Geometric mean pooling improves multiplicative signal detection in data
Geometric Mean Pooling for Equal-Weight Multiplicative Coarse-Graining
Machine Learning
Summary
Pooling methods in machine learning help combine information from many features into simpler summaries. The authors introduce geometric mean pooling (GMP), which combines the signs and magnitudes of features multiplicatively rather than additively like average or max pooling. This better captures patterns that multiply together, such as those inspired by physics problems. They tested GMP on different tasks and found it can better detect product-based signals and resist noise, though its usefulness depends on the data and settings.
What this means in practice
- •For machine learning engineers: Use geometric mean pooling to improve feature aggregation when target signals combine multiplicatively, enhancing model robustness to multiplicative noise.
- •For computational chemists: Incorporate geometric mean pooling in molecular property prediction models to better capture multiplicative relationships affecting lipophilicity.
Authors
Ang-Kun Wu, Fangdi Wen, Jingtao Zhang
Abstract
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.