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I will introduce the Lund jet plane, a powerful representation of radiation patterns within a jet, and adopt this framework to explore a range of recent machine learning methods of particular relevance for LHC physics. I will then discuss limitations of existing dipole showers in accurately describing emissions across multiple energy scales, and show how this can lead to bias in machine learning models. Finally, I will introduce systematic tools to assess the logarithmic accuracy of a parton shower and introduce two novel showers that can achieve next-to-leading logarithmic accuracy for a broad range of observables.