# Statistically Motivated Second Order Pooling

arXiv: https://arxiv.org/abs/1801.07492 · HTML: https://mlsanity.com/paper/1801.07492/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2018.

## Built on by (most cited first, 5 of 5)

- [Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2407.10484/) (2024)
- [Landmark Regularization: Ranking Guided Super-Net Training in Neural Architecture Search](https://mlsanity.com/paper/2104.05309/) (2021)
- [Learning Partial Correlation based Deep Visual Representation for Image Classification](https://mlsanity.com/paper/2304.11597/) (2023)
- [Learning Log-Determinant Divergences for Positive Definite Matrices](https://mlsanity.com/paper/2104.06461/) (2021)
- [SPVSoAP3D: A Second-order Average Pooling Approach to enhance 3D Place Recognition in Horticultural Environments](https://mlsanity.com/paper/2410.17017/) (2024)

## Abstract (arXiv)

Second-order pooling, a.k.a.~bilinear pooling, has proven effective for deep learning based visual recognition. However, the resulting second-order networks yield a final representation that is orders of magnitude larger than that of standard, first-order ones, making them memory-intensive and cumbersome to deploy. Here, we introduce a general, parametric compression strategy that can produce more compact representations than existing compression techniques, yet outperform both compressed and uncompressed second-order models. Our approach is motivated by a statistical analysis of the network's activations, relying on operations that lead to a Gaussian-distributed final representation, as inherently used by first-order deep networks. As evidenced by our experiments, this lets us outperform the state-of-the-art first-order and second-order models on several benchmark recognition datasets.