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Why Dilated Convolutional Neural Networks: A Proof of Their Optimality.
Jonatan Contreras1, Martine Ceberio1, Vladik Kreinovich1
1Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.
Entropy (Basel, Switzerland)
|July 2, 2021
Summary
Dilated convolution, a technique in convolutional neural networks, processes specific neighboring data points for improved accuracy. This paper proves dilated convolution is the most efficient method for image processing tasks.
Area of Science:
- Computer Science
- Artificial Intelligence
- Image Processing
Background:
- Convolutional neural networks (CNNs) are effective for image processing.
- Standard convolutional layers process all neighboring input signals.
- Improved accuracy requires selective processing of neighboring data.
Purpose of the Study:
- To explain the empirical efficiency of dilated convolution.
- To mathematically prove the superiority of dilated convolution over alternatives.
- To provide theoretical justification for using dilated convolution in CNNs.
Main Methods:
- Analyzing convolutional layers in neural networks.
- Investigating the properties of dilated convolution.
- Developing mathematical proofs for optimality criteria.
Main Results:
- Dilated convolution selects neighboring points based on divisibility by a constant ℓ.
- Empirical efficiency of dilated convolution is explained.
- Proof demonstrates dilated convolution is optimal for reasonable criteria.
Conclusions:
- Dilated convolution offers superior performance in image processing tasks.
- The findings provide a theoretical foundation for the effectiveness of dilated convolution.
- This research validates the use of dilated convolution in advanced CNN architectures.
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