My research interests include not only Free Probability Theory itself, but also its applications. Random Matrix Theory, Statistical Learning Theory, Operator Algebras, Functional analysis, Quantum Information Theory are also in my interests. Currently I am working on the analysis of deep networks with random weight via free probability theory.

The symbol (*) indicates an invited talk.

(*) Asymptotic freeness in MLP and related topics, Random Matrices and Applications [url], Kyoto, Japan, June 5--9, 2023.

Ryo Karakida, Tomoumi Takase, Tomohiro Hayase & Kazuki Osawa , "Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Bias", In

Benoit Collins, Tomohiro Hayase, "Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron : The Haar Orthogonal Case", In

Takayuki Kameoka, Tomohiro Hayase, "Preliminary Study of Haptic Presentation in a VR Environment Using LRAs".

Benoit Collins, Tomohiro Hayase, "Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron : The Haar Orthogonal Case", In

Tomohiro Hayase, "Identifiability of parametric random matrix models", In

Tomohiro Hayase, "Cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents", In

Tomohiro Hayase, "Free deterministic equivalent Z-scores of compound Wishart models: A goodness of fit test of 2DARMA models", In

Tomohiro Hayase, "De Finetti theorem for a Boolean anaolgue of easy quantum groups", In

Ryo Karakida, Tomoumi Takase, Tomohiro Hayase & Kazuki Osawa , "Understanding Gradient Regularization in Deep Learning: Efficient Finite-Difference Computation and Implicit Bias", In

Kubota Shohei, Hideaki Hayashi, Tomohiro Hayase, Seiichi Uchida, "Layer-wise Interpretation of deep neural networks usng identity initialization", In

Takefumi Hiraki, Tomohiro Hayase, Yuichi Ike, Takashi Tsuboi, Michio Yoshiwaki, "Viewpoint Planning of Projector Placement for Spatial Augmented Reality using Star-Kernel Decomposition", In

Tomohiro Hayase, Ryo Karakida, "The Spectrum of Fisher Information of Deep Networks Achieving Dynamical Isometry", In

T.Hayase, Suguru Yasutomi, Takashi Kato, "Selective Forgetting of Deep Networks at a Finer Level than Samples", In

The symbol (*) indicates an invited talk.

(*) Asymptotic freeness in MLP and related topics, Random Matrices and Applications [url], Kyoto, Japan, June 5--9, 2023.

(*) Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron, Japan-China International Conference on Matrix Theory with Applications, Ritsumeikan Univ., Dec. 16--18, 2022.

(*) Random Matrices, Free Probability and Deep Learning, Noncommutative Probability and Related Topics, Sapporo and Zoom, Nov. 7--8, 2022.

(*) Astmptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron, Noncommutative Probability and Related Fields [url], Nagoya, Nov. 23--24, 2021.

(*) 深層神経回路の数理：無限次元近似, ランダム行列, 及び自由確率論, RIMS共同研究「作用素環と量子力学系」, Feb. 3, 2021.

(*) Random matrix approach to deep learning, Noncommutative Probability and Related Fields [url], zoom, Dec. 3--4, 2020.

(*) 自由確率論による深層神経回路網の解析, 情報系 WINTER FESTA Episode 5, Tokyo, Dec., 2019.

(Poster) Asymptotic Freeness in Jacobian of Deep Neural Networks, ACML, Nagoya, Nov., 2019.

(Poster) Asymptotic Freeness in Jacobian of Deep Neural Networks, Deep Learning and Physics, Yukawa Institute for theoretical physics, Nov., 2019.

(Poster) Spectral Parameter Estimation of Random Matrix Models (Cauchy雑音損失による次元復元), 異分野異業種交流会, Meiji University, Nov., 2018.

(Poster) Spectral Parameter Estimation of Random Matrix Models, IBISML, Sapporo, Nov., 2018.

*Parameter Estimation of Random Matrix Models via Free Probability Theory, Recent Development of Operator Algebras, Sep., 2018.

(Poster) Cauchy noise loss for stochastic optimization of random matrix models via free deterministic equivalents, Random matrices and their applications, Kyoto University, May, 2018.

Cauchy noise loss: A machine learning approach to random matrices and free probability, Noncommutative probability theory and its applications, Ochanomizu University (Japan), Dec., 2017.

(*) De Finetti theorems for a Boolean analogue of easy quantum groups, , UC Berkeley (USA), Mar., 2016.

Free product of von Neumann algebras, Workshop of Free monotone transport, Chiba (Japan), Mar., 2016.

Cumulants in noncommutative probability, The 50-th Functional Analysis Workshop, Karuizawa (Japan), Sep., 2015.

A symmetry in free probability: Quantum de Finetti theorem, The 49-th Functional Analysis Workshop, , Gifu (Japan), Aug., 2014.