[13] Vladimir N Vapnik. An overview of statistical learning theory. IEEE Transactions on Neural Networks, 10(5):988-999, 1999.
[14] Krzysztof Marcin Choromanski, Valerii Likhosherstov, David Dohan, Xingyou Song, Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Quincy Davis, Afroz Mohiuddin, Lukasz Kaiser, David Benjamin Belanger, Lucy J Colwell, and Adrian Weller. Rethinking attention with performers. In International Conference on Learning Representations, 2021.
[15] Alaaeldin Ali, Hugo Touvron, Mathilde Caron, Piotr Bojanowski, Matthijs Douze, Armand Joulin, Ivan Laptev, Natalia Neverova, Gabriel Synnaeve, Jakob Verbeek, et al. XCiT: Cross-covariance image transformers. Advances in neural information processing systems, 34:20014-20027, 2021.
[16] Tam Minh Nguyen, Tan Minh Nguyen, Dung DD Le, Duy Khuong Nguyen, Viet-Anh Tran, Richard Baraniuk, Nhat Ho, and Stanley Osher. Improving transformers with probabilistic attention keys. In Proceedings of the International Conference on Machine Learning, pages 16595-16621. PMLR, 2022.
[17] Tan Nguyen, Minh Pham, Tam Nguyen, Khai Nguyen, Stanley Osher, and Nhat Ho. Fourierformer: Transformer meets generalized fourier integral theorem. Advances in Neural Information Processing Systems, 35:29319-29335, 2022.
[18] Ta-Chung Chi, Ting-Han Fan, Peter J Ramadge, and Alexander Rudnicky. Kerple: Kernelized relative positional embedding for length extrapolation. Advances in Neural Information Processing Systems, 35:8386-8399, 2022.
[19] Tan Minh Nguyen, Tam Minh Nguyen, Nhat Ho, Andrea L. Bertozzi, Richard Baraniuk, and Stanley Osher. A primal-dual framework for transformers and neural networks. In International Conference on Learning Representations, 2023.
[20] James Mercer. Functions of positive and negative type, and their connection with the theory of integral equations. Philosophical Transactions of the Royal Society A, 209(441-458):415-446, January 1909.
[21] Matthew A Wright and Joseph E Gonzalez. Transformers are deep infinite-dimensional non-Mercer binary kernel machines. arXiv preprint arXiv:2106.01506, 2021.
[22] Haizhang Zhang, Yuesheng Xu, and Jun Zhang. Reproducing kernel banach spaces for machine learning. Journal of Machine Learning Research, 10(12), 2009.
[23] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In IEEE conference on computer vision and pattern recognition, pages 248–255, 2009.
[24] Rong Rong Lin, Hai Zhang Zhang, and Jun Zhang. On reproducing kernel banach spaces: Generic definitions and unified framework of constructions. Acta Mathematica Sinica, English Series, 38(8):1459-1483, 2022.
[25] Pando G Georgiev, Luis Sánchez-González, and Panos M Pardalos. Construction of pairs of reproducing kernel banach spaces. In Constructive Nonsmooth Analysis and Related Topics, pages 39-57. Springer, 2013.
[26] Gilbert Strang. Linear algebra and its applications. Belmont, CA: Thomson, Brooks/Cole, 2006.
[27] Johan A.K. Suykens. SVD revisited: A new variational principle, compatible feature maps and nonlinear extensions. Applied and Computational Harmonic Analysis, 40(3):600-609, 2016.
[28] Johan A.K. Suykens, Tony Van Gestel, Joseph De Brabanter, Bart De Moor, and Joos PL Vandewalle. Least Squares Support Vector Machines. World scientific, 2002.
[29] Cornelius Lanczos. Linear systems in self-adjoint form. The American Mathematical Monthly, 65(9):665-679, 1958.