Think, But Don't Overthink: Reproducing Recursive Language Models

LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet existing RLMs depend on an open-ended read-eval-print loop (REPL) in which the model generates arbitrary control code, making execution difficult to verify, predict, and analyse. We introduce $λ$-RLM, a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in $λ$-calculus. It executes a compact library of pre-verified combinators and uses neural inference only on bounded leaf subproblems, turning recursive reasoning into a structured functional program with explicit control flow. We show that $λ$-RLM admits formal guarantees absent from standard RLMs, including termination, closed-form cost bounds, controlled accuracy scaling with recursion depth, and an optimal partition rule under a simple cost model. Empirically, across four long-context reasoning tasks and nine base models, $λ$-RLM outperforms standard RLM in 29 of 36 model-task comparisons, improves average accuracy by up to +21.9 points across model tiers, and reduces latency by up to 4.1x. These results show that typed symbolic control yields a more reliable and efficient foundation for long-context reasoning than open-ended recursive code generation. The complete implementation of $λ$-RLM, is open-sourced for the community at: https://github.com/lambda-calculus-LLM/lambda-RLM.

Long context reasoning in large language models (LLMs) is usually constrained by the fact that a single inference trajectory has to simultaneously explore the context, store intermediate state, verify evidence, and produce the final answer. This becomes particularly difficult in tasks that require extraction, counting, ordering, or multi-hop reasoning, where an early mistake can propagate until the final response. In this work, we propose Chained Recursive Language Models (Chained RLM), an inference-time architecture, in which the same underlying model is called repeatedly as a sequence of fresh reasoning roots. Each root receives the original problem and context, but does not inherit the full conversational history. Instead, it receives a compact plain-text summary, a plain-text blackboard, and some durable task-specific artifacts written by predecessor roots. The motivation is to manage the context by chopping into partial tasks rather than one large inference response; in each staged computation, intermediate artifacts can be inspected, corrected, and extended by a later fresh inference by the same model. We describe the system model, handoff mechanism, artifact workspace, and evaluation protocol for this system. We study when fresh-context artifact continuation gives a measurable gain in accuracy over direct LLM answering even with recursive tool-calling.

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 test two settings: fine-tuning a pretrained base model for recursive SAT solving, and training a small model from scratch on Go traces generated by exact game-tree search. Both show improved long-horizon accuracy with small active contexts.