Numerical Analysis

Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika et al.

For optimization researchers, this work demystifies the success of Muon, suggesting that geometric narratives may be overemphasized, though the findings are incremental in nature.

Edoardo Calvello, Elizabeth Carlson, Nikola Kovachki et al.

It addresses the lack of analysis for data-driven methods in data assimilation and forecasting, providing foundational theory for researchers in machine learning and dynamical systems.

Kyurae Kim, Samuel Gruffaz, Ji Won Park et al.

For researchers using Langevin Monte Carlo for sampling, this work extends theoretical guarantees to the overdamped regime, showing the exponential integrator remains stable and effective.

Panos Tsimpos, Edoardo Calvello, Ayoub Belhadji et al.

For researchers in probabilistic inference and Bayesian methods, this work provides theoretical foundations for amortized conditioning, potentially enabling foundation models for Bayesian inference.

Ziyuan Tang, Tianshi Xu, Yousef Saad et al.

For deep learning practitioners using Muon-type optimizers, HiMuon offers a computationally cheaper alternative that maintains similar training efficiency.

Lizhang Chen, Jonathan Li, Chen Liang et al.

It provides a method to enhance frozen transformer models at test time, offering a practical way to boost performance without additional training.

Jiahe Huang, Sihan Xu, Sharvaree Vadgama et al.

This work addresses the speed-fidelity trade-off in generative models for scientific emulation, enabling high-fidelity one- and few-step dynamic generation for physics-based tasks.

Alexandre Pannier, Cristopher Salvi

This provides a new computational tool for solving path-dependent PDEs, which is important for quantitative finance applications like option pricing, though it appears incremental as an extension of kernel methods to this domain.

Lifu Wei, Yinuo Ren, Naichen Shi et al.

It provides a computationally efficient and unbiased method for inference-time guidance in diffusion models, addressing the bottleneck of repeated score/gradient evaluations.

James Rowbottom, Nick Huang, Carola-Bibiane Schönlieb et al.

For scientists and engineers needing to place sensors for state estimation in complex, non-Gaussian systems, this work provides a theoretically principled and practically superior method.

Xun Huan, Jayanth Jagalur, Youssef Marzouk

For researchers and practitioners in modeling and prediction across sciences and engineering, this survey provides a comprehensive overview of OED methods and identifies key open problems.

Michel Fabrice Serret, Alice Cortinovis, Yijun Dong et al.

This is an incremental survey that synthesizes existing work to help researchers and practitioners accelerate attention mechanisms for large-scale inference.

Matthew S. Zhang, Jason M. Altschuler, Sinho Chewi

This resolves the computational bottleneck of finding warm starts for HMC, which is crucial for practitioners in statistics, engineering, and sciences who rely on HMC for high-dimensional sampling, though it is incremental as it builds on prior theoretical work.

Haibo Liu, Guang Lin

For researchers solving PDE-constrained inverse problems, DiLO provides a principled framework to integrate neural operators with diffusion priors without out-of-distribution issues, improving reconstruction accuracy and efficiency.

Adrien Weihs, Hayden Schaeffer

Provides theoretical guarantees for multi-task operator learning, establishing that it follows the same scaling laws as single-task learning, which is important for practitioners in scientific computing and engineering.

Samuel N. Cohen, Filippo de Feo, Jackson Hebner et al.

This work addresses infinite-dimensional PDEs and optimal control problems, which are foundational in applied sciences like physics and stochastic systems, representing a novel paradigm rather than an incremental improvement.

Johnny Guzmán, Pratyush Potu

For researchers in numerical analysis and computational geometry, it provides a rigorous theoretical foundation for DEC methods, enabling convergence guarantees and error analysis.

Huimin Yu, Liu Liu, Yu Feng et al.

For researchers in uncertainty quantification of tumor growth models, this work provides a method to reduce computational cost while maintaining accuracy, though it is an incremental combination of existing techniques.

Ruihan Xu, Jiajin Li, Yiping Lu

This addresses the challenge of stable optimizer scaling for deep learning practitioners, offering a principled method for learning-rate transfer across model widths, though it builds incrementally on existing scaling theories.

Qinghua Ma, Reetam Sen Biswas, Denis Osipov et al.

This work addresses the need for early warning diagnosis to enhance grid resilience against extreme events, representing an incremental improvement by integrating persistency constraints into existing optimization methods.