Lean Formalization of Generalization Error Bound by Rademacher Complexity and Dudley's Entropy Integral.

Sho Sonoda Sho Sonoda Kazumi Kasaura Yuma Mizuno Kei Tsukamoto Naoto Onda Lean Formalization of Generalization Error Bound by Rademacher Complexity and Dudley's Entropy Integral. 8:1-8:17 2026 ITP https://doi.org/10.4230/LIPIcs.ITP.2026.8 conf/itp/2026 db/conf/itp/itp2026.html#SonodaKMTO26

Sho Sonoda Shunta Akiyama Yuya Uezato Don't Eliminate Cut: Exponential Separations in LLM-Based Theorem Proving. 2026 February abs/2602.10512 CoRR https://doi.org/10.48550/arXiv.2602.10512 db/journals/corr/corr2602.html#abs-2602-10512 streams/journals/corr

Sho Sonoda Shunta Akiyama Yuya Uezato Why Agentic Theorem Prover Works: A Statistical Provability Theory of Mathematical Reasoning Models. 2026 February abs/2602.10538 CoRR https://doi.org/10.48550/arXiv.2602.10538 db/journals/corr/corr2602.html#abs-2602-10538 streams/journals/corr

Koichi Taniguchi Sho Sonoda Generalization Error Bounds for Picard-Type Operator Learning in Nonlinear Parabolic PDEs. 2026 May abs/2605.10277 CoRR https://doi.org/10.48550/arXiv.2605.10277 db/journals/corr/corr2605.html#abs-2605-10277 streams/journals/corr

Natsuto Isogai Hayata Yamasaki Sho Sonoda Mio Murao Winning Lottery Tickets in Neural Networks via a Quantum-Inspired Classical Algorithm. 2026 May abs/2605.13979 CoRR https://doi.org/10.48550/arXiv.2605.13979 db/journals/corr/corr2605.html#abs-2605-13979 streams/journals/corr

Kazumi Kasaura Kei Tsukamoto Kento Mori Risa Mizuno Takahiro Namatame Yuta Oriike Masaya Taniguchi Sho Sonoda Hayata Yamasaki Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information. 2026 July abs/2607.05492 CoRR https://doi.org/10.48550/arXiv.2607.05492 db/journals/corr/corr2607.html#abs-2607-05492 streams/journals/corr

Sho Sonoda Yuka Hashimoto Isao Ishikawa Masahiro Ikeda Deep Ridgelet Transform and Unified Universality Theorem for Deep and Shallow Joint-Group-Equivariant Machines. 2025 ICML https://proceedings.mlr.press/v267/sonoda25a.html https://openreview.net/forum?id=JKsxKPXXUd conf/icml/2025 db/conf/icml/icml2025.html#SonodaHII25

Sho Sonoda Kazumi Kasaura Yuma Mizuno Kei Tsukamoto Naoto Onda Lean Formalization of Generalization Error Bound by Rademacher Complexity. 2025 March abs/2503.19605 CoRR https://doi.org/10.48550/arXiv.2503.19605 db/journals/corr/corr2503.html#abs-2503-19605 streams/journals/corr

Sho Sonoda Yuka Hashimoto Isao Ishikawa Masahiro Ikeda Generalization Through Growth: Hidden Dynamics Controls Depth Dependence. 2025 May abs/2505.15064 CoRR https://doi.org/10.48550/arXiv.2505.15064 db/journals/corr/corr2505.html#abs-2505-15064 streams/journals/corr

Naoto Onda Kazumi Kasaura Yuta Oriike Masaya Taniguchi Akiyoshi Sannai Sho Sonoda LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving. 2025 June abs/2506.22005 CoRR https://doi.org/10.48550/arXiv.2506.22005 db/journals/corr/corr2506.html#abs-2506-22005 streams/journals/corr

Kazumi Kasaura Naoto Onda Yuta Oriike Masaya Taniguchi Akiyoshi Sannai Sho Sonoda Discovering New Theorems via LLMs with In-Context Proof Learning in Lean. 2025 September abs/2509.14274 CoRR https://doi.org/10.48550/arXiv.2509.14274 db/journals/corr/corr2509.html#abs-2509-14274 streams/journals/corr

Yuka Hashimoto Sho Sonoda Isao Ishikawa Masahiro Ikeda Why High-rank Neural Networks Generalize?: An Algebraic Framework with RKHSs. 2025 September abs/2509.21895 CoRR https://doi.org/10.48550/arXiv.2509.21895 db/journals/corr/corr2509.html#abs-2509-21895 streams/journals/corr

Yuka Hashimoto Sho Sonoda Isao Ishikawa Atsushi Nitanda Taiji Suzuki Koopman-based generalization bound: New aspect for full-rank weights. 2024 ICLR https://openreview.net/forum?id=JN7TcCm9LF conf/iclr/2024 db/conf/iclr/iclr2024.html#HashimotoSINS24

Toshinori Kitamura Tadashi Kozuno Masahiro Kato Yuki Ichihara Soichiro Nishimori Akiyoshi Sannai Sho Sonoda Wataru Kumagai Yutaka Matsuo A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees. 2024 abs/2401.17780 CoRR https://doi.org/10.48550/arXiv.2401.17780 db/journals/corr/corr2401.html#abs-2401-17780

Sho Sonoda Isao Ishikawa Masahiro Ikeda A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks. 2024 abs/2402.15984 CoRR https://doi.org/10.48550/arXiv.2402.15984 db/journals/corr/corr2402.html#abs-2402-15984

Sho Sonoda Yuka Hashimoto Isao Ishikawa Masahiro Ikeda Constructive Universal Approximation Theorems for Deep Joint-Equivariant Networks by Schur's Lemma. 2024 abs/2405.13682 CoRR https://doi.org/10.48550/arXiv.2405.13682 db/journals/corr/corr2405.html#abs-2405-13682

Kaito Watanabe Kotaro Sakamoto Ryo Karakida Sho Sonoda Shun-ichi Amari Deep learning in random neural fields: Numerical experiments via neural tangent kernel. 148-163 2023 March 160 Neural Networks https://doi.org/10.1016/j.neunet.2022.12.020 db/journals/nn/nn160.html#WatanabeSKSA23

Ming Li 0065 Sho Sonoda Feilong Cao Yu Guang Wang 0001 Jiye Liang How Powerful are Shallow Neural Networks with Bandlimited Random Weights? 19960-19981 2023 ICML https://proceedings.mlr.press/v202/li23aa.html conf/icml/2023 db/conf/icml/icml2023.html#LiSCWL23 Hayata Yamasaki Sathyawageeswar Subramanian Satoshi Hayakawa Sho Sonoda Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation. 39008-39034 2023 ICML https://proceedings.mlr.press/v202/yamasaki23a.html conf/icml/2023 db/conf/icml/icml2023.html#YamasakiSHS23 Sho Sonoda Hideyuki Ishi Isao Ishikawa Masahiro Ikeda Joint Group Invariant Functions on Data-Parameter Domain Induce Universal Neural Networks. 129-144 2023 NeurReps https://proceedings.mlr.press/v228/sonoda24a.html conf/neurreps/2023 db/conf/neurreps/neurreps2023.html#SonodaIII23 streams/conf/neurreps

Hayata Yamasaki Sathyawageeswar Subramanian Satoshi Hayakawa Sho Sonoda Quantum Ridgelet Transform: Winning Lottery Ticket of Neural Networks with Quantum Computation. 2023 abs/2301.11936 CoRR https://doi.org/10.48550/arXiv.2301.11936 db/journals/corr/corr2301.html#abs-2301-11936

Yuka Hashimoto Sho Sonoda Isao Ishikawa Atsushi Nitanda Taiji Suzuki Koopman-Based Bound for Generalization: New Aspect of Neural Networks Regarding Nonlinear Noise Filtering. 2023 abs/2302.05825 CoRR https://doi.org/10.48550/arXiv.2302.05825 db/journals/corr/corr2302.html#abs-2302-05825

Ryutaro Yamauchi Sho Sonoda Akiyoshi Sannai Wataru Kumagai LPML: LLM-Prompting Markup Language for Mathematical Reasoning. 2023 abs/2309.13078 CoRR https://doi.org/10.48550/arXiv.2309.13078 db/journals/corr/corr2309.html#abs-2309-13078

Sho Sonoda Yuka Hashimoto Isao Ishikawa Masahiro Ikeda Deep Ridgelet Transform: Voice with Koopman Operator Proves Universality of Formal Deep Networks. 2023 abs/2310.03529 CoRR https://doi.org/10.48550/arXiv.2310.03529 db/journals/corr/corr2310.html#abs-2310-03529

Sho Sonoda Hideyuki Ishi Isao Ishikawa Masahiro Ikeda Joint Group Invariant Functions on Data-Parameter Domain Induce Universal Neural Networks. 2023 abs/2310.03530 CoRR https://doi.org/10.48550/arXiv.2310.03530 db/journals/corr/corr2310.html#abs-2310-03530

Sho Sonoda Isao Ishikawa Masahiro Ikeda Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis. 20405-20422 2022 ICML https://proceedings.mlr.press/v162/sonoda22a.html conf/icml/2022 db/conf/icml/icml2022.html#SonodaII22 Sho Sonoda Isao Ishikawa Masahiro Ikeda Universality of Group Convolutional Neural Networks Based on Ridgelet Analysis on Groups. 2022 conf/nips/2022 NeurIPS http://papers.nips.cc/paper_files/paper/2022/hash/fcc3dc27672a12510babe448d665e152-Abstract-Conference.html db/conf/nips/neurips2022.html#SonodaII22

Kaito Watanabe Kotaro Sakamoto Ryo Karakida Sho Sonoda Shun-ichi Amari Deep Learning in Random Neural Fields: Numerical Experiments via Neural Tangent Kernel. 2022 abs/2202.05254 CoRR https://arxiv.org/abs/2202.05254 db/journals/corr/corr2202.html#abs-2202-05254

Sho Sonoda Isao Ishikawa Masahiro Ikeda Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysis. 2022 abs/2203.01631 CoRR https://doi.org/10.48550/arXiv.2203.01631 db/journals/corr/corr2203.html#abs-2203-01631

Sho Sonoda Isao Ishikawa Masahiro Ikeda Universality of group convolutional neural networks based on ridgelet analysis on groups. 2022 abs/2205.14819 CoRR https://doi.org/10.48550/arXiv.2205.14819 db/journals/corr/corr2205.html#abs-2205-14819

Sho Sonoda Isao Ishikawa Masahiro Ikeda Ridge Regression with Over-parametrized Two-Layer Networks Converge to Ridgelet Spectrum. 2674-2682 2021 AISTATS http://proceedings.mlr.press/v130/sonoda21a.html conf/aistats/2021 db/conf/aistats/aistats2021.html#SonodaII21 Stefano Massaroli Michael Poli Sho Sonoda Taiji Suzuki Jinkyoo Park Atsushi Yamashita Hajime Asama Differentiable Multiple Shooting Layers. 16532-16544 2021 NeurIPS https://proceedings.neurips.cc/paper/2021/hash/89b9c689a57b82e59074c6ba09aa394d-Abstract.html conf/nips/2021 db/conf/nips/neurips2021.html#MassaroliPSSPYA21

Stefano Massaroli Michael Poli Sho Sonoda Taiji Suzuki Jinkyoo Park Atsushi Yamashita Hajime Asama Differentiable Multiple Shooting Layers. 2021 abs/2106.03885 CoRR https://arxiv.org/abs/2106.03885 db/journals/corr/corr2106.html#abs-2106-03885

Sho Sonoda Isao Ishikawa Masahiro Ikeda Ghosts in Neural Networks: Existence, Structure and Role of Infinite-Dimensional Null Space. 2021 abs/2106.04770 CoRR https://arxiv.org/abs/2106.04770 db/journals/corr/corr2106.html#abs-2106-04770

Hayata Yamasaki Sho Sonoda Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning. 2021 abs/2106.09028 CoRR https://arxiv.org/abs/2106.09028 db/journals/corr/corr2106.html#abs-2106-09028

Hayata Yamasaki Sathyawageeswar Subramanian Sho Sonoda Masato Koashi Learning with Optimized Random Features: Exponential Speedup by Quantum Machine Learning without Sparsity and Low-Rank Assumptions. 2020 NeurIPS https://proceedings.neurips.cc/paper/2020/hash/9ddb9dd5d8aee9a76bf217a2a3c54833-Abstract.html conf/nips/2020 db/conf/nips/neurips2020.html#YamasakiSSK20

Hayata Yamasaki Sathyawageeswar Subramanian Sho Sonoda Masato Koashi Fast Quantum Algorithm for Learning with Optimized Random Features. 2020 abs/2004.10756 CoRR https://arxiv.org/abs/2004.10756 db/journals/corr/corr2004.html#abs-2004-10756

Sho Sonoda Isao Ishikawa Masahiro Ikeda Gradient Descent Converges to Ridgelet Spectrum. 2020 abs/2007.03441 CoRR https://arxiv.org/abs/2007.03441 db/journals/corr/corr2007.html#abs-2007-03441

Sho Sonoda Ming Li 0065 Feilong Cao Changqin Huang Yu Guang Wang 0001 On the Approximation Lower Bound for Neural Nets with Random Weights. 2020 abs/2008.08427 CoRR https://arxiv.org/abs/2008.08427 db/journals/corr/corr2008.html#abs-2008-08427

Sho Sonoda Noboru Murata Transport Analysis of Infinitely Deep Neural Network. 2019 20 J. Mach. Learn. Res. https://jmlr.org/papers/v20/16-243.html db/journals/jmlr/jmlr20.html#SonodaM19 2:1-2:52

Sho Sonoda Numerical Integration Method for Training Neural Network. 2019 abs/1902.00648 CoRR http://arxiv.org/abs/1902.00648 db/journals/corr/corr1902.html#abs-1902-00648

Sho Sonoda Keita Nakamura Yuki Kaneda Hideitsu Hino Shotaro Akaho Noboru Murata Eri Miyauchi Masahiro Kawasaki EEG dipole source localization with information criteria for multiple particle filters. 68-82 2018 108 Neural Networks https://doi.org/10.1016/j.neunet.2018.08.008 https://www.wikidata.org/entity/Q91260575 db/journals/nn/nn108.html#SonodaNKHAMMK18

Keita Nakamura Sho Sonoda Hideitsu Hino Masahiro Kawasaki Shotaro Akaho Noboru Murata Localizing Current Dipoles from EEG Data Using a Birth-Death Process. 2645-2651 2018 BIBM https://doi.ieeecomputersociety.org/10.1109/BIBM.2018.8621504 conf/bibm/2018 db/conf/bibm/bibm2018.html#NakamuraSHKAM18

Sho Sonoda Isao Ishikawa Masahiro Ikeda Kei Hagihara Yoshihiro Sawano Takuo Matsubara Noboru Murata Integral representation of the global minimizer. 2018 abs/1805.07517 CoRR http://arxiv.org/abs/1805.07517 db/journals/corr/corr1805.html#abs-1805-07517

Sho Sonoda Noboru Murata Transportation analysis of denoising autoencoders: a novel method for analyzing deep neural networks. 2017 abs/1712.04145 CoRR http://arxiv.org/abs/1712.04145 db/journals/corr/corr1712.html#abs-1712-04145

Sho Sonoda Noboru Murata Decoding Stacked Denoising Autoencoders. 2016 abs/1605.02832 CoRR http://arxiv.org/abs/1605.02832 db/journals/corr/corr1605.html#SonodaM16

Sho Sonoda Noboru Murata Neural Network with Unbounded Activations is Universal Approximator. 2015 abs/1505.03654 CoRR http://arxiv.org/abs/1505.03654 db/journals/corr/corr1505.html#SonodaM15

Sho Sonoda Noboru Murata Sampling Hidden Parameters from Oracle Distribution. 539-546 2014 ICANN https://doi.org/10.1007/978-3-319-11179-7_68 conf/icann/2014 db/conf/icann/icann2014.html#SonodaM14

Sho Sonoda Noboru Murata Nonparametric Weight Initialization of Neural Networks via Integral Representation. 2013 abs/1312.6461 CoRR http://arxiv.org/abs/1312.6461 db/journals/corr/corr1312.html#SonodaM13

Shotaro Akaho Shunta Akiyama Shun-ichi Amari Hajime Asama Feilong Cao Kei Hagihara Yuka Hashimoto Satoshi Hayakawa Hideitsu Hino Changqin Huang Yuki Ichihara Masahiro Ikeda Hideyuki Ishi Isao Ishikawa Natsuto Isogai Yuki Kaneda Ryo Karakida Kazumi Kasaura Masahiro Kato Masahiro Kawasaki Toshinori Kitamura Masato Koashi Tadashi Kozuno Wataru Kumagai Ming Li 0065 Jiye Liang Stefano Massaroli Takuo Matsubara Yutaka Matsuo Eri Miyauchi Risa Mizuno Yuma Mizuno Kento Mori Mio Murao Noboru Murata Keita Nakamura Takahiro Namatame Soichiro Nishimori Atsushi Nitanda Naoto Onda Yuta Oriike Jinkyoo Park Michael Poli Kotaro Sakamoto Akiyoshi Sannai Yoshihiro Sawano Sathyawageeswar Subramanian Taiji Suzuki Koichi Taniguchi Masaya Taniguchi Kei Tsukamoto Yuya Uezato Yu Guang Wang 0001 Kaito Watanabe Hayata Yamasaki Atsushi Yamashita Ryutaro Yamauchi