1 citations · 1 across the 8 of their papers we have counts for
9 papers
Geometric Asymptotics of Score Mixing and Guidance in Diffusion Models
Kang Liu, Enrique Zuazua
Diffusion models are routinely guided in practice by combining multiple score fields, yet the mathematical structure of score mixing is still poorly understood. We study the small-…
Dual Certified White-Box Inference for Input Convex Neural Networks
Kang Liu, Jianchen Hu, Wei Peng
Input convex neural networks (ICNNs) are used to learn convex objectives whose minimizers define decisions, making efficient and reliable optimization central to inference. At nons…
Budget-aware Auto Optimizer Configurator
Kang Liu, Wei Peng, Jianchen Hu
Optimizer states occupy massive GPU memory in large-scale model training. However, gradients in different network blocks exhibit distinct behaviors, such as varying directional sta…
A PDE Perspective on Generative Diffusion Models
Kang Liu, Enrique Zuazua
Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains. Despite their empirical success, their mat…
Deep Neural ODE Operator Networks for PDEs
Ziqian Li, Kang Liu, Yongcun Song +2
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often o…
Moments, Time-Inversion and Source Identification for the Heat Equation
Kang Liu, Enrique Zuazua
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical T…
Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics
Kang Liu, Enrique Zuazua
In this work, we address three non-convex optimization problems associated with the training of shallow neural networks (NNs) for exact and approximate representation, as well as f…
Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning
Kang Liu, Ziqi Wang, Enrique Zuazua
In federated learning (FL), a central server typically allocates training efforts to clients. However, from a market-oriented perspective, clients may independently choose their tr…
Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
Ziqian Li, Kang Liu, Lorenzo Liverani +1
In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the univ…