论文标题
Boltzmann分布的变形
Deformations of Boltzmann Distributions
论文作者
论文摘要
考虑Boltzmann分布的一个参数家族$ P_T（X）= \ TFRAC {1} {Z_T} E^{ - S_T（X）} $。这项工作研究了从$ p_ {t_0} $采样的问题，首先从$ p_ {t_1} $进行采样，然后应用转换$ψ_{t_1}^{t_0} $，以便转换后的样本遵循$ p_ {t_0} $。我们得出了与$ψ$的方程式和不均衡的日志样本$ s_t $的相应家族。通过将其定义的动作$ s_0 $扩展到一个$ s_t $的家族并找到$τ$，因此在学习Boltzmann分布$ P_T $中，与学习$ p_0 $相比，在学习Boltzmann分布$ P_0 $方面的表现更好。
Consider a one-parameter family of Boltzmann distributions $p_t(x) = \tfrac{1}{Z_t}e^{-S_t(x)}$. This work studies the problem of sampling from $p_{t_0}$ by first sampling from $p_{t_1}$ and then applying a transformation $Ψ_{t_1}^{t_0}$ so that the transformed samples follow $p_{t_0}$. We derive an equation relating $Ψ$ and the corresponding family of unnormalized log-likelihoods $S_t$. The utility of this idea is demonstrated on the $ϕ^4$ lattice field theory by extending its defining action $S_0$ to a family of actions $S_t$ and finding a $τ$ such that normalizing flows perform better at learning the Boltzmann distribution $p_τ$ than at learning $p_0$.
