Verbalized Algorithms: Classical Algorithms are All You Need (Mostly)

Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we should not treat them as general-purpose reasoners, and as an alternative, we propose a paradigm we call \emph{verbalized algorithms} (VAs), which combines LLMs and various algorithms with established guarantees. Instead of betting on LLM's ability to solve a reasoning task, VAs limit their scope by decomposing the task down to simple elementary operations on strings that they can answer reliably. For example, sorting a list of natural language strings could be done by using an LLM as a binary comparison oracle in a parallel or approximate sorting algorithm. We push the accuracy-runtime Pareto front with \emph{verbalized maximum}, \emph{sorting}, \emph{clustering}, and \emph{submodular maximization}, for numerical reasoning, topic clustering, Wi-Fi access point optimization, and multi-hop Q\&A RAG task. These results suggest improving LLM-based reasoning through standard algorithmic analysis is a feasible and better grounded research direction.