发表机构
University of Tennessee, Knoxville; Rutgers University; Google（田纳西大学诺克斯维尔分校; 罗格斯大学; 谷歌）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出几何平均池化（GMP），一种结合符号乘积与幅度几何均值的带符号池化算子，用于等权乘法粗粒化，在合成任务上优于平均和最大池化，但图像和分子数据上效果依赖具体设置。
AI 中文摘要
作为平均池化和最大池化的加性及极值偏差的替代方案，我们引入了几何平均池化（GMP），这是一种带符号的池化算子，将特征符号的乘积与特征幅度的几何平均值相结合。受量子多体物理中从局部到全局组合的启发，GMP在无需引入可学习的池化参数的情况下，保留了联合符号信息和特征性的乘法尺度。我们证明了非重叠的分层GMP能保持相应的全局乘法统计量，并在合成序列任务、迭代粗粒化、图像分类和分子亲脂性回归上对其进行了评估。在合成任务上，GMP比平均池化和最大池化更准确地恢复基于乘积的信号，并在测试的乘法输入噪声水平下保持预测性能。然而，在图像和分子数据上，其有效性取决于表示、目标参数化和局部与全局池化的放置。这些结果将GMP定位为一种互补的、依赖于特定领域的归纳偏置，适用于等权乘法组合可能合理的任务，而非标准池化算子的通用替代品。
英文摘要
As an alternative to the additive and extremal biases of average and max pooling, we introduce Geometric Mean Pooling (GMP), a signed pooling operator that combines the product of feature signs with the geometric mean of feature magnitudes. Motivated by local-to-global composition in quantum many-body physics, GMP retains both joint sign information and a characteristic multiplicative scale without introducing learnable pooling parameters. We show that non-overlapping hierarchical GMP preserves the corresponding global multiplicative statistic and evaluate it on synthetic sequence tasks, iterative coarse-graining, image classification, and molecular lipophilicity regression. On the synthetic tasks, GMP recovers product-based signals more accurately than average and max pooling and maintains predictive performance under the tested levels of multiplicative input noise. On image and molecular data, however, its effectiveness depends on the representation, target parameterization, and placement of local and global pooling. These results position GMP as a complementary, regime-dependent inductive bias for tasks in which equal-weight multiplicative composition is plausible, rather than as a universal replacement for standard pooling operators.
Comments17 pages, 6 figures
