Many prompt engineering techniques have been successful in practice, even when optimizing over a large prompt space with with a small amount of task-specific data. Recent work has partially explained this success by showing generalization bounds which apply PAC-Bayes theory to the discrete prompt space, but they are non-vacuous only in data-rich scenarios. We argue that such widespread success can be more fully explained through more carefully considering data- or distribution-dependent perplexity, which acts as an effective prior and steers the optimization towards prompts that are more ``natural'' for the task at hand. We derive novel generalization bounds that are non-vacuous for data-scarce prompt optimization via more useful priors, formally analyzing how perplexity regularization tightens these bounds by limiting exploration. Empirically, we explore both the bounds' effectiveness and the practical benefits of perplexity regularization in improving prompt generalization.

翻译：许多提示工程技术在实践中取得了成功，即使是在使用少量任务特定数据优化大规模提示空间的情况下。近期研究通过将PAC-Bayes理论应用于离散提示空间推导泛化边界，部分解释了这种成功现象，但这些边界仅在数据充足场景下具有非平凡性。我们认为，通过更细致地考虑数据或分布相关的困惑度——其作为有效先验引导优化过程趋向对当前任务更"自然"的提示，可以更完整地解释这种广泛存在的成功现象。我们推导出通过更具实用性的先验实现数据稀缺场景下提示优化的非平凡泛化边界，并形式化分析了困惑度正则化如何通过限制探索空间来收紧这些边界。在实证研究中，我们同时探究了边界的有效性以及困惑度正则化在提升提示泛化能力方面的实际优势。