Recent work has shown that renormalisation group theory is a useful framework with which to describe the process of pruning neural networks via iterative magnitude pruning. This report formally describes the link between RG theory and IMP and extends previous results around the Lottery Ticket Hypothesis and Elastic Lottery Hypothesis to Hamiltonian Neural Networks for solving differential equations. We find lottery tickets for two Hamiltonian Neural Networks and demonstrate transferability between the two systems, with accuracy being dependent on integration times. The universality of the two systems is then analysed using tools from an RG perspective.

翻译：近期研究表明，重正化群理论为通过迭代幅度剪枝进行神经网络剪枝过程提供了有用框架。本报告正式描述了重正化群理论与迭代幅度剪枝之间的联系，并将先前关于彩票假说和弹性彩票假说的结果推广至用于求解微分方程的哈密顿神经网络。我们在两个哈密顿神经网络中找到了中奖彩票，并证明了这两个系统之间的可迁移性，其准确性依赖于积分时间。随后，从重正化群视角利用相关工具分析了这两个系统的普适性。