arXiv:2509.05016v1 Announce Type: cross Abstract: The $f$-divergence is a fundamental notion that measures the difference between two distributions. In this paper, we study the problem of approximating the $f$-divergence between two Ising models, which is a generalization of recent work on approximating the TV-distance. Given two Ising models $nu$ and $mu$, which are specified by their interaction matrices and external fields, the problem is to approximate the $f$-divergence $D_f(nu,|,mu)$ within an arbitrary relative error $mathrm{e}^{pm varepsilon}$. For $chi^alpha$-divergence with a constant integer $alpha$, we establish both algorithmic and hardness results. The algorithm works in a parameter regime that matches the hardness result. Our algorithm can be extended to other $f$-divergences such as $alpha$-divergence, Kullback-Leibler divergence, R'enyi divergence, Jensen-Shannon divergence, and squared Hellinger distance.
Original: https://arxiv.org/abs/2509.05016