Combinatorial Approach to Machine Learning

Reference No.	2022a026
Type/Category	Grant for Supporting the Advancement of Female Researchers-Short-term Joint Research
Title of Research Project	Combinatorial Approach to Machine Learning
Principal Investigator	Yujie Gu（Faculty of Information Science and Electrical Engineering, Kyushu University・Assistant Professor）
Research Period	September 20,2022. ～ September 22,2022.
Keyword(s) of Research Fields	Machine Learning, Statistical Science, Combinatorics, Graph Theory, Information Science
Abstract for Research Report	In recent years, combinatorial and graph-theoretic methods have evolved not only in mathematics but also in numerous fields such as statistical science and computer science. For example, in statistical experimental designs, the experiments which meet the requirements of Fisher's three principles (i.e., local control, randomization, and repetition) could be established by means of deterministic combinatorial structures, such as combinatorial designs and graphs, which could guarantee the data acquisition with high efficiency and high estimation accuracy in the meanwhile. On the other hand, very recently, the sparsification on neural networks using random dropout method has been proposed to prevent the overfitting problem in machine learning. Notably, Fisher's three principles are effective in designing sparse neural networks as well. Also it is important to sequence the training data to increase their independence and minimize their residual effect. In addition, by introducing combinatorial structures, it is expected to have advantages of reducing the computational cost and improving the predication/learning accuracy. However, so far, the joint research on combinatorics and machine learning is just in the very early stage by only few individual groups worldwide, and further development requires systematic and collaborative research by academic and industrial communities. The objectives of this project are as follows. (1) First, to design neural networks by virtue of existing examples of combinatorial structures and to sequence the training data to enhance their independence. Accordingly, the combinatorial properties of neural networks are expected to be formulated based on the examples with excellent experimental performance. Then using algebraic and graph-theoretic techniques (such as finite fields and graph coloring), theoretical construction methods for neural networks are expected to be established and the corresponding properties are expected to be analyzed as well. (2) To implement neural networks with combinatorial properties formulated in (1), and to explore their practical applications in industry based on the joint discussions and cooperation among participants from mathematical and industrial communities. In this project, new research communication and cooperation opportunities for researchers in combinatorics and machine learning areas will be provided. Combinatorial approaches for neural network models required by practical applications are expected to be established. Furthermore, their applications to practical technologies in industry are expected as well.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Yoshinobu Kawahara（Kyushu University・Professor） Tsutomu Kumazawa（SRA(Software Research Associates, Inc.)・Researcher） Yujie Gu（Kyushu University・Assistant Professor） Masanori Sawa（Kobe University・Associate Professor） Ryoh Fuji-hara（University of Tsukuba ・Professor） Ying Miao（University of Tsukuba ・Professor） Xiao-Nan Lu（University of Yamanashi・Assistant Professor）