# Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree

arXiv: https://arxiv.org/abs/1509.08985 · HTML: https://mlsanity.com/paper/1509.08985/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2015.

## Built on by (most cited first, 30 of 36)

- [AdaPool: Exponential Adaptive Pooling for Information-Retaining Downsampling](https://mlsanity.com/paper/2111.00772/) (2021)
- [FEAR: Fast, Efficient, Accurate and Robust Visual Tracker](https://mlsanity.com/paper/2112.07957/) (2021)
- [Refining activation downsampling with SoftPool](https://mlsanity.com/paper/2101.00440/) (2021)
- [Learning strides in convolutional neural networks](https://mlsanity.com/paper/2202.01653/) (2022)
- [Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networks](https://mlsanity.com/paper/2210.08001/) (2022)
- [Keep It SimPool: Who Said Supervised Transformers Suffer from Attention Deficit?](https://mlsanity.com/paper/2309.06891/) (2023)
- [LiftPool: Bidirectional ConvNet Pooling](https://mlsanity.com/paper/2104.00996/) (2021)
- [OccamNets: Mitigating Dataset Bias by Favoring Simpler Hypotheses](https://mlsanity.com/paper/2204.02426/) (2022)
- [Self-Attentive Pooling for Efficient Deep Learning](https://mlsanity.com/paper/2209.07659/) (2022)
- [Quantum-limited stochastic optical neural networks operating at a few quanta per activation](https://mlsanity.com/paper/2307.15712/) (2023)
- [Comparison of Methods Generalizing Max- and Average-Pooling](https://mlsanity.com/paper/2103.01746/) (2021)
- [Self-Supervision Enhances Instance-based Multiple Instance Learning Methods in Digital Pathology: A Benchmark Study](https://mlsanity.com/paper/2505.01109/) (2025)
- [Content-Adaptive Downsampling in Convolutional Neural Networks](https://mlsanity.com/paper/2305.09504/) (2023)
- [Learning to Pool in Graph Neural Networks for Extrapolation](https://mlsanity.com/paper/2106.06210/) (2021)
- [Learnable Discrete Wavelet Pooling (LDW-Pooling) For Convolutional Networks](https://mlsanity.com/paper/2109.06638/) (2021)
- [Backpropagation Neural Tree](https://mlsanity.com/paper/2202.02248/) (2022)
- [MolNet: A Chemically Intuitive Graph Neural Network for Prediction of Molecular Properties](https://mlsanity.com/paper/2203.09456/) (2022)
- [Unsupervised HDR Imaging: What Can Be Learned from a Single 8-bit Video?](https://mlsanity.com/paper/2202.05522/) (2022)
- [Regularized Optimal Transport Layers for Generalized Global Pooling Operations](https://mlsanity.com/paper/2212.06339/) (2022)
- [NOAH: Learning Pairwise Object Category Attentions for Image Classification](https://mlsanity.com/paper/2402.02377/) (2024)
- [Maximal function pooling with applications](https://mlsanity.com/paper/2103.01292/) (2021)
- [Enhancing Deep Neural Network Saliency Visualizations with Gradual Extrapolation](https://mlsanity.com/paper/2104.04945/) (2021)
- [Frequency Pooling: Shift-Equivalent and Anti-Aliasing Downsampling](https://mlsanity.com/paper/2109.11839/) (2021)
- [Hierarchical Spherical CNNs with Lifting-based Adaptive Wavelets for Pooling and Unpooling](https://mlsanity.com/paper/2205.15571/) (2022)
- [QuickNets: Saving Training and Preventing Overconfidence in Early-Exit Neural Architectures](https://mlsanity.com/paper/2212.12866/) (2022)
- [Progressive Meta-Pooling Learning for Lightweight Image Classification Model](https://mlsanity.com/paper/2301.10038/) (2023)
- [PEMNET: A Transfer Learning-based Modeling Approach of High-Temperature Polymer Electrolyte Membrane Electrochemical Systems](https://mlsanity.com/paper/2105.03057/) (2021)
- [Revisiting Global Pooling through the Lens of Optimal Transport](https://mlsanity.com/paper/2201.09191/) (2022)
- [FedHeN: Federated Learning in Heterogeneous Networks](https://mlsanity.com/paper/2207.03031/) (2022)
- [MultiScale Probability Map guided Index Pooling with Attention-based learning for Road and Building Segmentation](https://mlsanity.com/paper/2302.09411/) (2023)

## Abstract (arXiv)

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in place of average or max pooling. We experimentally demonstrate that the proposed pooling operations provide a boost in invariance properties relative to conventional pooling and set the state of the art on several widely adopted benchmark datasets; they are also easy to implement, and can be applied within various deep neural network architectures. These benefits come with only a light increase in computational overhead during training and a very modest increase in the number of model parameters.