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 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.

翻译：现代语言模型的推理能力受限于有界上下文，这一固有约束构成了长程推理的根本障碍。我们提出递归是克服此障碍的核心原则，并构建递归模型作为其最小化实现——该模型可通过递归调用自身在隔离上下文中解决子任务。我们证明任何可计算问题都存在递归分解，其中每个子任务所需的活跃上下文规模相对于标准自回归模型呈指数级缩减；这严格超越了所有局限于单一序列的上下文管理方法（如摘要技术）。我们进一步将框架推广至具有任意上下文处理与控制流的现代智能体系统，并证明递归模型在此更广泛的类别中能够达到最优效能。实验方面，我们训练了一个30亿参数的递归推理模型，并在需要长程组合搜索的布尔可满足性问题中对其评估，其表现显著超越了前沿大语言模型。