The performance of modern language models (LMs) has been improved by chain-of-thought (CoT) reasoning, i.e., the process of generating intermediate results that guide the model towards a final answer. A possible explanation for this improvement is that CoT reasoning extends an LM's computational power, as RNNs and transformers with additional scratch space are known to be Turing complete. Comparing LMs to Turing machines, however, introduces a category error - Turing machines decide language membership, whereas LMs define distributions over strings. To bridge this gap, we formalize CoT reasoning in a probabilistic setting. We present several results on the representational capacity of recurrent and transformer LMs with CoT reasoning, showing that they can represent the same family of distributions over strings as probabilistic Turing machines.

翻译：现代语言模型（LM）的性能通过思维链（CoT）推理得到了提升，即生成中间结果以引导模型得出最终答案的过程。这种改进的一个可能解释是，CoT推理扩展了语言模型的计算能力，因为已知配备额外暂存空间的循环神经网络和Transformer模型具有图灵完备性。然而，将语言模型与图灵机进行类比会引入范畴错误——图灵机判定语言成员资格，而语言模型定义字符串上的概率分布。为弥合这一差距，我们在概率框架下形式化CoT推理。针对具备CoT推理能力的循环及Transformer语言模型，我们提出了若干关于其表征能力的结果，证明它们能够表示与概率图灵机相同的字符串分布族。