Data-driven nonlinear model reduction
Learning low-dimensional dynamics from high-dimensional, multiscale stochastic systems while preserving the geometry and structure that make long-time prediction trustworthy.
About
My research lies at the intersection of scientific computing and machine learning, with mathematical structure as the unifying theme. I use machine learning to discover and preserve structure in stochastic scientific models, and ideas from scientific computing, probability, and dynamical systems to make modern AI more scalable and reliable.
Research areas
Optimal transport at accelerator scale
Connecting entropic optimal transport with attention to develop analytic sensitivity methods and IO-aware GPU kernels for large-scale Sinkhorn computation.
Long-context inference and state space models
Building probabilistic and dynamical foundations for memory, stability, discretization, and quantization in selective state space models and long-context inference.
Multimodal AI
Collaborative work on fine-grained audio-visual reasoning, video moment retrieval, efficient token selection, and multimodal generative modeling.
Current & awarded support
Awarded support for research in nonlinear model reduction, optimal transport, and state space models.
Data-Driven Nonlinear Model Reduction for High-dimensional Multi-scale Stochastic Dynamical Systems
$200,000 · September 2026–August 2029
PI: Felix X.-F. Ye · Co-PI: Barbara Giunti
BayesianMamba: Probabilistic Perspective of Generalization of State Space Models
$170,265 total · January 2025–December 2026
Single PI · Includes an approved extension through December 31, 2026
Data-driven Model Reduction in Stochastic Dynamical Systems
$42,000 · 2023–2028
Single PI · Travel Support for Mathematicians
Block-Semiseparable 1-SS for Certain Type of Linear Attention
$10,000 in cloud compute · December 2025–December 2026
Single PI
Prior support: AMS–Simons Travel Grant, $5,000, 2020–2023.
Selected work
FlashSinkhorn: IO-Aware Entropic Optimal Transport on GPU
Forty-third International Conference on Machine Learning (ICML 2026) · Code
DropKV: Decoupling Residual-Output Perturbation for Near-Optimal KV-Cache Eviction
Robust First- and Second-Order Differentiation for Regularized Optimal Transport
SIAM Journal on Scientific Computing, 47(3), C630–C654
Nonlinear Model Reduction for Slow-Fast Stochastic Systems Near Unknown Invariant Manifolds
Journal of Nonlinear Science, 34, Article 22
* Corresponding author.
Publications
Listed in reverse chronological order. See Google Scholar for citation records.
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2026
RatSeizure: A Benchmark and Saliency-Context Transformer for Rat Seizure Localization
Ting Yu Tsai, An Yu, Linda Lee, Felix X.-F. Ye, Daniel S. Shin, Tsang-Jiun Kao, Xingjie Li, and Ming-Ching Chang · MICCAI 2026, accepted. -
2026
SMART: Shot-Aware Multimodal Video Moment Retrieval with Audio-Enhanced MLLM
An Yu, Weiyu Lu, Jiazhi Li, Zhaorun Zhang, Yifan Shen, Felix X.-F. Ye, and Ming-Ching Chang · IEEE Transactions on Multimedia, accepted. -
2026
Memory Along the Chain: Disentangling Dynamics from Discretization in Mamba
Felix X.-F. Ye, Ting Yu Tsai, Ming-Ching Chang, and Davis Wertheimer · Submitted. -
2026
DropKV: Decoupling Residual-Output Perturbation for Near-Optimal KV-Cache Eviction
Aozhong Zhang, Selcuk Gurses, Yanxia Deng, Naigang Wang, Chi-Chun Liu, Davis Wertheimer, Derrick Liu, Xin Li, Zi Yang, Felix X.-F. Ye, and Penghang Yin · Submitted. -
2026
FAVE: A Structured Benchmark for Fine-Grained Audio-Visual Temporal Evaluation in Multimodal LLMs
Weiyu Lu, An Yu, Jiazhi Li, Zhaorun Zhang, Felix X.-F. Ye, and Ming-Ching Chang · CVPR 2026, Poster. -
2026
Minimal Intersection Radius for n Growing, Non-Homogeneous Ellipsoids in Rd
Barbara Giunti, Sean Hill, and Felix X.-F. Ye · Submitted. -
2026
Geometric Regularization of Autoencoders via Observed Stochastic Dynamics
Sean Hill and Felix X.-F. Ye · Submitted. -
2026
ReDiPrune: Relevance-Diversity Pre-Projection Token Pruning for Efficient Multimodal LLMs
An Yu, Ting Yu Tsai, Zhaorun Zhang, Weiyu Lu, Felix X.-F. Ye, and Ming-Ching Chang · Submitted. -
2026
FlashSinkhorn: IO-Aware Entropic Optimal Transport on GPU
Felix X.-F. Ye, Xingjie Li, An Yu, Ming-Ching Chang, Linsong Chu, and Davis Wertheimer · ICML 2026, Oral (Top 0.7%). -
2025
Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces
Kevin Rojas, Yuchen Zhu, Sichen Zhu, Felix X.-F. Ye, and Molei Tao · ICML 2025, Poster. -
2025
Robust First- and Second-Order Differentiation for Regularized Optimal Transport
Xingjie Li, Fei Lu, Molei Tao, and Felix X.-F. Ye · SIAM Journal on Scientific Computing, 47(3), C630–C654. -
2024
Nonlinear Model Reduction for Slow-Fast Stochastic Systems Near Unknown Invariant Manifolds
Felix X.-F. Ye, Sichen Yang, and Mauro Maggioni · Journal of Nonlinear Science, 34, Article 22. -
2024
Estimate Exponential Memory Decay in Hidden Markov Model and Its Applications to Inference
Felix X.-F. Ye, Yi-an Ma, and Hong Qian · Physica D: Nonlinear Phenomena, 460, 134053. -
2023
NySALT: Nyström-type Inference-Based Schemes Adaptive to Large Time-Stepping
Xingjie Li, Fei Lu, Molei Tao, and Felix X.-F. Ye · Journal of Computational Physics, 477, 111952. -
2022
ISALT: Inference-Based Schemes Adaptive to Large Time-Stepping for Locally Lipschitz Ergodic Systems
Xingjie Li, Fei Lu, and Felix X.-F. Ye · Discrete and Continuous Dynamical Systems - S, 15(4), 747–771. -
2021
Quantifying Information Accumulation Encoded in the Dynamics of Biochemical Signaling
Ying Tang, Adewunmi Adelaja, Felix X.-F. Ye, Eric J. Deeds, Roy Wollman, and Alexander Hoffmann · Nature Communications, 12(1), 1–10. -
2020
Synchronization in Discrete-Time, Discrete-State Random Dynamical Systems
Wen Huang, Hong Qian, Shirou Wang, Felix X.-F. Ye, and Yingfei Yi · SIAM Journal on Applied Dynamical Systems, 19(1), 233–251. -
2019
Stochastic Dynamics II: Finite Random Dynamical Systems, Linear Representation, and Entropy Production
Felix X.-F. Ye and Hong Qian · Discrete and Continuous Dynamical Systems - B, 24(8), 4341–4366. -
2019
Time-Dependent Saddle–Node Bifurcation: Breaking Time and the Point of No Return in a Non-Autonomous Model of Critical Transitions
Jeremiah H. Li, Felix X.-F. Ye, Hong Qian, and Sui Huang · Physica D: Nonlinear Phenomena, 395, 7–14. -
2018
Dynamic Looping of a Free-Draining Polymer
Felix X.-F. Ye, Panos Stinis, and Hong Qian · SIAM Journal on Applied Mathematics, 78(1), 104–123. -
2017
Stochastic Dynamics: Models for Intrinsic and Extrinsic Noises and Their Applications
Yi-an Ma, Hong Qian, and Felix X.-F. Ye · SCIENTIA SINICA Mathematica, 47(12), 1693–1702. -
2016
Stochastic Dynamics: Markov Chains and Random Transformations
Felix X.-F. Ye, Yue Wang, and Hong Qian · Discrete and Continuous Dynamical Systems - B, 21(7), 2337–2361. -
2013
Evolution of Recombination Rates in a Multi-Locus, Haploid-Selection, Symmetric-Viability Model
J. R. Chasnov and Felix X.-F. Ye · Theoretical Population Biology, 83, 155–165.