Recursive Models for Long-Horizon Reasoning

TL;DR

This paper introduces recursive models for long-horizon reasoning in language models, demonstrating their theoretical advantages in context management and empirical success on complex reasoning tasks.

Contribution

It proposes recursive models as a minimal approach to extend reasoning capabilities, with theoretical proofs and experimental validation showing superior long-horizon problem solving.

Findings

Recursive decomposition reduces context size exponentially.

Recursive models outperform standard LLMs on Boolean satisfiability.

Theoretical proofs establish optimal power of recursive models.

Abstract

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.