Performance of large language models (LLMs) may vary with different prompts or instructions of even the same task. One commonly recognized factor for this phenomenon is the model's familiarity with the given prompt or instruction, which is typically estimated by its perplexity. However, finding the prompt with the lowest perplexity is challenging, given the enormous space of possible prompting phrases. In this paper, we propose monotonic paraphrasing (MonoPara), an end-to-end decoding strategy that paraphrases given prompts or instructions into their lower perplexity counterparts based on an ensemble of a paraphrase LM for prompt (or instruction) rewriting, and a target LM (i.e. the prompt or instruction executor) that constrains the generation for lower perplexity. The ensemble decoding process can efficiently paraphrase the original prompt without altering its semantic meaning, while monotonically decreasing the perplexity of each generation as calculated by the target LM. We explore in detail both greedy and search-based decoding as two alternative decoding schemes of MonoPara. Notably, MonoPara does not require any training and can monotonically lower the perplexity of the paraphrased prompt or instruction, leading to improved performance of zero-shot LM prompting as evaluated on a wide selection of tasks. In addition, MonoPara is also shown to effectively improve LMs' generalization on perturbed and unseen task instructions.

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