{"paper":{"title":"Autoregressive Language Models are Secretly Energy-Based Models: Insights into the Lookahead Capabilities of Next-Token Prediction","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Autoregressive language models are equivalent to energy-based models in function space through a bijection from the chain rule of probability.","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Germain Vivier-Ardisson, Mathieu Blondel, Michael E. Sander, Tianlin Liu, Vincent Roulet","submitted_at":"2025-12-17T17:14:26Z","abstract_excerpt":"Autoregressive models (ARMs) currently constitute the dominant paradigm for large language models (LLMs). Energy-based models (EBMs) represent another class of models, which have historically been less prevalent in LLM development, yet naturally characterize the optimal policy in post-training alignment. In this paper, we provide a unified view of these two model classes. Taking the chain rule of probability as a starting point, we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entro"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The chain rule of probability directly yields the claimed bijection in function space with no additional restrictions on model capacity, training dynamics, or the form of the energy function.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Autoregressive language models are equivalent to energy-based models through a bijection that corresponds to the soft Bellman equation, explaining their lookahead capabilities despite next-token training.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Autoregressive language models are equivalent to energy-based models in function space through a bijection from the chain rule of probability.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6b47076c5be2662fa6bc21165739fa785c814ce5a6b927f9e6cdd423af4e178f"},"source":{"id":"2512.15605","kind":"arxiv","version":4},"verdict":{"id":"c18701b4-f004-403c-b076-bcad8e1ad5b9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T21:25:35.218166Z","strongest_claim":"we establish an explicit bijection between ARMs and EBMs in function space, which we show to correspond to a special case of the soft Bellman equation in maximum entropy reinforcement learning","one_line_summary":"Autoregressive language models are equivalent to energy-based models through a bijection that corresponds to the soft Bellman equation, explaining their lookahead capabilities despite next-token training.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The chain rule of probability directly yields the claimed bijection in function space with no additional restrictions on model capacity, training dynamics, or the form of the energy function.","pith_extraction_headline":"Autoregressive language models are equivalent to energy-based models in function space through a bijection from the chain rule of probability."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.15605/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"56eea985e085013488def317f330effba9b0b6efd5b0b6b965b0fd26e2503002"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}