A research team led by Professor Jong Chul Ye from the Department of Bio and Brain Engineering discovered the mathematical principles for producing high-performance artificial neural networks that can be utilized in medical imaging or other fields where precision is essential.

The study was done by PhD candidates Yoseob Han and Eunju Cha and was published in the international journal Society for Industrial and Applied Mathematics (SIAM) Journal of Imaging Sciences on April 26.

In the past few years, there has been an explosive growth of interest in and research on artificial intelligence (AI). Deep learning and deep neural networks, the technology through which deep learning is implemented, have been at the core of this growth. However, despite the high performance of deep neural networks, the specific principles behind the technology are unknown, sometimes leading to unexpected results or errors. As a result, there is a greater social and technological demand for explainable AI, or XAI.

Professor Ye’s research team developed a new harmonic analysis technology named Deep Convolutional Framelets, which revealed the mathematical principles of deep neural networks. Through this revelation, it is possible to patch over the various shortcomings in existing neural network structures.

The research team discovered that deep neural network structures were developed through the decomposition of the Hankel Matrix, a higher-dimensional structure that has been intensively studied in the field of signal processing. This allowed the team to propose a theoretical framework through which the filtering and pooling structures of deep neural networks can be obtained through the decomposition of the Hankel Matrix.

The team was then able to produce a desired deep neural network structure by determining the number of basis functions and depth of the neural network depending on the complexity of the input signal. The structure proposed through the mathematical principles was then tested on a variety of problems: image noise reduction, image pixel restoration, and medical image restoration. Their tests found that the given structure resulted in good performance and results.

Professor Ye stated, “Unlike traditional deep neural networks, which are designed through repetitive trial and error, we can design and predict the effects of deep neural network structures optimized for desired applications through mathematical principles.” He added, “The results can be applied to a variety of fields that require explainable artificial intelligence, such as medical imaging.”