Ishikawa Isao

イシカワイサオ | Ishikawa Isao

Affiliation and department：
Job title： Associate Professor

Research field (5)： Algebra , Applied mathematics and statistics , Basic analysis , Applied mathematics and statistics , Basic analysis

Research keywords (8)： Deep Learning , Reproducing kernel Hilbert space , number theory , Koopman operator , composition operator , generalized spectrum , machine learning , dynamical system

Research theme for competitive and other funds (8)：

2024 - 2028 Bidirectional study of composition operators and dynamical systems
2024 - 2027 正定値性を中心とした函数解析と複素解析の総合的研究
2024 - 2025 Data-driven analysis for dynamical systems using Koopman operators in Besov spaces
2020 - 2024 Theoretical analysis of Koopman operators for data analysis via the theory of function space
2019 - 2024 Operator theoretic data analysis of complicated dynamics and its integrated utilization with mathematical models

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Papers (28)：

Sho Sonoda, Isao Ishikawa, Masahiro Ikeda. A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks. Journal of Statistical Planning and Inference. 2024. 233. 106184-106184
Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano. Global Universality of the Two-Layer Neural Network with the k-Rectified Linear Unit. Journal of Function Spaces. 2024
Yuka Hashimoto, Sho Sonoda, Isao Ishikawa, Atsushi Nitanda, Taiji Suzuki. Koopman-based generalization bound: New aspect for full-rank weights. The Twelfth International Conference on Learning Representations. 2024
Hayato Chiba, Masahiro Ikeda, Isao Ishikawa. Generalized Eigenvalues of the Perron-Frobenius Operators of Symbolic Dynamical Systems. SIAM Journal on Applied Dynamical Systems. 2023. 22. 4. 2825-2855
Isao Ishikawa. Bounded composition operators on functional quasi-Banach spaces and stability of dynamical systems. Advances in Mathematics. 2023. 424. 109048

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MISC (4)：

Isao Ishikawa. Finite-dimensional approximations of push-forwards on locally analytic functionals and truncation of least-squares polynomials. 2024
Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda, Yoshinobu Kawahara. Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces. 2024
Sho Sonoda, Isao Ishikawa, Masahiro Ikeda. Gradient Descent Converges to Ridgelet Spectrum. CoRR. 2020. abs/2007.03441
石川勲. GL2上のASAI表現に付随するEPSILON因子について. 数理解析研究所講究録. 2019. 94-108

Patents (2)：

関係性抽出装置及び関係性抽出方法
異常検知装置、異常検知方法、及びプログラム

Lectures and oral presentations (41)：

重み付き合成作用素の有界性と力学系の安定性について
(One day workshop on harmonic analysis and PDE 2023)
JetDMD: Rigged再生核Hilbert空間におけるデータ駆動型Koopman固有展開
(数理・情報系研究集会 2023)
可逆ニューラルネットワークの表現力について
(ipi - ダイキンシンポジウム 2023)
JetDMD: Rigged再生核Hilbert空間におけるデータ駆動型Koopman固有展開
(数理情報研究交流会 2023)
Banditフィードバックによる力学系の構造推定
(情報論的学習理論と機械学習研究会 2023)

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Education (2)：

2012 - 2017 Kyoto University Graduate School of Science Department of mathematics
2008 - 2012 Tokyo Institute of Technology

Professional career (1)：

理学 (京都大学)

Work history (3)：

2022/03 - 現在 Ehime University Center for Data Science Associate Professor
2020/04 - 2022/03 Ehime University Center for Data Science
2017/04 - 2020/03 RIKEN Center for Advanced Interigence Project, Generic Technology Research Group, Mathematical Science Team Postdoctoral Researcher

Awards (1)：

2019 - 理化学研究所理化学研究所桜舞賞(研究奨励賞)

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