{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Daily Paper Cast","title":"The $\\mathbf{Y}$-Combinator for LLMs: Solving Long-Context Rot with $λ$-Calculus","html":"<iframe width=\"100%\" height=\"180\" frameborder=\"no\" scrolling=\"no\" seamless src=\"https://share.transistor.fm/e/78d7908d\"></iframe>","width":"100%","height":180,"duration":1568,"description":"\n            🤗 Upvotes: 25 | cs.LG, cs.AI\n\n            Authors:\n            Amartya Roy, Rasul Tutunov, Xiaotong Ji, Matthieu Zimmer, Haitham Bou-Ammar\n\n            Title:\n            The $\\mathbf{Y}$-Combinator for LLMs: Solving Long-Context Rot with $λ$-Calculus\n\n            Arxiv:\n            http://arxiv.org/abs/2603.20105v1\n\n            Abstract:\n            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.\n            ","thumbnail_url":"https://img.transistorcdn.com/8lOVNnuwhrA3rxrDMv7Osu4j_t1-jORooO6NfGcQhcw/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS81Zjg1/YzRhODczMDU4MmE4/OGMwN2FiNDlmYzI2/MDliMi5qcGVn.webp","thumbnail_width":300,"thumbnail_height":300}