{"id":"arxiv:2605.12466","title":"Solve the Loop: Attractor Models for Language and Reasoning","date":"2026-05-12","section":"Reasoning and the \"physics\" of language models","quality":null,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/","source_url":"https://arxiv.org/abs/2605.12466","text_available":true,"authors":["Jacob Fein-Ashley","Paria Rashidinejad"],"outgoing":[{"source":"arxiv:2605.12466","target":"arxiv:1807.03819","evidence":"id","id":"arxiv:1807.03819","title":"Universal Transformers","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d843516d980c3404cb622a2a490edb535a3afe27a85a980335a54b5fcd2220a/"},{"source":"arxiv:2605.12466","target":"arxiv:2407.21783","evidence":"title","id":"arxiv:2407.21783","title":"The Llama 3 Herd of Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/de3cebb4c28bc5d41a843279f219dca14476284991ea5c7c0aeab7068a40e306/"},{"source":"arxiv:2605.12466","target":"arxiv:2412.06769","evidence":"id","id":"arxiv:2412.06769","title":"Training Large Language Models to Reason in a Continuous Latent Space","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/68c71dc1a042dedd5e3c4d9c1ad32c9d046fd31b8dc79080bd6dff1c9800abc7/"},{"source":"arxiv:2605.12466","target":"arxiv:2502.05171","evidence":"id","id":"arxiv:2502.05171","title":"Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/24a6ab865777290627cecebd3f06ea3daef01622f102d32a95f7fb2a5a42880f/"},{"source":"arxiv:2605.12466","target":"arxiv:2506.08007","evidence":"title","id":"arxiv:2506.08007","title":"Reinforcement Pre-Training","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/a5ae77d4a2dcd6843e856083ecc6c30a72563e6896503d6efdfae117b8b007e6/"},{"source":"arxiv:2605.12466","target":"arxiv:2506.21734","evidence":"id","id":"arxiv:2506.21734","title":"Hierarchical Reasoning Model","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/3604312101ff09ab9903e7d6a32c7b2b8a9a7ece6a9d145d04ea01c9d13ffa3a/"},{"source":"arxiv:2605.12466","target":"arxiv:2507.10524","evidence":"id","id":"arxiv:2507.10524","title":"Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/7b25702c35f07446cea97d6a98afc489c8fdda54560c05fbeb1b3b139a9da622/"},{"source":"arxiv:2605.12466","target":"arxiv:2509.20317","evidence":"id","id":"arxiv:2509.20317","title":"SIM-CoT: Supervised Implicit Chain-of-Thought","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/72b64dd6a30c71d99920cafabbb2c909d03febab8991eeaf3c091b16cb7ed348/"},{"source":"arxiv:2605.12466","target":"arxiv:2509.25239","evidence":"id","id":"arxiv:2509.25239","title":"A Formal Comparison Between Chain of Thought and Latent Thought","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/8399816be05fff6a7002f5c3439ec43ffe7b468424759b4cc70f5efc7739ea9e/"},{"source":"arxiv:2605.12466","target":"arxiv:2510.04871","evidence":"id","id":"arxiv:2510.04871","title":"Less is More: Recursive Reasoning with Tiny Networks","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/4345eebe9dc7e67f82617896772f55f0970971516995c1688b6812f9ebf054f6/"},{"source":"arxiv:2605.12466","target":"arxiv:2604.09168","evidence":"id","id":"arxiv:2604.09168","title":"ELT: Elastic Looped Transformers for Visual Generation","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/63d4e5f1a267b96ed4474fa233f7d3bb2171aae949c0139db37b58b4e45eca47/"},{"source":"arxiv:2605.12466","target":"arxiv:2604.11791","evidence":"id","id":"arxiv:2604.11791","title":"A Mechanistic Analysis of Looped Reasoning Language Models","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/ae8c682d5708c6c47d65c4eb540dd5bccb877c5e332852765507128d6d1b985d/"},{"source":"arxiv:2605.12466","target":"arxiv:2604.21999","evidence":"id","id":"arxiv:2604.21999","title":"Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/"}],"incoming":[{"source":"arxiv:2606.18206","target":"arxiv:2605.12466","evidence":"title","id":"arxiv:2606.18206","title":"Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/37ea2d83a92ece4ab3ba4434af71f291d1fdc5040676f75110210f40aad3b81a/"},{"source":"arxiv:2606.29150","target":"arxiv:2605.12466","evidence":"id","id":"arxiv:2606.29150","title":"Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/8be1801f0f562711039ced2b42f324434c6ab829f544b8d736bc85405b64021b/"}],"text_parts":[{"start":0,"end":15912,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html"},{"start":15912,"end":31096,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html"},{"start":31096,"end":46518,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html"},{"start":46518,"end":56626,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html"}],"contents":[{"title":"Solve the Loop: Attractor Models for Language and Reasoning","offset":105,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"Abstract","offset":168,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"1 Introduction","offset":2071,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"1.1 Contributions","offset":5611,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"2 Background: Looped Architectures","offset":10089,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"3 Solve the Loop with Attractor Models","offset":12461,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"3.1 Attractor Model: Backbone and Attractor Modules","offset":13936,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-1.html#text"},{"title":"3.2 Training and Inference of Attractor Models","offset":18834,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html#text"},{"title":"3.3 Equilibrium Internalization and Stability in Attractor Models","offset":23363,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html#text"},{"title":"4 Experiments","offset":25083,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html#text"},{"title":"4.1 Attractor Models Improve Large-Scale Language Modeling","offset":25533,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html#text"},{"title":"4.2 Attractor Models Lead to Significant Gains in Hard Reasoning Tasks","offset":28137,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html#text"},{"title":"4.3 Equilibrium Internalization and Test-Time Behavior","offset":31036,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-2.html#text"},{"title":"4.4 Ablations","offset":33649,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"5 Conclusion and Future Work","offset":38124,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"Appendix A Related Work","offset":39101,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"Appendix B Theory of Looped and Attractor Models","offset":43718,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"B.1 Well-posedness and the implicit gradient","offset":43771,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"Assumption 1 (Local contraction) .","offset":44525,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"Theorem 1 (Well-posedness and implicit gradient) .","offset":45247,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"Proof.","offset":46281,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-3.html#text"},{"title":"B.2 Looped language models are fixed-point iterators","offset":48310,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"Corollary 1 (LoopLM as a truncated approximation) .","offset":48892,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"Proof.","offset":49386,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"B.3 Where looped language models fall short","offset":50607,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"B.3.1 Attractor Models","offset":50656,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"B.3.2 Standard looped LMs","offset":52117,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"B.3.3 Implicit-Gradient Barrier","offset":52756,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"B.3.4 Interpretation","offset":54115,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"Appendix C Hyperparamter and Experimental Settings","offset":55109,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"},{"title":"Instructions for reporting errors","offset":55662,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/part-4.html#text"}],"text_code_points":56626,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/source.md"}