Top-H Decoding: Adapting the Creativity and Coherence with Bounded Entropy in Text Generation

Large language models (LLMs), despite their impressive performance across a wide range of tasks, often struggle to balance two competing objectives in open-ended text generation: fostering diversity and creativity while preserving logical coherence. Existing truncated sampling techniques, including temperature scaling, top-$p$ (nucleus) sampling, and min-$p$ sampling, aim to manage this trade-off. However, they exhibit limitations, particularly in the effective incorporation of the confidence of the model into the corresponding sampling strategy. For example, min-$p$ sampling relies on a single top token as a heuristic for confidence, eventually underutilizing the information of the probability distribution. Toward effective incorporation of the confidence of the model, in this paper, we present top-H decoding. We first establish the theoretical foundation of the interplay between creativity and coherence in truncated sampling by formulating an entropy-constrained minimum divergence problem. We then prove this minimization problem to be equivalent to an entropy-constrained mass maximization (ECMM) problem, which is NP-hard. Finally, we present top-H decoding, a computationally efficient greedy algorithm to solve the ECMM problem. Extensive empirical evaluations demonstrate that top-H outperforms the state-of-the-art (SoTA) alternative of min-$p$ sampling by up to 25.63% on creative writing benchmarks, while maintaining robustness on question-answering datasets such as GPQA, GSM8K, and MT-Bench. Additionally, an LLM-as-judge evaluation confirms that top-H indeed produces coherent outputs even at higher temperatures, where creativity is especially critical. In summary, top-H advances SoTA in open-ended text generation and can be easily integrated into creative writing applications. The code is available at https://github.com/ErfanBaghaei/Top-H-Decoding.