Recursive Models for Long-Horizon Reasoning

Modern language models reason within bounded context, an inherent constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in isolated contexts. We prove that any computable problem admits a recursive decomposition of reasoning in which each subtask requires only exponentially smaller active context than standard autoregressive models; this strictly surpasses any context management approach confined to a single sequence, such as summarization. We further generalize our framework to modern agentic systems with arbitrary context processing and control flows, and prove that recursive models can achieve optimal power within this broader class. Experimentally, we train a 3B model to reason recursively and evaluate on Boolean satisfiability, a task requiring long-horizon combinatorial search, where it significantly outperforms frontier LLMs.

Language models can only read a limited amount of text at once, which makes long reasoning tasks difficult. We study a simple recursive approach: the model can split a problem into subproblems, solve each one in a separate context, and return only the needed answer. We show that this can greatly reduce the active context needed for long computations, and train a model that uses recursion to solve challenging problems more effectively.