9 papers
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…
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-…
A PDE Perspective on Generative Diffusion Models
Kang Liu, Enrique Zuazua
Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success,…
Exact Dual Geometry of SOC-ICNN Value Functions
Kang Liu, Jianchen Hu, Wei Peng
Input Convex Neural Networks (ICNNs) are commonly used in a two-stage manner: one first trains a convex network and then minimizes it over its input in a downstream inference probl…
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…
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…