We derive finite-sample generalization bounds for Transformers trained with dynamic programming recursions. Building on the doubly lifted, measure-valued formulation of Transformer dynamics, we view data sets as probability laws on pairs of empirical input-output measures, allowing us to interpret the training problem as a finite-horizon Markovian control problem.
arXiv:2607. 27975v1 Announce Type: new Abstract: We derive finite-sample generalization bounds for Transformers trained with dynamic programming recursions.
By Ka\u{g}an Akman, Naci Saldi, Serdar Y\"uksel
arXiv:2607. 24513v1 Announce Type: new Abstract: Transformer architectures have attracted increasing attention for solving partial differential equations (PDEs), owing to their flexibility in handling irregular discretizations and their ability to capture long-range physical dependencies.
By Guoze Sun, Rui Zhang, Jiankai Tang, Mengtao Yan, Runze Mao, Zhi X. Chen, Hao Sun
arXiv:2606. 09434v2 Announce Type: replace Abstract: Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs.
By Li Zeng, Xiaoliang Wan, Yaobin Wang, Fabio Nobile, Tao Zhou
arXiv:2510. 09904v2 Announce Type: replace-cross Abstract: Despite their widespread use, training deep Transformers can be unstable.
By Kelvin Kan, Xingjian Li, Benjamin J. Zhang, Tuhin Sahai, Stanley Osher, Krishna Kumar, Markos A. Katsoulakis
arXiv:2601. 17257v2 Announce Type: replace Abstract: We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms.
By Javier Porras-Valenzuela, Samar Hadou, Alejandro Ribeiro
arXiv:2603. 18907v2 Announce Type: replace Abstract: We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution, parametrically with respect to the location of the initial mass.
By Riccardo Saporiti, Fabio Nobile
arXiv:2602. 18948v2 Announce Type: replace Abstract: Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively.
By J. Fran\c{c}ois, L. Ravera
arXiv:2508. 07743v2 Announce Type: replace Abstract: While transformers excel in many settings, their application in the field of automated planning is limited.
By Markus Fritzsche, Elliot Gestrin, Jendrik Seipp
arXiv:2601. 22002v5 Announce Type: replace Abstract: Transformers achieve superior performance on many tasks, but impose heavy compute and memory requirements during inference.
By Anderson de Andrade, Alon Harell, Ivan V. Baji\'c
arXiv:2607. 22550v1 Announce Type: cross Abstract: We propose a learning-augmented Benders decomposition framework to solve large-scale two-stage stochastic mixed-integer programs.
By Seung Jin Choi, Kimiya Jozani, Josh Cooper, Esra Buyuktahtakin Toy
arXiv:2604. 06531v3 Announce Type: replace-cross Abstract: The mean-field Schr\"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline.
By Asmaa Eldesoukey, Yongxin Chen, Abhishek Halder