Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree (1509.08985v2)

Abstract: 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.

• The paper introduces three innovative pooling functions—mixed, gated, and tree—to enhance CNN flexibility and improve performance.
• It employs a learned gating mechanism and binary tree structure to dynamically adjust pooling operations, yielding lower error rates on datasets like CIFAR10 and ImageNet.
• Experimental results demonstrate increased robustness to spatial transformations with significant performance gains across varied CNN architectures.

Generalizing Pooling Functions in CNNs: Mixed, Gated, and Tree

The paper "Generalizing Pooling Functions in Convolutional Neural Networks: Mixed, Gated, and Tree" by Chen-Yu Lee, Patrick W. Gallagher, and Zhuowen Tu focuses on enhancing deep neural networks by diversifying and augmenting the traditional pooling operations in convolutional neural networks (CNNs). Pooling operations are critical for achieving spatial invariance, yet their conventional forms—average, max, and stochastic pooling—remain limited in scope. This research introduces three novel pooling strategies aimed at generalization: mixed, gated, and tree-based pooling functions.

Summary of Pooling Strategies

The paper investigates two main directions for pooling generalization: combining differing types of pooling and learning pooling functions through a hierarchical tree structure.

1. Mixed Max-Average Pooling: This approach uses a fixed combination of max and average pooling, tuned by specific mixing proportion parameters derived from the data. Notably, various configurations for parameter learning were examined, ranging from global to highly localized.
2. Gated Max-Average Pooling: In contrast to the non-responsive nature of mixed pooling, gated pooling introduces a learned gating mask that varies the pooling response dynamically based on characteristics of the input region. This adaptability enhances the pooling operation’s flexibility.
3. Tree Pooling: Pooling operations are learned as part of a binary tree, where learned filters at the leaves are combined up the tree with a responsive fusion, allowing for nuanced aggregation of different pooling operations.

The theoretical foundations ensure that all proposed methods maintain differentiability, enabling integration with backpropagation frameworks.

Experimental Results

The authors conducted experiments on datasets including MNIST, CIFAR10, CIFAR100, and SVHN, demonstrating performance improvements consistent across various CNN architectures, including well-known models such as AlexNet and GoogLeNet. Particularly, the mixed and gated max-average pooling achieved superior results over standard methods, with smaller networks benefiting substantially from these pooling modifications.

• CIFAR10: The tree+max-avg configuration improved error rates significantly to 7.62%, compared to a baseline of 9.10%.
• ImageNet: A relative reduction in top-5 error was achieved by simply replacing max pooling in AlexNet with the proposed techniques, indicating minimal overhead with practical performance gains.

Additional evidence suggests that these methods yield improved robustness in accommodating spatial transformations such as rotation, translation, and scaling—vital characteristics for real-world image classification tasks.

Implications and Future Directions

The implications of these generalized pooling functions are substantial. The ability to learn and adapt pooling strategies increases the model’s flexibility and performance without drastically increasing computational resources or parameters. These features open avenues for further research into adaptive learning structures that can dynamically respond to varying inputs, potentially extending beyond image recognition to other domains requiring hierarchical feature aggregation.

Future exploration might consider extending tree pooling structures to even more complex architectures, alongside investigating deeper integration with other adaptive learning mechanisms, such as attention mechanisms in neural networks.

Conclusion

By introducing and validating these generalized pooling methods, the authors contribute significantly to the toolkit available for designing flexible and efficient neural network architectures. As the field progresses, such enhancements in foundational operations like pooling promise to further elevate the overall capability and adaptability of machine learning models in complex environments.