{"id":"arxiv:2507.01098","title":"Proof of a perfect platonic representation hypothesis","date":"2025-07-01","section":"Representation alignment","quality":-0.084344,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/","source_url":"https://arxiv.org/abs/2507.01098","text_available":true,"authors":["Liu Ziyin","Isaac Chuang"],"outgoing":[{"source":"arxiv:2507.01098","target":"arxiv:2405.07987","evidence":"id","id":"arxiv:2405.07987","title":"The Platonic Representation 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hypothesis","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"Abstract","offset":57,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"1 Introduction","offset":1308,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"2 Problem 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.","offset":7602,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"Model.","offset":9692,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"Data and loss function.","offset":11357,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"Entropic loss due to SGD training.","offset":14158,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-1.html#text"},{"title":"Main result.","offset":16132,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-2.html#text"},{"title":"Theorem 1 .","offset":16211,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-2.html#text"},{"title":"3 Most global minima are not platonic","offset":18584,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-2.html#text"},{"title":"4 Proof","offset":20305,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-2.html#text"},{"title":"Remark .","offset":35467,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-3.html#text"},{"title":"5 What breaks the perfect plato?","offset":37677,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-3.html#text"},{"title":"Weight Decay Breaks PRH.","offset":38531,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-3.html#text"},{"title":"Gradient Flow Breaks PRH.","offset":40546,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-3.html#text"},{"title":"Label Transformations Breaks PRH.","offset":42220,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-3.html#text"},{"title":"Convergence to Saddle or Local Minima Breaks the PRH.","offset":44558,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"Data Discrepancy / Heterogeneity Breaks the PRH.","offset":45051,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"Edge of Stability (EOS) breaks PRH.","offset":45572,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"6 Discussion","offset":47798,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"Cause of the Platonic Representation Hypothesis.","offset":48171,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"Imperfect Platonic Representation Hypothesis.","offset":49075,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"Emergent Invariances in Learning Algorithms.","offset":50027,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/39afe7519b574380221abb205b8d481666b312a8b366e8145fe64c41caad5c32/part-4.html#text"},{"title":"Universal Phenomena and Unified 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