Least-to-most Prompting Enables Complex Reasoning In Large Language Models

“However, chain-of-thought prompting has a key limitation—it often performs poorly on tasks that require generalization of solving problems harder than the demonstration examples, such as compositional generalization (Lake & Baroni, 2018; Keysers et al., 2020). To tackle such easy-to-hard generalization issues, we propose least-to-most prompting. It consists of two stages: first decomposing a complex problem into a list of easier subproblems, and then sequentially solving these subproblems, whereby solving a given subproblem is facilitated by the answers to previously solved subproblems. Both stages are implemented by few-shot prompting, so that there is no training or finetuning in either stage. An example usage of least-to-most prompting is illustrated in Figure 1. The term least-to-most prompting is borrowed from educational psychology (Libby et al., 2008), where it is used to denote the technique of using a progressive sequence of prompts to help a student to learn a new skill. Here we apply this technique for teaching humans to teach language models. Empirical results on symbolic manipulation, compositional generalization, and math reasoning show that least-to-most prompting can indeed generalize to problems harder than those demonstrated.

Least-to-most prompting teaches language models how to solve a complex problem by decomposing it to a series of simpler subproblems. It consists of two sequential stages: 1. Decomposition. The prompt in this stage contains constant examples that demonstrate the decomposition, followed by the specific question to be decomposed. 2. Subproblem solving. The prompt in this stage consists of three parts:

(1) constant examples demonstrating how subproblems are solved;

(2) a potentially empty list of previously answered subquestions and generated solutions, and (3) the question to be answered next.

In the example shown in Figure 1, the language model is first asked to decompose the original problem into subproblems. The prompt that is passed to the model consists of examples that illustrate how to decompose complex problems (which are not shown in the figure), followed by the specific problem to be decomposed (as shown in the figure). The language model figures out that the original problem can be solved via solving an intermediate problem “How long does each trip take?”.

In the next phase, we ask the language model to sequentially solve the subproblems from the problem decomposition stage. The original problem is appended as the final subproblem. The solving starts from passing to the language model a prompt that consists of examples that illustrate how problems are solved (not shown in the figure), followed by the first subproblem “How long does each trip take?”. We then take the answer generated by the language model (“... each trip takes 5 minutes.”) and construct the next prompt by appending the generated answer to the previous prompt, followed by the next subproblem, which happens to be the original problem in this example. The new prompt is then passed back to the language model, which returns the final answer.

Least-to-most prompting can be combined with other prompting techniques like chain-of-thought (Wei et al., 2022) and self-consistency (Wang et al., 2022b), but does not need to be. Also, for some tasks, the two stages in least-to-most prompting can be merged to form a single-pass prompt.”