An Intriguing Failing of Convolutional Neural Networks and the CoordConv Solution (1807.03247v2)

Abstract: Few ideas have enjoyed as large an impact on deep learning as convolution. For any problem involving pixels or spatial representations, common intuition holds that convolutional neural networks may be appropriate. In this paper we show a striking counterexample to this intuition via the seemingly trivial coordinate transform problem, which simply requires learning a mapping between coordinates in (x,y) Cartesian space and one-hot pixel space. Although convolutional networks would seem appropriate for this task, we show that they fail spectacularly. We demonstrate and carefully analyze the failure first on a toy problem, at which point a simple fix becomes obvious. We call this solution CoordConv, which works by giving convolution access to its own input coordinates through the use of extra coordinate channels. Without sacrificing the computational and parametric efficiency of ordinary convolution, CoordConv allows networks to learn either complete translation invariance or varying degrees of translation dependence, as required by the end task. CoordConv solves the coordinate transform problem with perfect generalization and 150 times faster with 10--100 times fewer parameters than convolution. This stark contrast raises the question: to what extent has this inability of convolution persisted insidiously inside other tasks, subtly hampering performance from within? A complete answer to this question will require further investigation, but we show preliminary evidence that swapping convolution for CoordConv can improve models on a diverse set of tasks. Using CoordConv in a GAN produced less mode collapse as the transform between high-level spatial latents and pixels becomes easier to learn. A Faster R-CNN detection model trained on MNIST showed 24% better IOU when using CoordConv, and in the RL domain agents playing Atari games benefit significantly from the use of CoordConv layers.

• The paper identifies CNNs' inability to learn coordinate transformations, hindering spatial precision in key tasks.
• It proposes CoordConv layers that integrate explicit coordinate channels, enabling precise spatial learning without added complexity.
• Empirical evidence shows CoordConv layers outperform standard CNNs, achieving perfect accuracy and improved results across diverse applications.

An Intriguing Failing of Convolutional Neural Networks and the CoordConv Solution

The paper "An intriguing failing of convolutional neural networks and the CoordConv solution" examines a fundamental shortcoming of convolutional neural networks (CNNs) in accurately handling coordinate transform problems. Despite the widespread success of CNNs in numerous applications involving spatial representations, this research reveals that CNNs encounter significant difficulties when tasked with translating between Cartesian coordinates and pixel-based representations.

Key Findings and Contributions

The paper’s primary contributions can be summarized as follows:

1. Identification of the Coordinate Transform Problem: The authors present the coordinate transform problem, which is deceptively simple: learning a mapping between $(x,y)$ Cartesian coordinates and one-hot pixel representations. This problem is pivotal in tasks requiring spatial precision, yet CNNs fail to generalize effectively even in closely supervised settings.
2. CoordConv Layer Introduction: In response to the identified issue, the paper introduces the CoordConv layer. This layer extends the traditional convolutional layers by incorporating extra coordinate channels, allowing convolutional filters to know their position in the input space. CoordConv layers retain computational and parametric efficiency while providing the flexibility to learn translation invariance or dependence as needed.
3. Empirical Validation: Through extensive experiments, the paper demonstrates that CoordConv layers solve the coordinate transform problem with perfect generalization. Comparatively, CNNs struggle significantly, achieving only 86% accuracy on simpler tasks and failing completely on more challenging scenarios. CoordConv models, by contrast, not only achieve perfect accuracy but do so with significantly fewer parameters and faster convergence.
4. Impact Across Diverse Tasks: The paper also explores the broader implications of CoordConv in various machine learning domains, including object detection, generative modeling, and reinforcement learning. For instance, in object detection scenarios using Faster R-CNN on MNIST digits, CoordConv layers led to a 24% improvement in intersection-over-union (IOU) scores. In generative adversarial networks (GANs) generating LSUN bedroom scenes, CoordConv significantly mitigated mode collapse and enhanced the geometric coherence of generated images. In reinforcement learning, Atari game agents equipped with CoordConv layers achieved markedly higher scores in several games without any adverse effects.

Practical and Theoretical Implications

Practical Implications

• Efficiency and Precision: The CoordConv layer provides a simple yet highly effective means to boost the performance of spatially aware tasks, offering significant improvements in both accuracy and computational efficiency.
• Application Flexibility: By integrating CoordConv layers into existing architectures across various tasks, practitioners can achieve better generalization and robustness, particularly in problems where precise spatial relationships are critical.
• API Readiness: The paper includes the open-source implementation of CoordConv layers, facilitating easy adoption and experimentation within the larger research community.

Theoretical Implications

• Inductive Bias of CNNs: This research challenges and expands the understanding of CNN inductive biases, demonstrating that while CNNs are adept at recognizing translational invariances, they are notably deficient in modelling explicit coordinate transforms.
• Model Design Considerations: The findings advocate for a reconsideration of model architecture design, stressing the importance of integrating mechanisms to handle coordinate systems explicitly, especially in tasks involving spatial transformations and manipulations.
• Future Research Trajectories: The research sets a precedent for exploring further applications of CoordConv layers in more complex environments and datasets, investigating their impact on relational reasoning, video prediction, and other domains where spatial manipulations are integral.

Conclusion

The paper brings to light a critical failing of convolutional neural networks in handling coordinate transforms and proposes the CoordConv layer as an effective solution. The CoordConv layer not only rectifies this issue but also demonstrates significant performance enhancements across various tasks. This work prompts a reevaluation of current deep learning practices and opens avenues for advanced spatially-aware neural architectures. Future research will likely extend the use of CoordConv layers to broader applications, probing further into their potential benefits and integration into contemporary model architectures.