Language Models As Compilers: Simulating Pseudocode Execution Improves Algorithmic Reasoning in Language Models

Algorithmic reasoning refers to the ability to understand the complexpatterns behind the problem and decompose them into a sequence of reasoningsteps towards the solution. Such nature of algorithmic reasoning makes it achallenge for large language models (LLMs), even though they have demonstratedpromising performance in other reasoning tasks. Within this context, somerecent studies use programming languages (e.g., Python) to express thenecessary logic for solving a given instance/question (e.g.,Program-of-Thought) as inspired by their strict and precise syntaxes. However,it is non-trivial to write an executable code that expresses the correct logicon the fly within a single inference call. Also, the code generatedspecifically for an instance cannot be reused for others, even if they are fromthe same task and might require identical logic to solve. This paper presentsThink-and-Execute, a novel framework that decomposes the reasoning process oflanguage models into two steps. (1) In Think, we discover a task-level logicthat is shared across all instances for solving a given task and then expressthe logic with pseudocode; (2) In Execute, we further tailor the generatedpseudocode to each instance and simulate the execution of the code. Withextensive experiments on seven algorithmic reasoning tasks, we demonstrate theeffectiveness of Think-and-Execute. Our approach better improves LMs' reasoningcompared to several strong baselines performing instance-specific reasoning(e.g., CoT and PoT), suggesting the helpfulness of discovering task-levellogic. Also, we show that compared to natural language, pseudocode can betterguide the reasoning of LMs, even though they are trained to follow naturallanguage instructions.