{"id":"arxiv:2110.09485","title":"Learning in High Dimension Always Amounts to Extrapolation","date":"2021-10-18","section":"Data, training, optimization","quality":-0.296541,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/","source_url":"https://arxiv.org/abs/2110.09485","text_available":true,"authors":["Randall Balestriero","Jerome Pesenti","Yann LeCun"],"outgoing":[],"incoming":[{"source":"arxiv:2608.23875","target":"arxiv:2110.09485","evidence":"id","id":"arxiv:2608.23875","title":"AI Finds A Way","url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/afe34dd5ee58c2e9739f9651349c4c9180d95dabff51994a13339f48dfd0bb27/"}],"text_parts":[{"start":0,"end":15518,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html"},{"start":15518,"end":20285,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-2.html"}],"contents":[{"title":"Learning in High Dimension Always Amounts to Extrapolation","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"Abstract","offset":62,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"1 Introduction","offset":1029,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"Definition 1 .","offset":1560,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"Theorem 1 ( Bárány and Füredi, (1988) ) .","offset":4689,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"2 Interpolation is Doomed by the Curse of Dimensionality","offset":5340,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"2.1 The Role of the Intrinsic, Ambient and Convex Hull Dimensions","offset":6124,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"2.2 Real Datasets and Embeddings are no Exception","offset":8167,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"3 Theoretical Quantification of Interpolation Probabilities","offset":14130,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"Definition 2 (Convex position problem) .","offset":14893,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"Theorem 2 ( Valtr, (1995) ; Valtr, (1996) ) .","offset":15464,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-1.html#text"},{"title":"Theorem 3 ( Buchta, (1986) ) .","offset":16274,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-2.html#text"},{"title":"Theorem 4 ( Kabluchko and Zaporozhets, (2020) ) .","offset":17280,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-2.html#text"},{"title":"4 Conclusion","offset":18861,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/part-2.html#text"}],"text_code_points":20285,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/589d10ae90bda37ab0288fb5eadf87b368c249900944a0fe8b21a2f9bb267c01/source.md"}