通过设计力场构建新型生成模型，提升得分匹配与生成质量。
Hamiltonian Score Matching and Generative Flows
- 用哈密顿轨迹增强数据，实现新型得分匹配方法
- 提出哈密顿生成流，涵盖扩散模型等主流方法
- 引入振荡型力场，拓展生成模型设计空间
经典哈密顿力学在机器学习中常以哈密顿蒙特卡洛形式用于预设力场的问题。本文探索主动设计哈密顿微分方程力场的潜力，提出哈密顿速度预测器（HVPs）作为得分匹配与生成模型的工具。我们构建了两项创新：哈密顿得分匹配（HSM），通过哈密顿轨迹扩充数据来估计得分函数；以及哈密顿生成流（HGFs），一种新生成模型，包含零力场时的扩散模型与流匹配模型。通过引入受简谐振子启发的振荡型HGFs，展示了力场设计空间的扩展。实验验证了HSM作为新型得分匹配度量的理论洞察，并表明HGFs可媲美领先生成建模技术。
原文摘要 · Abstract (English)
Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this work, we explore the potential of deliberately designing force fields for Hamiltonian ODEs, introducing Hamiltonian velocity predictors (HVPs) as a tool for score matching and generative models. We present two innovations constructed with HVPs: Hamiltonian Score Matching (HSM), which estimates score functions by augmenting data via Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments validate our theoretical insights about HSM as a novel score matching metric and demonstrate that HGFs rival leading generative modeling techniques.
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