{"id":"arxiv:2604.21999","title":"Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning","date":"2026-04-23","section":"Reasoning and the \"physics\" of language models","quality":null,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/","source_url":"https://arxiv.org/abs/2604.21999","text_available":true,"authors":["Grigory Sapunov"],"outgoing":[{"source":"arxiv:2604.21999","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:2604.21999","target":"arxiv:2404.07143","evidence":"id","id":"arxiv:2404.07143","title":"Leave No Context Behind: Efficient Infinite Context Transformers with Infini-attention","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/fcdbb3ceff27039e0eeeeac187ebf2570e2dc8b6f58ed5ee278f4259e88cfab1/"},{"source":"arxiv:2604.21999","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:2604.21999","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:2604.21999","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:2604.21999","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:2604.21999","target":"arxiv:2512.14693","evidence":"id","id":"arxiv:2512.14693","title":"Universal Reasoning Model","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/fcb1a389a132d64ca93fac5551d8f8b653c5e093908cb515e2a2d901524941a7/"}],"incoming":[{"source":"arxiv:2605.12466","target":"arxiv:2604.21999","evidence":"id","id":"arxiv:2605.12466","title":"Solve the Loop: Attractor Models for Language and Reasoning","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/eb46f81cd5718eb6b9256c583cf9dd2e97b793b4d14337e487c16285f96e2b9a/"}],"text_parts":[{"start":0,"end":15798,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html"},{"start":15798,"end":31182,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html"},{"start":31182,"end":44830,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html"}],"contents":[{"title":"Universal Transformers Need Memory: Depth-State Trade-offs in Adaptive Recursive Reasoning","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"Abstract","offset":94,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"1 Introduction","offset":1680,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"2 Architecture","offset":4541,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"2.1 Universal Transformer with Memory Tokens","offset":4560,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"2.2 Adaptive Computation Time","offset":5502,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"2.3 Deep-Start Initialization","offset":6109,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"3 The Router Initialization Trap","offset":7411,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"3.1 Diagnosis","offset":7448,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"3.2 Deep Start Resolves the Trap","offset":8090,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"3.3 DerfNorm Is Not the Cause","offset":8371,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4 Memory Tokens for Recursive Reasoning","offset":8956,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4.1 Task and Setup","offset":9000,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4.2 Memory-Token Curve","offset":9399,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4.3 Memory-Depth Tradeoff","offset":10314,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4.4 Fixed-Depth vs ACT Processing","offset":13752,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4.5 How Memory Tokens Function: Attention Analysis","offset":14572,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"4.6 Small-Dataset Generalization","offset":15667,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-1.html#text"},{"title":"5 Making ACT Efficient","offset":16133,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"5.1 Lambda Warmup","offset":16160,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"5.2 Inference Beyond Trained Depth","offset":16573,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6 Related Work and Architectural Convergence","offset":17362,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6.1 Universal Transformers and Adaptive Computation Time","offset":17799,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6.2 Memory Tokens and Registers","offset":20094,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6.3 Recursive Reasoning on Combinatorial Benchmarks","offset":21788,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6.4 Recursive Transformers at Language-Modeling Scale","offset":25554,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6.5 Adjacent: External Memory and Adaptive Long Context","offset":31121,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-2.html#text"},{"title":"6.6 Mapping the Design Space","offset":31891,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"},{"title":"6.7 What the Convergence Suggests","offset":36678,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"},{"title":"7 Future Work","offset":39516,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"},{"title":"8 Limitations","offset":40875,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"},{"title":"9 Conclusion","offset":42120,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"},{"title":"Appendix A Puzzle Solving Visualization","offset":43822,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"},{"title":"Instructions for reporting errors","offset":43866,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/part-3.html#text"}],"text_code_points":44830,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/963f6bb396c25bff462a25854c82e7d92b77803fa60c891fadd9963cc56c8fea/source.md"}