We propose a theoretical framework for formulating language model decoder
algorithms with dynamic programming and information theory. With dynamic
programming, we lift the design of decoder algorithms from the logit space to
the action-state value function space, and show that the decoding algorithms
are consequences of optimizing the action-state value functions. Each component
in the action-state value function space has an information theoretical
interpretation. With the lifting and interpretation, it becomes evident what
the decoder algorithm is optimized for, and hence facilitating the arbitration
of the tradeoffs in sensibleness, diversity, and attribution.

我们提出了一个理论框架，用于利用动态规划和信息论来构建语言模型解码器算法。通过动态规划，我们将解码器算法的设计从逻辑空间提升到动作 - 状态值函数空间，并展示解码算法是优化动作 - 状态值函数的结果。动作 - 状态值函数空间的每个组件都具有信息论解释。通过提升和解释，变得明显解码器算法的优化目标是什么，因此有助于在合理性、多样性和权衡中进行调节。