Preprints:
A Sannai, Y Hikima, K Kobayashi, A Tanaka, N Hamada, Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization, arXiv: 2205.11099
A Sannai, M Kawano, W Kumagai, Equivariant and Invariant Reynolds Networks, arXiv preprint arXiv:2110.08092
Akinori Tanaka, Akiyoshi Sannai, Ken Kobayashi, Naoki Hamada, Approximate Bayesian Computation of Bézier Simplices, arXiv preprint arXiv:2104.04679
Wataru Kumagai, Akiyoshi Sannai, Universal Approximation Theorem for Equivariant Maps by Group CNNs, arXiv preprint arXiv:2012.13882
A Sannai, Y Takai, M Cordonnier, Universal approximations of permutation invariant/equivariant functions by deep neural networks, arXiv preprint arXiv:1903.01939
A Sannai, Reconstruction of training samples from loss functions, arXiv preprint arXiv:1805.07337
Papers (Refereed) :
A Sannai, M Imaizumi, M Kawano, Improved generalization bound of permutation invariant deep neural networks, The Conference on Uncertainty in Artificial Intelligence (2021)
M Kawano, W Kumagai, A Sannai, Y Iwasawa, Y Matsuo, Group Equivariant Conditional Neural Processes, International Conference on Learning Representations (2021)
Y Takai, A Sannai, M Cordonnier On the number of linear functions composing deep neural network: Towards a refined definition of neural networks complexity The 24th International Conference on Artificial Intelligence and Statistics (2021)
A Tanaka, A Sannai, K Kobayashi, N Hamada, Asymptotic Risk of Bezier Simplex Fitting, To appear in Proceedings of the AAAI Conference on Artificial Intelligence 34
S Ejiri, A Sannai, A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II, International Mathematics Research Notices 2019 (19), 5975-5988
K Kobayashi, N Hamada, A Sannai, A Tanaka, K Bannai, M Sugiyama, Bézier simplex fitting: Describing Pareto fronts of simplicial problems with small samples in multi-objective optimization, Proceedings of the AAAI Conference on Artificial Intelligence 33, 2304-2313
A Sannai, Invariant subring of the Cox ring of K3 surfaces, Le Matematiche 74 (1), 3-11
A Sannai, H Tanaka, Infinitely generated symbolic Rees algebras over finite fields, Algebra & Number Theory 13 (8), 1879-1891
A Sannai, H Tanaka, A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf, Mathematische Annalen 366 (3-4), 1067-1087
A Sannai, On dual F-signature, International Mathematics Research Notices 2015 (1), 197-211
S Mochizuki, A Sannai, Generalized Koszul resolution, Tokyo Journal of Mathematics 36 (2), 459-472
A Sannai, AK Singh, Galois extensions, plus closure, and maps on local cohomology, Advances in Mathematics 229 (3), 1847-1861
Yoshinori Gongyo, Shinnosuke Okawa, Akiyoshi Sannai and Shunsuke Takagi, Characterization of varieties of Fano type via singularities of Cox rings, J. Algebraic Geom. 24 (2015), 159-182
Shihoko Ishii, Akiyoshi Sannai and Kei-ichi Watanabe, Jet schemes of homogeneous hypersurfaces , Singularities in Geometry and Topology, Strasbourg 2009, IRMA Lectures in Math, 20,. 39-49 (2012)
Akiyoshi Sannai, Kei-ichi Watanabe, F-signature of graded Gorenstein rings, J. Pure and Appl. Algebra, 215 (2011), 2190-2195
Papers (not refereed):
三内 顕義 F-signature of graded Gorenstein rings, 第20回可換環論セミナー報告集, 31-37, (2009)
Akiyoshi Sannai, Anurag Singh,Galois extentions and maps on local cohomology, Proceedings of The 32nd Symposium, The 6th Japan-Vietnam Joint Seminar on Commutative Algebra (2011) 259-270,
三内 顕義, Characterization of varieties of Fano type via Cox rings, 第24回可換環論セミナー報告集, (2012)
Shihoko Ishii, Akiyoshi Sannai, Kei-ichi Watanabe,Jet schemes of homogeneous hypersurfaces, the Proceedings of fifth Franco-Japanese Conference of Singularities 39-50
三内 顕義, Dual F-signature, 第25回可換環論セミナー報告集,(2013)
三内 顕義, Dual F-signature, 第9回数学総合若手研究集会報告集,(2013)
三内顕義, F-signature and F-pure threshold 第38回可換環論シンポジウム報告集, (2016)
三内顕義 decomposability of Frobenius push-forward of structure sheaves 都の西北代数幾何学シンポジウム報告集(2016)