Publications

Under Review

  1. T. Furuya, D. Mis, I. Dokmanić, M. V. de Hoop, M. Lassas.
    Function Graph Transformers Universally Approximate Operators between Function Spaces.
    arXiv:2605.17968 (2026).

  2. R. Barboni, T. Furuya, M. V. de Hoop, G. Peyré.
    Training Infinitely Deep and Wide Transformers.
    arXiv:2605.17660 (2026).

  3. T. Furuya, Y. Korolev, T. Yaguchi.
    Approximation of Maximally Monotone Operators: A Graph Convergence Perspective.
    arXiv:2605.12301 (2026).

  4. T. Furuya, R. Ozawa, Jenn-Nan Wang.
    Approximation Theory of Laplacian-Based Neural Operators for Reaction-Diffusion System.
    arXiv:2605.12025 (2026).

  5. T. Furuya, A. Kratsios, D. Possamaï, B. Raonić.
    One Model to Solve Them All: 2BSDE Families via Neural Operators.
    arXiv:2511.01125 (2025).

  6. T. Furuya, M. V. de Hoop, M. Lassas.
    Transformers through the Lens of Support-Preserving Maps between Measures.
    arXiv:2509.25611 (2025).

  7. A. Kratsios, T. Furuya.
    Is In-Context Universality Enough? MLPs Are Also Universal In-Context.
    arXiv:2502.03327 (2025).

  8. A. Kratsios, T. Furuya.
    Simultaneously Solving FBSDEs with Neural Operators of Logarithmic Depth, Constant Width, and Sublinear Rank.
    arXiv:2410.14788 (2024).

  9. A. Kratsios, T. Furuya, L. B. J. Antonio, M. Lassas, M. V. de Hoop.
    Mixture of Experts Soften the Curse of Dimensionality in Operator Learning.
    arXiv:2404.09101 (2024).

  10. T. Furuya, H. Kusumoto, K. Taniguchi, N. Kanno, K. Suetake.
    Theoretical Error Analysis of Entropy Approximation for Gaussian Mixtures.
    arXiv:2202.13059 (2022).

Publications

  1. T. Furuya, D. Murari, C. B. Schönlieb.
    Approximation Theory for Lipschitz Continuous Transformers.
    International Conference on Machine Learning (ICML), 2026.

  2. A. Kratsios, B. J. Kim, T. Furuya.
    Approximation Rates in Besov Norms and Sample-Complexity of Kolmogorov-Arnold Networks with Residual Connections.
    Neural Networks, 200, 108797 (2026).

  3. T. Furuya, P. Z. Kow, J. N. Wang.
    Consistency of the Bayes Method for the Inverse Scattering Problem with Randomly Truncated Sieve Priors.
    Inverse Problems and Imaging, 21, 222–244 (2026).

  4. D. Murari, T. Furuya, C. B. Schönlieb.
    Approximation Theory for 1-Lipschitz ResNets.
    Advances in Neural Information Processing Systems (NeurIPS), 38, 142888–142919 (2025).

  5. T. Furuya, M. V. de Hoop, G. Peyré.
    Transformers Are Universal In-Context Learners.
    International Conference on Learning Representations (ICLR), 80820–80845 (2025).

  6. T. Furuya, K. Taniguchi, S. Okuda.
    Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equations.
    International Conference on Learning Representations (ICLR), 85528–85556 (2025).

  7. T. Furuya, J. N. Wang.
    The Bernstein–von Mises Theorem for the Inverse Scattering Problem.
    Communications in Mathematical Sciences, 23(4), 1023–1042 (2025).

  8. H. S. O. Borde, T. Furuya, A. Kratsios, M. T. Law.
    Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts.
    Transactions on Machine Learning Research (2025).

  9. T. Furuya, M. Puthawala, M. Lassas, M. V. de Hoop.
    Can Neural Operators Always Be Continuously Discretized?
    Advances in Neural Information Processing Systems (NeurIPS), 37, 98936–98993 (2024).

  10. T. Furuya, S. Okuda, K. Suetake, Y. Sawada.
    Convergences for Minimax Optimization Problems over Infinite-Dimensional Spaces Towards Stability in Adversarial Training.
    Transactions on Machine Learning Research (2024).

  11. L. B. J. Antonio, T. Furuya, F. Faucher, A. Kratsios, X. Tricoche, M. V. de Hoop.
    Out-of-Distribution Risk Bounds for Neural Operators with Applications to the Helmholtz Equation.
    Journal of Computational Physics, 513, 113168 (2024).

  12. T. Furuya, P. Z. Kow, J. N. Wang.
    Consistency of the Bayes Method for the Inverse Scattering Problem.
    Inverse Problems, 40, 055001 (2024).

  13. T. Furuya, M. Puthawala, M. Lassas, M. V. de Hoop.
    Globally Injective and Bijective Neural Operators.
    Advances in Neural Information Processing Systems (NeurIPS), 36, 57713–57753 (2023).

  14. M. V. de Hoop, T. Furuya, C. L. Lin, G. Nakamura, M. Vashisth.
    Local Recovery of a Piecewise Constant Anisotropic Conductivity in EIT on Domains with Exposed Corners.
    Inverse Problems, 39, 025005 (2023).

  15. T. Furuya, R. Potthast.
    Inverse Medium Scattering Problems with Kalman Filter Techniques.
    Inverse Problems, 38, 095003 (2022).

  16. T. Furuya, K. Suetake, K. Taniguchi, H. Kusumoto, R. Saiin, T. Daimon.
    Spectral Pruning for Recurrent Neural Networks.
    Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR Vol. 151 (2022).

  17. T. Furuya.
    Remarks on the Factorization and Monotonicity Method for Inverse Acoustic Scattering.
    Inverse Problems, 37, 065006 (2021).

  18. T. Furuya.
    The Factorization and Monotonicity Method for the Defect in an Open Periodic Waveguide.
    Inverse and Ill-Posed Problems, 28, 783–796 (2020).

  19. T. Furuya.
    Scattering by the Local Perturbation of an Open Periodic Waveguide in the Half Plane.
    Journal of Mathematical Analysis and Applications, 489, 124149 (2020).

  20. T. Furuya.
    The Direct and Inverse Scattering Problem for the Semilinear Schrödinger Equation.
    NoDEA Nonlinear Differential Equations and Applications, 27, Article 24 (2020).

  21. T. Daimon, T. Furuya, R. Saiin.
    The Monotonicity Method for the Inverse Crack Scattering Problem.
    Inverse Problems in Science and Engineering, 28, 1570–1581 (2020).

  22. T. Furuya.
    A Modification of the Factorization Method for Scatterers with Different Physical Properties.
    Mathematical Methods in the Applied Sciences, 42, 4017–4030 (2019).

  23. H. Chihara, T. Furuya, T. Koshikawa.
    Hermite Expansions of Some Tempered Distributions.
    Journal of Pseudo-Differential Operators and Applications, 9, 105–124 (2017).