampling with mathematical guarantees of uniform coverage. This framework provides the regularization benefits of randomness while maintaining comprehensive feature representation, without requiring sensitive hyperparameter tuning. Extensive experiments demonstrate that LDS3Pool consistently outperforms baseline methods across multiple datasets and a range of architectures, from classic models like VGG11 to modern networks like ResNet18, achieving significant accuracy gains with moderate computational overhead. The method’s empirical success is supported by a rigorous theoretical analysis, including a quantitative evaluation of the Hilbert curve’s superior, size-independent locality preservation. In summary, LDS3Pool represents a theoretically sound and empirically effective pooling method that enhances CNN generalization through a principled, quasi-random sampling framework.

Keywords: CNN; image pooling; low-discrepancy sequences; Hilbert curve (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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