Naoya Maeda | Searcharxiv

arXiv2023

Introduction of Probabilistic Algebraic Variety

Historically, probability theory has been studied for a long time, and Kolmogorov, Levy Ito Kiyoshi, and others have mathematically developed modern probability in conjunction with measurement theory. On the other hand, commutative algebra and algebraic geometry have historically been the subject of interdisciplinary research led by Grothendiek. Many Japanese, notably Matsumura, Hironaka, and Kodaira, have contributed to this field. This paper is an attempt to focus on the research theme of Professor Sumio Watanabe of Tokyo Institute of Technology, "Algebraic Geometry and Probability Theory," from my own perspective. The mathematical theory development starts from Kolmogorov's axioms, and the proof and introduction of "Probabilistic Algebraic Variety" are given. Problems in computation and applications, analysis by computational homology, and unsolved problems in regression problems will be introduced as applications to statistics.

math.GM↗

arXiv2019

Brain-mediated Transfer Learning of Convolutional Neural Networks

The human brain can effectively learn a new task from a small number of samples, which indicate that the brain can transfer its prior knowledge to solve tasks in different domains. This function is analogous to transfer learning (TL) in the field of machine learning. TL uses a well-trained feature space in a specific task domain to improve performance in new tasks with insufficient training data. TL with rich feature representations, such as features of convolutional neural networks (CNNs), shows high generalization ability across different task domains. However, such TL is still insufficient in making machine learning attain generalization ability comparable to that of the human brain. To examine if the internal representation of the brain could be used to achieve more efficient TL, we introduce a method for TL mediated by human brains. Our method transforms feature representations of audiovisual inputs in CNNs into those in activation patterns of individual brains via their association learned ahead using measured brain responses. Then, to estimate labels reflecting human cognition and behavior induced by the audiovisual inputs, the transformed representations are used for TL. We demonstrate that our brain-mediated TL (BTL) shows higher performance in the label estimation than the standard TL. In addition, we illustrate that the estimations mediated by different brains vary from brain to brain, and the variability reflects the individual variability in perception. Thus, our BTL provides a framework to improve the generalization ability of machine-learning feature representations and enable machine learning to estimate human-like cognition and behavior, including individual variability.

cs.CV↗