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Geometric Mean Pooling for Equal-Weight Multiplicative Coarse-Graining

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

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, itera

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