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Steerable CNNs (1612.08498v1)

Published 27 Dec 2016 in cs.LG and stat.ML

Abstract: It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and flexible class of equivariant convolutional networks. We show that steerable CNNs achieve state of the art results on the CIFAR image classification benchmark. The mathematical theory of steerable representations reveals a type system in which any steerable representation is a composition of elementary feature types, each one associated with a particular kind of symmetry. We show how the parameter cost of a steerable filter bank depends on the types of the input and output features, and show how to use this knowledge to construct CNNs that utilize parameters effectively.

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Authors (2)
  1. Taco S. Cohen (28 papers)
  2. Max Welling (202 papers)
Citations (472)

Summary

  • The paper introduces a type system based on representation theory to construct steerable CNNs that efficiently share parameters.
  • It employs steerable filter banks to enhance equivariance, achieving robust performance on the CIFAR10 benchmark with limited labeled data.
  • The framework offers practical benefits for resource-constrained applications and sets the stage for future research in dynamic feature optimization.

Steerable CNNs: A Comprehensive Overview

The development of Steerable Convolutional Neural Networks (CNNs), as articulated by Cohen and Welling, represents a significant advancement in the pursuit of enhancing the statistical efficiency and flexibility of deep learning architectures, specifically within the domain of computer vision. This paradigm addresses and extends the capabilities of equivariant networks, aiming to bridge the gap between effective parameter utilization and sophisticated representations that are not solely reliant on extensive labeled datasets.

Core Contributions

At the heart of this paper is the introduction of Steerable CNNs, which are designed to manage and exploit the equivariance properties of visual representations. The authors leverage mathematical foundations rooted in representation theory to conceptualize a type system for steerable representations. This theoretical framework delineates how any steerable representation can be considered as a composition of elementary feature types, each associated with specific symmetrical properties.

One of the strong claims of the paper involves the efficiency with which these steerable representations utilize parameters. By employing steerable filter banks, the parameter cost is shown to be highly dependent on the input-output feature types, allowing for the construction of CNNs that efficiently leverage their parameters. This results in a sophisticated level of parameter sharing, extending the capabilities of traditional convolutional layers by enabling filter applications across various poses, rather than just spatial positions.

Numerical Results and Empirical Findings

Steerable CNNs achieve state-of-the-art results on the CIFAR10 image classification benchmark, an indication of their robustness and competence in handling complex pattern recognition tasks. The empirical analysis highlights the network's ability to generalize and perform substantially better than previous architectures when trained on limited labeled data, further underscoring its efficacy as a tool for scenarios where data acquisition is constrained or costly.

Theoretical and Practical Implications

The implications of this research are multifold. Theoretically, by employing group representation theory, Steerable CNNs provide a novel lens through which we can understand and enhance neural networks’ inherent geometrical capabilities. The introduction of a type system naturally arising from the decomposition of group representations signifies a deeper integration of mathematical concepts into neural network design, paving the way for future models that could handle continuous and high-dimensional groups.

Practically, the reduced parameter costs coupled with the enhanced learning dynamics offer a promising perspective for deploying deep learning models in resource-constrained environments. Applications could extend beyond typical vision tasks to areas necessitating efficient data processing, such as medical imaging or autonomous navigation, where data is either scarce or high-dimensional transformations are prevalent.

Speculation on Future Developments

Future avenues of research could explore the scalability of steerable representations in continuous group settings or their applicability in more complex tasks such as motion estimation and dynamic control. Moreover, learning feature types dynamically, through optimization rather than manual selection, could transform the adaptability of these networks to real-world problems.

In conclusion, the conceptual and empirical contributions of Steerable CNNs establish a strong foundation for future research and development in the area of geometrically-aware neural networks. Through a meticulous blend of mathematical rigor and empirical validation, this work pushes the boundaries of what is achievable in machine learning, offering a robust framework for designing networks that are not only more efficient but inherently more intelligent in handling varied inputs and transformations.

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