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"models", "without", "incurring", "superfluous", "computing", "and", "energy", "costs", ".", "It", "is", "difficult", "to", "provide", "clear", "-", "cut", "guidelines", "for", "ML", "researchers", "to", "follow", "in", "order", "to", "reduce", "the", "carbon", "emissions", ",", "or", "specific", "benchmarks", "for", "the", "training", "time", "that", "a", "given", "model", "or", "task", "warrants", ".", "Nonetheless", ",", "we", "think", "that", "there", "are", "certain", "best", "practices", "and", "actionable", "items", "that", "can", "be", "adopted", "by", "our", "community", "to", "reduce", "environmental", "impact", "of", "the", "ML", "domain", ".", "We", "present", "some", "of", "these", ",", "along", "with", "our", "ML", "emissions", "calculator", ",", "in", "the", "current", "section", ".", "Quantify", "Your", "Emissions", "Being", "informed", "regarding", "the", "factors", "that", "impact", "the", "quantity", "of", "carbon", "emissions", "produced", "by", "ML", "research", "is", "the", "first", "step", "to", "making", "positive", "changes", ".", "It", "is", "for", "this", "reason", "that", "we", "created", "our", "ML", "Emissions", "Calculator", ".", "This", "tool", ",", "currently", "in", "its", "alpha", "version", ",", "takes", "as", "input", "the", "details", "regarding", "the", "training", "of", "an", "ML", "model", ":", "the", "geographical", "zone", "of", "the", "server", ",", "the", "type", "of", "GPU", ",", "and", "the", "training", "time", ",", "and", "gives", "as", "output", "the", "approximate", "amount", "of", "CO", "2", "eq", "produced", ".", "We", "collected", "publicly", "available", "data", "for", "the", "4", "main", "variables", "of", "this", "computation", ":", "(", "i", ")", "the", "energy", "consumption", "of", "hardware", "(", "see", "\"", "Choose", "More", "Efficient", "Hardware", "\"", "below", ")", ",", "(", "ii", ")", "the", "location", "of", "providers", "'", "regions", "of", "compute", "-", "which", "we", "assumed", "to", "be", 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"solar", "and", "wind", "farms", "directly", "on", "local", "grids", "through", "RECs", "[", "13", "]", ".", "Microsoft", "Azure", "is", "also", "certified", "carbon", "neutral", "and", "44", "%", "of", "its", "electricity", "consumption", "directly", "comes", "from", "renewable", "energy", ",", "according", "to", "a", "2016", "estimate", "[", "14", "]", ".", "Finally", ",", "to", "the", "best", "of", "our", "knowledge", ",", "while", "not", "yet", "100", "%", "carbon", "neutral", "on", "an", "organizational", "level", ",", "Amazon", "Web", "Services", "is", "also", "funding", "renewable", "energy", "projects", "and", "some", "of", "their", "data", "centers", "are", "powered", "by", "renewable", "energy", "[", "15", "]", ".", "Another", "major", "energy", "consumption", "factor", "of", "server", "installations", "is", "the", "power", "usage", "effectiveness", "(", "PUE", ")", "of", "the", "centers", "where", "the", "GPUs", "are", "hosted", ",", "which", "represents", "the", 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"carbon", "neutrality", "and", "have", "a", "significant", "impact", "at", "scale", ".", "Select", "Data", "Center", "Location", "While", "many", "cloud", "providers", "are", "carbon", "neutral", ",", "some", "of", "their", "data", "centers", "may", "still", "be", "carbon", "intensive", "due", "to", "the", "local", "grid", "that", "they", "are", "connected", "to", ",", "whereas", "others", "will", "be", "low", "carbon", "and", "powered", "solely", "by", "renewable", "energy", "sources", ".", "Hence", ",", "selecting", "the", "data", "center", "location", "where", "an", "algorithm", "will", "be", "trained", "has", "a", "large", "impact", "on", "its", "direct", "carbon", "emissions", ".", "This", "choice", "can", "be", "achieved", "by", "consciously", "selecting", "the", "server", "location", "before", "dispatching", "your", "jobs", ".", "As", "we", "illustrated", "in", "previous", "sections", ",", "this", "single", "choice", "can", "make", "the", "direct", "emissions", "of", "an", 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0.04449769854545593, "NIL"], [1926, 1928, 0.04261617735028267, "NIL"], [1912, 1913, 0.04148506000638008, "NIL"], [1907, 1907, 0.04055403172969818, "NIL"], [1901, 1905, 0.040250133723020554, "NIL"]], [[1937, 1938, 0.6382697224617004, "Method"], [1956, 1956, 0.19192460179328918, "NIL"], [1935, 1936, 0.1852230578660965, "NIL"], [1936, 1936, 0.1659637838602066, "NIL"], [1934, 1936, 0.15027400851249695, "NIL"], [1956, 1957, 0.08974511176347733, "NIL"], [1935, 1938, 0.08376612514257431, "NIL"], [1936, 1938, 0.08329813182353973, "NIL"], [1949, 1949, 0.08178785443305969, "NIL"], [1934, 1938, 0.07951299101114273, "NIL"], [1937, 1937, 0.07143012434244156, "NIL"], [1949, 1951, 0.06516484916210175, "NIL"], [1949, 1952, 0.06374331563711166, "NIL"], [1959, 1960, 0.059677183628082275, "NIL"], [1934, 1934, 0.058957234025001526, "NIL"], [1938, 1938, 0.05868959426879883, "NIL"], [1954, 1956, 0.04768514260649681, "NIL"], [1949, 1950, 0.041795749217271805, "NIL"], [1934, 1935, 0.03901427611708641, "NIL"], [1947, 1949, 0.03884324058890343, "NIL"], [1950, 1951, 0.038770027458667755, "NIL"], [1954, 1957, 0.03822219371795654, "NIL"], [1944, 1944, 0.03224360570311546, "NIL"], [1956, 1960, 0.0314590223133564, "NIL"], [1959, 1959, 0.030854016542434692, "NIL"], [1935, 1935, 0.02941921539604664, "NIL"], [1957, 1957, 0.028554093092679977, "NIL"], [1936, 1937, 0.02776562049984932, "NIL"], [1951, 1951, 0.027276882901787758, "NIL"], [1947, 1951, 0.025542302057147026, "NIL"], [1934, 1937, 0.02478746324777603, "NIL"], [1950, 1952, 0.0247554499655962, "NIL"], [1949, 1957, 0.024272765964269638, "NIL"], [1950, 1950, 0.023148994892835617, "NIL"], [1956, 1959, 0.020626410841941833, "NIL"], [1941, 1941, 0.020026126876473427, "NIL"], [1935, 1937, 0.019972091540694237, "NIL"], [1949, 1956, 0.019795062020421028, "NIL"], [1943, 1944, 0.018508771434426308, "NIL"], [1949, 1960, 0.018466340377926826, "NIL"], [1947, 1947, 0.01845310814678669, "NIL"], [1951, 1952, 0.016501372680068016, "NIL"], [1946, 1947, 0.01628836616873741, "NIL"], [1949, 1959, 0.015864966437220573, "NIL"], [1949, 1954, 0.015293581411242485, "NIL"], [1947, 1948, 0.01506594754755497, "NIL"], [1952, 1952, 0.014897579327225685, "NIL"], [1947, 1952, 0.013799005188047886, "NIL"], [1954, 1954, 0.013776848092675209, "NIL"], [1953, 1957, 0.012440089136362076, "NIL"], [1957, 1960, 0.012227104976773262, "NIL"], [1956, 1961, 0.012027924880385399, "NIL"], [1952, 1957, 0.011985404416918755, "NIL"], [1950, 1957, 0.011938127689063549, "NIL"], [1946, 1949, 0.011406282894313335, "NIL"], [1953, 1954, 0.011262600310146809, "NIL"], [1960, 1960, 0.011180556379258633, "NIL"], [1946, 1951, 0.011144512332975864, "NIL"], [1959, 1961, 0.010933098383247852, "NIL"], [1951, 1957, 0.01059831865131855, "NIL"]], [[1995, 1995, 0.9392895698547363, "ReferenceLink"], [1991, 1991, 0.9285748600959778, "ReferenceLink"], [1993, 1993, 0.9278424978256226, "ReferenceLink"], [1969, 1970, 0.682318925857544, "Method"], [1988, 1989, 0.6222845315933228, "Method"], [1978, 1980, 0.1615835726261139, "NIL"], [1987, 1989, 0.15664042532444, "NIL"], [1991, 1993, 0.15518304705619812, "NIL"], [1969, 1974, 0.12870198488235474, "NIL"], [1969, 1969, 0.1141422763466835, "NIL"], [2000, 2001, 0.10542498528957367, "NIL"], [1973, 1973, 0.10483354330062866, "NIL"], [1969, 1975, 0.0917278602719307, "NIL"], [1993, 1995, 0.08082679659128189, "NIL"], [1986, 1989, 0.07936163991689682, "NIL"], [1989, 1989, 0.06972434371709824, "NIL"], [1999, 2001, 0.06545135378837585, "NIL"], [1988, 1996, 0.06528280675411224, "NIL"], [1988, 1988, 0.0631631463766098, "NIL"], [1973, 1974, 0.05974326282739639, "NIL"], [1968, 1970, 0.05713806301355362, "NIL"], [1979, 1980, 0.05382422357797623, "NIL"], [1978, 1981, 0.046938322484493256, "NIL"], [1969, 1976, 0.04586850851774216, "NIL"], [1980, 1980, 0.04367761313915253, "NIL"], [2000, 2000, 0.04195477068424225, "NIL"], [1970, 1970, 0.040334898978471756, "NIL"], [1964, 1964, 0.039499133825302124, "NIL"], [1991, 1995, 0.03904811292886734, "NIL"], [1973, 1975, 0.03645188361406326, "NIL"], [1995, 1996, 0.029592933133244514, "NIL"], [1971, 1974, 0.029040737077593803, "NIL"], [1999, 1999, 0.027843693271279335, "NIL"], [1976, 1976, 0.02782169170677662, "NIL"], [1970, 1974, 0.025986095890402794, "NIL"], [1999, 2000, 0.02499786950647831, "NIL"], [1968, 1974, 0.02495456114411354, "NIL"], [1998, 2001, 0.024460507556796074, "NIL"], [1999, 2002, 0.024035990238189697, "NIL"], [1987, 1987, 0.02375175803899765, "NIL"], [1978, 1978, 0.02347327396273613, "NIL"], [1980, 1981, 0.02344781905412674, "NIL"], [1988, 1991, 0.023168174549937248, "NIL"], [2000, 2002, 0.022485528141260147, "NIL"], [1969, 1973, 0.022049903869628906, "NIL"], [1962, 1962, 0.021124036982655525, "NIL"], [2001, 2001, 0.020984632894396782, "NIL"], [1987, 1988, 0.020787831395864487, "NIL"], [1987, 1996, 0.020441435277462006, "NIL"], [1979, 1981, 0.02032165229320526, "NIL"], [1984, 1989, 0.018918707966804504, "NIL"], [1985, 1989, 0.018725469708442688, "NIL"], [1990, 1996, 0.017785536125302315, "NIL"], [1998, 1999, 0.017016882076859474, "NIL"], [1975, 1976, 0.016776246950030327, "NIL"], [1986, 1987, 0.01665000431239605, "NIL"], [1968, 1975, 0.016128892078995705, "NIL"], [1984, 1984, 0.015937674790620804, "NIL"], [1981, 1981, 0.01588469371199608, "NIL"], [1978, 1979, 0.015692943707108498, "NIL"]], [[2031, 2032, 0.3928073048591614, "Method"], [2034, 2035, 0.3760152757167816, "Method"], [2006, 2007, 0.35198044776916504, "NIL"], [2013, 2013, 0.2998499572277069, "NIL"], [2038, 2041, 0.25372621417045593, "Method"], [2040, 2041, 0.16225120425224304, "NIL"], [2013, 2014, 0.1551782190799713, "NIL"], [2027, 2028, 0.10768654942512512, "NIL"], [2041, 2041, 0.08978742361068726, "NIL"], [2031, 2041, 0.07794448733329773, "NIL"], [2034, 2041, 0.07489613443613052, "NIL"], [2034, 2034, 0.06672930717468262, "NIL"], [2031, 2035, 0.06653062254190445, "NIL"], [2020, 2020, 0.06308780610561371, "NIL"], [2031, 2031, 0.059952374547719955, "NIL"], [2007, 2007, 0.056120287626981735, "NIL"], [2009, 2011, 0.05240379646420479, "NIL"], [2020, 2021, 0.05201406031847, "NIL"], [2028, 2028, 0.04543648287653923, "NIL"], [2027, 2032, 0.043724175542593, "NIL"], [2025, 2028, 0.04281039163470268, "NIL"], [2009, 2014, 0.042341168969869614, "NIL"], [2006, 2006, 0.041488081216812134, "NIL"], [2027, 2035, 0.04000147059559822, "NIL"], [2032, 2032, 0.03656868264079094, "NIL"], [2035, 2035, 0.03619508817791939, "NIL"], [2025, 2032, 0.0328267365694046, "NIL"], [2025, 2035, 0.03054097481071949, "NIL"], [2010, 2011, 0.02961084432899952, "NIL"], [2025, 2025, 0.028281347826123238, "NIL"], [2011, 2011, 0.028280701488256454, "NIL"], [2021, 2021, 0.02625691518187523, "NIL"], [2041, 2042, 0.024691229686141014, "NIL"], [2038, 2038, 0.02358805201947689, "NIL"], [2040, 2040, 0.02358333393931389, "NIL"], [2009, 2013, 0.022179385647177696, "NIL"], [2031, 2034, 0.02202684059739113, "NIL"], [2040, 2042, 0.021308433264493942, "NIL"], [2035, 2041, 0.02095712348818779, "NIL"], [2010, 2014, 0.020725440233945847, "NIL"], [2018, 2018, 0.020652834326028824, "NIL"], [2038, 2040, 0.02062864601612091, "NIL"], [2017, 2018, 0.020536178722977638, "NIL"], [2032, 2041, 0.020419009029865265, "NIL"], [2034, 2040, 0.02018383890390396, "NIL"], [2025, 2031, 0.02018374763429165, "NIL"], [2031, 2040, 0.020069070160388947, "NIL"], [2014, 2014, 0.019922275096178055, "NIL"], [2038, 2042, 0.019257070496678352, "NIL"], [2031, 2042, 0.0191606767475605, "NIL"], [2028, 2031, 0.01887160912156105, "NIL"], [2003, 2003, 0.018787607550621033, "NIL"], [2034, 2042, 0.018575748428702354, "NIL"], [2028, 2032, 0.018418148159980774, "NIL"], [2017, 2017, 0.018381744623184204, "NIL"], [2025, 2034, 0.017871949821710587, "NIL"], [2011, 2012, 0.017156515270471573, "NIL"], [2009, 2012, 0.016850996762514114, "NIL"], [2018, 2021, 0.016606543213129044, "NIL"], [2032, 2034, 0.01608232408761978, "NIL"]], [[2043, 2044, 0.34842967987060547, "NIL"], [2058, 2060, 0.31588810682296753, "NIL"], [2065, 2067, 0.2796267867088318, "NIL"], [2062, 2063, 0.18164297938346863, "NIL"], [2062, 2062, 0.12281850725412369, "NIL"], [2058, 2059, 0.10075879096984863, "NIL"], [2062, 2067, 0.09683503210544586, "NIL"], [2066, 2067, 0.08249112218618393, "NIL"], [2062, 2064, 0.07347197830677032, "NIL"], [2059, 2060, 0.07063349336385727, "NIL"], [2043, 2043, 0.059849563986063004, "NIL"], [2053, 2053, 0.05327411741018295, "NIL"], [2059, 2059, 0.050707753747701645, "NIL"], [2044, 2044, 0.04552481323480606, "NIL"], [2060, 2060, 0.04457119107246399, "NIL"], [2058, 2067, 0.03712120279669762, "NIL"], [2065, 2065, 0.030902938917279243, "NIL"], [2047, 2053, 0.030047858133912086, "NIL"], [2058, 2061, 0.029680786654353142, "NIL"], [2047, 2051, 0.02859087660908699, "NIL"], [2067, 2067, 0.028033064678311348, "NIL"], [2052, 2053, 0.027377154678106308, "NIL"], [2050, 2050, 0.02666233293712139, "NIL"], [2062, 2065, 0.026070337742567062, "NIL"], [2049, 2051, 0.025927674025297165, "NIL"], [2047, 2047, 0.025491373613476753, 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0.013161429204046726, "NIL"], [2061, 2064, 0.012564505450427532, "NIL"], [2056, 2056, 0.012108459137380123, "NIL"], [2059, 2062, 0.011630592867732048, "NIL"], [2060, 2064, 0.0115188118070364, "NIL"], [2060, 2063, 0.011107741855084896, "NIL"], [2058, 2065, 0.010421598330140114, "NIL"], [2060, 2068, 0.010232106782495975, "NIL"], [2056, 2067, 0.009972985833883286, "NIL"], [2058, 2068, 0.009866463951766491, "NIL"], [2060, 2065, 0.009317404590547085, "NIL"]], [[2088, 2092, 0.5301962494850159, "Method"], [2075, 2077, 0.3008905053138733, "NIL"], [2091, 2092, 0.22876520454883575, "NIL"], [2076, 2077, 0.1628447324037552, "NIL"], [2087, 2092, 0.15859059989452362, "NIL"], [2081, 2085, 0.09976772218942642, "NIL"], [2085, 2085, 0.09523143619298935, "NIL"], [2098, 2102, 0.0908500924706459, "NIL"], [2087, 2087, 0.08739446848630905, "NIL"], [2074, 2077, 0.08310317248106003, "NIL"], [2070, 2071, 0.08041494339704514, "NIL"], [2073, 2077, 0.07588287442922592, "NIL"], [2088, 2091, 0.06849363446235657, "NIL"], [2080, 2085, 0.0659487247467041, "NIL"], [2091, 2091, 0.06523703038692474, "NIL"], [2081, 2092, 0.06491290777921677, "NIL"], [2092, 2092, 0.06123516336083412, "NIL"], [2097, 2102, 0.05966636538505554, "NIL"], [2069, 2077, 0.05908305197954178, "NIL"], [2070, 2077, 0.057353805750608444, "NIL"], [2069, 2071, 0.05496842786669731, "NIL"], [2090, 2092, 0.0545395165681839, "NIL"], [2077, 2077, 0.05101862549781799, "NIL"], [2069, 2069, 0.046894390136003494, "NIL"], [2073, 2074, 0.04648340493440628, "NIL"], [2088, 2090, 0.04618755355477333, "NIL"], [2089, 2092, 0.04455995187163353, "NIL"], [2081, 2083, 0.042811088263988495, "NIL"], [2085, 2092, 0.04266681894659996, "NIL"], [2097, 2097, 0.042414117604494095, "NIL"], [2073, 2073, 0.042365722358226776, "NIL"], [2076, 2076, 0.03782658651471138, "NIL"], [2080, 2083, 0.03736859932541847, "NIL"], [2080, 2080, 0.03631136566400528, "NIL"], [2074, 2074, 0.03507274016737938, "NIL"], [2076, 2085, 0.03317023441195488, "NIL"], [2085, 2086, 0.03316468372941017, "NIL"], [2083, 2085, 0.032646745443344116, "NIL"], [2087, 2091, 0.03227817267179489, "NIL"], [2081, 2086, 0.030807575210928917, "NIL"], [2080, 2086, 0.030126985162496567, "NIL"], [2079, 2080, 0.029614228755235672, "NIL"], [2080, 2081, 0.02949979528784752, "NIL"], [2082, 2085, 0.029485242441296577, "NIL"], [2069, 2070, 0.029213247820734978, "NIL"], [2100, 2102, 0.028959913179278374, "NIL"], [2075, 2085, 0.028075769543647766, "NIL"], [2097, 2098, 0.027956653386354446, "NIL"], [2076, 2087, 0.02780962735414505, "NIL"], [2086, 2092, 0.027446063235402107, "NIL"], [2072, 2073, 0.02661547064781189, "NIL"], [2072, 2077, 0.02572522684931755, "NIL"], [2075, 2076, 0.025720098987221718, "NIL"], [2076, 2080, 0.025529442355036736, "NIL"], [2080, 2087, 0.025341827422380447, "NIL"], [2069, 2074, 0.025173470377922058, "NIL"], [2086, 2086, 0.024857206270098686, "NIL"], [2069, 2080, 0.024537134915590286, "NIL"], [2070, 2074, 0.0232368316501379, "NIL"], [2070, 2076, 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"0", "and", "another", "where", "it", "is", "6.", "Note", "that", "our", "syntactic", "divergence", "ignores", "lexical", "variation", ".", "Also", ",", "small", "divergence", "does", "not", "mean", "that", "a", "question", "is", "easy", "since", "there", "could", "be", "other", "candidates", "with", "similarly", "small", "divergence", ".", "We", "developed", "a", "logistic", "regression", "model", "and", "compare", "its", "accuracy", "with", "that", "of", "three", "baseline", "methods", ".", "Candidate", "answer", "generation", ".", "For", "all", "four", "methods", ",", "rather", "than", "considering", "all", "O", "(", "L", "2", ")", "spans", "as", "candidate", "answers", ",", "where", "L", "is", "the", "number", "of", "words", "in", "the", "sentence", ",", "we", "only", "use", "spans", "which", "are", "constituents", "in", "the", "constituency", "parse", "generated", "by", "Stanford", "CoreNLP", ".", "Ignoring", "punctuation", "and", "articles", ",", "we", "find", "that", "77.3", "%", "of", "the", "correct", "answers", "in", "the", "development", "set", "are", "constituents", ".", "This", "places", "an", "effective", "ceiling", "on", "the", "accuracy", "of", "our", "methods", ".", "During", "training", ",", "when", "the", "correct", "answer", "of", "an", "example", "is", "not", "a", "constituent", ",", "we", "use", "the", "shortest", "constituent", "containing", "the", "correct", "answer", "as", "the", "target", ".", "For", "each", "candidate", "answer", ",", "we", "compute", "the", "unigram", "/", "bigram", "overlap", "between", "the", "sentence", "containing", "it", "(", "excluding", "the", "candidate", "itself", ")", "and", "the", "question", ".", "We", "keep", "all", "the", "candidates", "that", "have", "the", "maximal", "overlap", ".", "Among", "these", ",", "we", "select", "the", "best", "one", "using", "the", "sliding", "-", "window", "approach", "proposed", "in", "Richardson", "et", "al", ".", "(", "2013", ")", ".", "In", "addition", "to", "the", "basic", "sliding", "window", "approach", ",", "we", "also", "implemented", "the", "distance", "-", "based", "extension", "(", "Richardson", "et", "al", ".", ",", "2013", ")", ".", "Whereas", "Richardson", "et", "al", ".", "(", "2013", ")", "used", "the", "entire", "passage", "as", "the", "context", "of", "an", "answer", ",", "we", "used", "only", "the", "sentence", "containing", "the", "candidate", "answer", "for", "efficiency", ".", "In", "our", "logistic", "regression", "model", ",", "we", "extract", "several", "types", "of", "features", "for", "each", "candidate", "answer", ".", "We", "discretize", "each", "continuous", "feature", "into", "10", "equallysized", "buckets", ",", "building", "a", "total", "of", "180", "million", "features", ",", "most", "of", "which", "are", "lexicalized", "features", "or", "dependency", "tree", "path", "features", ".", "The", "descriptions", "and", "examples", "of", "the", "features", "are", "summarized", "in", "Table", "4.", "The", "matching", "word", "and", "bigram", "frequencies", "as", "well", "as", "the", "root", "match", "features", "help", "the", "model", "pick", "the", "correct", "sentences", ".", "Length", "features", "bias", "the", "model", "towards", "picking", "common", "lengths", "and", "positions", "for", "answer", "spans", ",", "while", "span", "word", "frequencies", "bias", "the", "model", "against", "uninformative", "words", ".", "Constituent", "label", "and", "span", "POS", "tag", "features", "guide", "the", "model", "towards", "the", "correct", "answer", "types", ".", "In", "addition", "to", "these", "basic", "features", ",", "we", "resolve", "lexical", "variation", "using", "lexicalized", "features", ",", "and", "syntactic", "variation", "using", "dependency", "tree", "path", "features", ".", "The", "multiclass", "log", "-", "likelihood", "loss", "is", "optimized", "using", "AdaGrad", "with", "an", "initial", "learning", "rate", "of", "0.", "1", ".", "Each", "update", "is", "performed", "on", "the", "batch", "of", "all", "questions", "in", "a", "paragraph", "for", "efficiency", ",", "since", "they", "share", "the", "same", "candidates", ".", "L", "2", "regularization", "is", "used", ",", "with", "a", "coefficient", "of", "0.", "1", "divided", "by", "the", "number", "of", "batches", ".", "The", "model", "is", "trained", "with", "three", "passes", "over", "the", "train", "-", "Feature", "Groups", "We", "use", "two", "different", "metrics", "to", "evaluate", "model", "accuracy", ".", "Both", "metrics", "ignore", "punctuations", "and", "articles", "(", "a", ",", "an", ",", "the", ")", ".", "Exact", "match", ".", "This", "metric", "measures", "the", "percentage", "of", "predictions", "that", "match", "any", "one", "of", "the", "ground", "truth", "answers", "exactly", ".", "(", "Macro", "-", "averaged", ")", "F1", "score", ".", "This", "metric", "measures", "the", "average", "overlap", "between", "the", "prediction", "and", "ground", "truth", "answer", ".", "We", "treat", "the", "prediction", "and", "ground", "truth", "as", "bags", "of", "tokens", ",", "and", "compute", "their", "F1", ".", "We", "take", "the", "maximum", "F1", "over", "all", "of", "the", "ground", "truth", "answers", "for", "a", "given", "question", ",", "and", "then", "average", "over", "all", "of", "the", "questions", ".", "We", "assess", "human", "performance", "on", "SQuAD", "'s", "development", "and", "test", "sets", ".", "Recall", "that", "each", "of", "the", "questions", "in", "these", "sets", "has", "at", "least", "three", "answers", ".", "To", "evaluate", "human", "performance", ",", "we", "treat", "the", "second", "answer", "to", "each", "question", "as", "the", "human", "prediction", ",", "and", "keep", "the", "other", "answers", "as", "ground", "truth", "answers", ".", "The", "resulting", "human", "performance", "score", "on", "the", "test", "set", "is", "77.0", "%", "for", "the", "exact", "match", "metric", ",", "and", "86.8", "%", "for", "F1", ".", "Mismatch", "occurs", "mostly", "due", "to", "inclusion", "/", "exclusion", "of", "non", "-", "essential", "phrases", "(", "e.g.", ",", "monsoon", "trough", "versus", "movement", "of", "the", "monsoon", "trough", ")", "rather", "than", "fundamental", "disagreements", "about", "the", "answer", ".", "Table", "5", "shows", "the", "performance", "of", "our", "models", "alongside", "human", "performance", "on", "the", "v1.0", "of", "development", "and", "test", "sets", ".", "The", "logistic", "regression", "model", "significantly", "outperforms", "the", "baselines", ",", "but", "underperforms", "humans", ".", "We", "note", "that", "the", "model", "is", "able", "to", "select", "the", "sentence", "containing", "the", "answer", "correctly", "with", "79.3", "%", "accuracy", ";", "hence", ",", "the", "bulk", "of", "the", "difficulty", "lies", "in", "finding", "the", "exact", "span", "within", "the", "sentence", ".", "Feature", "ablations", ".", "In", "order", "to", "understand", "the", "features", "that", "are", "responsible", "for", "the", "performance", "of", "the", "logistic", "regression", "model", ",", "we", "perform", "a", "feature", "ablation", "where", "we", "remove", "one", "group", "of", "features", "from", "our", "model", "at", "a", "time", ".", "The", "results", ",", "shown", "in", "Table", "6", ",", "indicate", "that", "lexicalized", "and", "dependency", "tree", "path", "features", "are", "most", "important", ".", "Comparing", "our", "analysis", "to", "the", "one", "in", "Chen", "et", "al", ".", "(", "2016", ")", ",", "we", "note", "that", "the", "dependency", "tree", "path", "features", "play", "a", "much", "bigger", "role", "in", "our", "dataset", ".", "Additionally", ",", "we", "note", "that", "with", "lexicalized", "features", ",", "the", "model", "significantly", "overfits", "the", "training", "set", ";", "however", ",", "we", "found", "that", "increasing", "L", "2", "regularization", "hurts", "performance", "on", "the", "development", "set", ".", "Performance", "stratified", "by", 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"NIL"], [1911, 1913, 0.026658853515982628, "NIL"], [1911, 1912, 0.026497576385736465, "NIL"], [1910, 1910, 0.02579418011009693, "NIL"], [1906, 1906, 0.02327026054263115, "NIL"], [1917, 1925, 0.023144423961639404, "NIL"], [1919, 1919, 0.022382797673344612, "NIL"], [1916, 1922, 0.02201012335717678, "NIL"], [1912, 1917, 0.021778468042612076, "NIL"], [1914, 1922, 0.021140307188034058, "NIL"], [1919, 1925, 0.02005903236567974, "NIL"], [1922, 1925, 0.01932194083929062, "NIL"], [1906, 1908, 0.019254665821790695, "NIL"], [1914, 1915, 0.019040312618017197, "NIL"], [1916, 1925, 0.018651461228728294, "NIL"], [1915, 1916, 0.017962945625185966, "NIL"], [1913, 1916, 0.017943307757377625, "NIL"], [1910, 1913, 0.017575062811374664, "NIL"], [1917, 1920, 0.017163816839456558, "NIL"], [1913, 1921, 0.01649627275764942, "NIL"], [1924, 1926, 0.016276804730296135, "NIL"], [1925, 1926, 0.01594136282801628, "NIL"], [1915, 1920, 0.01548489648848772, "NIL"], [1911, 1922, 0.015358035452663898, "NIL"], [1914, 1925, 0.015111448243260384, "NIL"], [1921, 1921, 0.015062764286994934, "NIL"], [1912, 1920, 0.015031442977488041, "NIL"], [1910, 1912, 0.014845247380435467, "NIL"], [1913, 1924, 0.014783094637095928, "NIL"], [1917, 1926, 0.012978068552911282, "NIL"]], [[1928, 1929, 0.30226778984069824, "NIL"], [1953, 1955, 0.2992820739746094, "NIL"], [1935, 1937, 0.2717615067958832, "NIL"], [1948, 1951, 0.267275333404541, "NIL"], [1948, 1950, 0.2506518065929413, "NIL"], [1947, 1951, 0.2088232934474945, "NIL"], [1942, 1943, 0.1446002870798111, "NIL"], [1954, 1955, 0.10138504207134247, "NIL"], [1936, 1937, 0.09287270158529282, "NIL"], [1929, 1929, 0.08924766629934311, "NIL"], [1948, 1955, 0.08693473041057587, "NIL"], [1943, 1943, 0.0849447101354599, "NIL"], [1942, 1951, 0.07897432893514633, "NIL"], [1947, 1950, 0.07608917355537415, "NIL"], [1947, 1955, 0.07361216843128204, "NIL"], [1927, 1929, 0.0733170136809349, "NIL"], [1954, 1954, 0.07193697988986969, "NIL"], [1931, 1931, 0.0708259865641594, "NIL"], [1936, 1936, 0.06342367827892303, "NIL"], [1935, 1943, 0.06338372081518173, "NIL"], [1955, 1955, 0.06210605427622795, "NIL"], [1947, 1947, 0.06172718480229378, "NIL"], [1953, 1954, 0.05691249668598175, "NIL"], [1951, 1951, 0.05325902998447418, "NIL"], [1928, 1931, 0.04729125648736954, "NIL"], [1935, 1938, 0.04381876811385155, "NIL"], [1948, 1954, 0.04313782602548599, "NIL"], [1939, 1940, 0.042825594544410706, "NIL"], [1950, 1950, 0.0395418219268322, "NIL"], [1939, 1943, 0.03929439187049866, "NIL"], [1937, 1937, 0.03893905505537987, "NIL"], [1936, 1943, 0.03851066157221794, "NIL"], [1950, 1951, 0.03773243725299835, "NIL"], [1947, 1954, 0.03695870190858841, "NIL"], [1935, 1940, 0.03646894544363022, "NIL"], [1935, 1936, 0.03639453649520874, "NIL"], [1929, 1931, 0.03559303656220436, "NIL"], [1942, 1950, 0.03507993370294571, "NIL"], [1940, 1943, 0.03430458530783653, "NIL"], [1940, 1951, 0.03281395137310028, "NIL"], [1943, 1951, 0.03163415938615799, "NIL"], [1940, 1940, 0.030758904293179512, "NIL"], [1935, 1939, 0.030375728383660316, "NIL"], [1947, 1956, 0.02931869588792324, "NIL"], [1949, 1951, 0.029169244691729546, "NIL"], [1943, 1950, 0.02867678739130497, "NIL"], [1951, 1955, 0.027145003899931908, "NIL"], [1948, 1956, 0.02613295055925846, "NIL"], [1927, 1931, 0.026072772219777107, "NIL"], [1938, 1940, 0.02603260427713394, "NIL"], [1927, 1927, 0.025492830201983452, "NIL"], [1938, 1943, 0.024943610653281212, "NIL"], [1943, 1954, 0.02407294139266014, "NIL"], [1950, 1955, 0.023687487468123436, "NIL"], [1948, 1948, 0.023122284561395645, "NIL"], [1954, 1956, 0.023082735016942024, "NIL"], [1953, 1956, 0.022893067449331284, "NIL"], [1935, 1941, 0.022404391318559647, "NIL"], [1937, 1943, 0.021951857954263687, "NIL"], [1950, 1954, 0.021833688020706177, "NIL"]], [[1957, 1959, 0.425244003534317, "NIL"], [1958, 1959, 0.19945384562015533, "NIL"], [1957, 1958, 0.14560188353061676, "NIL"], [1958, 1958, 0.1420622020959854, "NIL"], [1959, 1959, 0.1288527101278305, "NIL"], [1957, 1960, 0.044620610773563385, "NIL"], [1957, 1957, 0.04098821058869362, "NIL"], [1958, 1960, 0.034574586898088455, "NIL"], [1959, 1960, 0.029439182952046394, "NIL"]], [[1969, 1969, 0.8316860198974609, "Dataset"], [1989, 1993, 0.7613353729248047, "DatasetGeneric"], [1982, 1984, 0.4351094961166382, "NIL"], [1973, 1974, 0.3046419024467468, "NIL"], [1986, 1993, 0.2532654106616974, "NIL"], [1986, 1987, 0.2514341175556183, "NIL"], [1980, 1984, 0.2510685324668884, "NIL"], [1966, 1967, 0.19242270290851593, "Method"], [1990, 1993, 0.14727695286273956, "NIL"], [1992, 1993, 0.1259572058916092, "NIL"], [1981, 1984, 0.1217382401227951, "NIL"], [1966, 1966, 0.114459328353405, "NIL"], [1983, 1984, 0.09382662922143936, "NIL"], [1992, 1992, 0.07447779178619385, "NIL"], [1982, 1993, 0.07442627847194672, "NIL"], [1984, 1984, 0.07349549978971481, "NIL"], [1982, 1982, 0.07221589982509613, "NIL"], [1982, 1987, 0.06444470584392548, "NIL"], [1980, 1987, 0.06338796019554138, "NIL"], [1979, 1984, 0.06282436102628708, "NIL"], [1989, 1990, 0.06268667429685593, "NIL"], [1990, 1990, 0.060925018042325974, "NIL"], [1987, 1987, 0.05896931514143944, "NIL"], [1982, 1983, 0.04688713327050209, "NIL"], [1973, 1976, 0.046779096126556396, "NIL"], [1973, 1975, 0.046026721596717834, "NIL"], [1989, 1992, 0.04386601224541664, "NIL"], [1980, 1982, 0.042528655380010605, "NIL"], [1974, 1974, 0.04104061797261238, "NIL"], [1986, 1992, 0.04021378979086876, "NIL"], [1980, 1981, 0.03776433318853378, "NIL"], [1964, 1967, 0.03649988770484924, "NIL"], [1990, 1992, 0.035794492810964584, "NIL"], [1963, 1967, 0.03447769209742546, "NIL"], [1986, 1986, 0.03337828442454338, "NIL"], [1979, 1987, 0.03286780044436455, "NIL"], [1963, 1964, 0.03282356262207031, "NIL"], [1980, 1980, 0.03264595568180084, "NIL"], [1964, 1966, 0.03262895345687866, "NIL"], [1981, 1982, 0.029386842623353004, "NIL"], [1980, 1983, 0.028980456292629242, "NIL"], [1964, 1964, 0.0286505538970232, "NIL"], [1979, 1979, 0.028173133730888367, "NIL"], [1982, 1992, 0.026049412786960602, "NIL"], [1981, 1987, 0.025850482285022736, "NIL"], [1983, 1987, 0.024522900581359863, "NIL"], [1984, 1987, 0.024061068892478943, "NIL"], [1992, 1994, 0.02364729717373848, "NIL"], [1993, 1993, 0.021473506465554237, "NIL"], [1962, 1964, 0.021311281248927116, "NIL"], [1990, 1994, 0.021085551008582115, "NIL"], [1983, 1983, 0.02050258405506611, "NIL"], [1982, 1986, 0.020146913826465607, "NIL"], [1967, 1967, 0.01990697532892227, "NIL"], [1979, 1982, 0.01961873471736908, "NIL"], [1981, 1981, 0.0191687922924757, "NIL"], [1979, 1981, 0.019093260169029236, "NIL"], [1986, 1990, 0.019076665863394737, "NIL"], [1979, 1980, 0.01882798969745636, "NIL"], [1963, 1966, 0.018077734857797623, "NIL"]], [[2007, 2008, 0.45638319849967957, "DatasetGeneric"], [1997, 1999, 0.4329053461551666, "NIL"], [1996, 2000, 0.3789575695991516, "NIL"], [2011, 2012, 0.3146071434020996, "DatasetGeneric"], [2002, 2003, 0.288679301738739, "NIL"], [2025, 2026, 0.19416594505310059, "NIL"], [2008, 2008, 0.17186890542507172, "NIL"], [2006, 2008, 0.16918028891086578, "NIL"], [2014, 2015, 0.16664893925189972, "NIL"], [2012, 2012, 0.16441337764263153, "NIL"], [2003, 2003, 0.1643373668193817, "NIL"], [2029, 2030, 0.13330620527267456, "NIL"], [1998, 1999, 0.11594808101654053, "Task"], [2021, 2023, 0.10898050665855408, "NIL"], [1997, 2000, 0.10389437526464462, "NIL"], [2026, 2026, 0.1027960479259491, "NIL"], [2007, 2012, 0.09169061481952667, "NIL"], [2015, 2015, 0.0891173705458641, "NIL"], [1996, 2003, 0.08092503994703293, "NIL"], [1997, 1998, 0.07773472368717194, "NIL"], [2025, 2030, 0.07457774132490158, "NIL"], [2007, 2009, 0.07291755080223083, "NIL"], [2022, 2023, 0.06820359081029892, "NIL"], [2028, 2030, 0.06496667116880417, "NIL"], [1997, 2003, 0.06306205689907074, "NIL"], [2020, 2023, 0.062487948685884476, "NIL"], [2008, 2012, 0.062326785176992416, "NIL"], [1999, 1999, 0.06208603456616402, "NIL"], [2018, 2018, 0.05754455178976059, "NIL"], [1997, 1997, 0.055560071021318436, "NIL"], [2030, 2030, 0.05456218123435974, "NIL"], [2011, 2015, 0.054200656712055206, "NIL"], [2021, 2026, 0.053963493555784225, "NIL"], [2020, 2020, 0.05373649299144745, "NIL"], [1995, 2000, 0.05320656672120094, "NIL"], [2023, 2023, 0.05113808810710907, "NIL"], [2021, 2030, 0.05084342882037163, "NIL"], [2012, 2015, 0.048397794365882874, "NIL"], [2007, 2015, 0.044725097715854645, "NIL"], [1996, 1999, 0.04380900785326958, "NIL"], [2015, 2026, 0.04363660514354706, "NIL"], [2011, 2013, 0.04271675646305084, "NIL"], [2014, 2023, 0.04232765734195709, "NIL"], [2006, 2012, 0.04080555588006973, "NIL"], [2020, 2030, 0.040651723742485046, "NIL"], [2027, 2030, 0.039288535714149475, "NIL"], [2012, 2013, 0.03840336948633194, "NIL"], [2028, 2028, 0.03696129843592644, "NIL"], [2009, 2012, 0.035982608795166016, "NIL"], [2019, 2020, 0.03582186996936798, "NIL"], [2020, 2026, 0.03339587524533272, "NIL"], [2026, 2030, 0.03278995305299759, "NIL"], [2015, 2023, 0.03265701234340668, "NIL"], [2018, 2020, 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[2053, 2056, 0.03403569012880325, "NIL"], [2055, 2055, 0.033240772783756256, "NIL"], [2037, 2037, 0.030705798417329788, "NIL"], [2048, 2049, 0.02881944738328457, "NIL"], [2040, 2043, 0.028534693643450737, "NIL"], [2042, 2045, 0.026364676654338837, "NIL"], [2048, 2051, 0.023415779694914818, "NIL"], [2050, 2055, 0.023225411772727966, "NIL"], [2049, 2055, 0.022949762642383575, "NIL"], [2036, 2037, 0.02263323962688446, "NIL"], [2032, 2032, 0.020958997309207916, "NIL"], [2049, 2056, 0.02051650732755661, "NIL"], [2049, 2050, 0.019916236400604248, "NIL"], [2047, 2047, 0.019709160551428795, "NIL"], [2052, 2053, 0.01957131177186966, "NIL"], [2047, 2049, 0.019286014139652252, "NIL"], [2049, 2053, 0.01891021430492401, "NIL"], [2043, 2045, 0.01581675186753273, "NIL"], [2047, 2051, 0.015494074672460556, "NIL"], [2040, 2045, 0.015353528782725334, "NIL"], [2052, 2055, 0.015321035869419575, "NIL"], [2055, 2056, 0.014987565577030182, "NIL"], [2036, 2036, 0.014563336968421936, "NIL"], [2039, 2039, 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"develop", "a", "more", "comprehensive", "annotation", "scheme", "they", "initially", "labeled", "a", "sample", "of", "tweets", ",", "allowing", "each", "tweet", "to", "belong", "to", "multiple", "classes", ".", "After", "analyzing", "the", "overlap", "between", "different", "classes", "they", "settled", "on", "a", "coding", "scheme", "with", "four", "distinct", "classes", ":", "abusive", ",", "hateful", ",", "spam", ",", "and", "normal", ".", "We", "use", "a", "dataset", "they", "published", "containing", "91", ",", "951", "tweets", "coded", "into", "these", "categories", "by", "crowdworkers", ".", "For", "each", "dataset", "we", "train", "a", "classifier", "to", "predict", "the", "class", "of", "unseen", "tweets", ".", "We", "use", "regularized", "logistic", "regression", "with", "bag", "-", "of", "-", "words", "features", ",", "a", "commonly", "used", "approach", "in", "the", "field", ".", "While", "we", "expect", "that", "we", "could", "improve", "predictive", "performance", "by", "using", "more", "sophisticated", "classifiers", ",", "we", "expect", "that", "any", "bias", "is", "likely", "a", "function", "of", "the", "training", "data", "itself", "rather", "than", "the", "classifier", ".", "Moreover", ",", "although", "features", "like", "word", "embeddings", "can", "work", "well", "for", "this", "task", "(", "Djuric", "et", "al", ".", ",", "2015", ")", "we", "wanted", "to", "avoid", "inducing", "any", "bias", "in", "our", "models", "by", "using", "pre", "-", "trained", "embeddings", "(", "Park", "et", "al", ".", ",", "2018", ")", ".", "We", "pre", "-", "process", "each", "tweet", "by", "removing", "excess", "white", "-", "space", "and", "replacing", "URLs", "and", "mentions", "with", "placeholders", ".", "We", "then", "tokenize", "them", ",", "stem", "each", "token", ",", "and", "construct", "n", "-", "grams", "with", "a", "maximum", "length", "of", "three", ".", "Next", "we", "transform", "each", "dataset", "into", "a", "TF", "-", "IDF", "matrix", ",", "with", "a", "maximum", "of", "10", ",", "000", "features", ".", "We", "use", "80", "%", "of", "each", "dataset", "to", "train", "models", "and", "hold", "out", "the", "remainder", "for", "validation", ".", "Each", "model", "is", "trained", "using", "stratified", "5fold", "cross", "-", "validation", ".", "We", "conduct", "a", "grid", "-", "search", "over", "different", "regularization", "strength", "parameters", "to", "identify", "the", "best", "performing", "model", ".", "Finally", ",", "for", "each", "dataset", "we", "identify", "the", "model", "with", "the", "best", "average", "F1", "score", "and", "retrain", "it", "using", "all", "of", "the", "training", "data", ".", "The", "performance", "of", "these", "models", "on", "the", "20", "%", "held", "-", "out", "validation", "data", "is", "reported", "in", "Table", "1.", "Overall", "we", "see", "varying", "performance", "across", "the", "classifiers", ",", "with", "some", "performing", "much", "were", "added", "to", "the", "dataset", "released", "by", "the", "authors", ".", "Some", "of", "the", "tweets", "in", "this", "dataset", "are", "duplicates", ":", "if", "all", "versions", "of", "a", "duplicated", "tweet", "were", "coded", "in", "the", "same", "way", "by", "the", "majority", "of", "coders", "we", "retained", "one", "copy", "and", "deleted", "the", "rest", ";", "if", "the", "labels", "disagreed", "we", "removed", "all", "copies", ".", "better", "out", "-", "of", "-", "sample", "than", "others", ".", "In", "particular", ",", "we", "see", "that", "hate", "speech", "and", "harassment", "are", "particularly", "difficult", "to", "detect", ".", "Since", "we", "are", "primarily", "interested", "in", "within", "classifier", ",", "between", "corpora", "performance", ",", "any", "variation", "between", "classifiers", "should", "not", "impact", "our", "results", ".", "We", "use", "a", "dataset", "of", "tweets", "labeled", "by", "race", "from", "Blodgett", "et", "al", ".", "(", "2016", ")", "to", "measure", "racial", "biases", "in", "these", "classifiers", ".", "They", "collected", "geolocated", "tweets", "in", "the", "U.S", ".", "and", "matched", "them", "with", "demographic", "data", "from", "the", "Census", "on", "the", "population", "of", "non", "-", "Hispanic", "whites", ",", "non", "-", "Hispanic", "blacks", ",", "Hispanics", ",", "and", "Asians", "in", "the", "block", "group", "where", "the", "tweets", "originated", ".", "They", "then", "identified", "words", "associated", "with", "particular", "demographics", "and", "trained", "a", "probabilistic", "mixed", "-", "membership", "language", "model", ".", "This", "model", "learns", "demographicallyaligned", "language", "models", "for", "each", "of", "the", "four", "demographic", "categories", "and", "is", "used", "to", "calculate", "the", "posterior", "proportion", "of", "language", "from", "each", "category", "in", "each", "tweet", ".", "Their", "validation", "analyses", "indicate", "that", "tweets", "with", "a", "high", "posterior", "proportion", "of", "non", "-", "Hispanic", "black", "language", "exhibit", "lexical", ",", "phonological", ",", "and", "syntactic", "variation", "consistent", "with", "prior", "research", "on", "AAE", ".", "Their", "publiclyavailable", "dataset", "contains", "59.2", "million", "tweets", ".", "We", "define", "a", "user", "as", "likely", "non", "-", "Hispanic", "black", "if", "the", "average", "posterior", "proportion", "across", "all", "of", "their", "tweets", "for", "the", "non", "-", "Hispanic", "black", "language", "model", "is", "\u2265", "0.", "80", "(", "and", "\u2264", "0.", "10", "Hispanic", "and", "Asian", "combined", ")", "and", "as", "non", "-", "Hispanic", "white", "using", "the", "same", "formula", "but", "for", "the", "white", "language", "model", ".", "5", "This", "allows", "us", "to", "restrict", "our", "analysis", "to", "tweets", "written", "by", "users", "who", "predominantly", "use", "one", "of", "the", "language", "models", ".", "Due", "to", "space", "constraints", "we", "discard", "users", "who", "predominantly", "use", "either", "the", "Hispanic", "or", "the", "Asian", "language", "model", ".", "This", "results", "in", "a", "set", "of", "1.", "1", "m", "tweets", "written", "by", "people", "who", "generally", "use", "non", "-", "Hispanic", "black", "language", "and", "14.5", "m", "tweets", "written", "by", "users", "who", "tend", "to", "use", "non", "-", "Hispanic", "white", "language", ".", "Following", "Blodgett", "and", "O'Connor", "(", "2017", ")", ",", "we", "call", "these", "datasets", "black", "-", "aligned", "and", "white", "-", "aligned", "tweets", ",", "reflecting", "5", "We", "use", "this", "threshold", "following", "Blodgett", "and", "O'Connor", "(", "2017", ")", "and", "after", "consulting", "with", "the", "lead", "author", ".", "While", "these", "cut", "-", "offs", "should", "provide", "high", "confidence", "that", "the", "users", "tend", "to", "use", "AAE", "or", "SAE", ",", "and", "hence", "serve", "as", "a", "proxy", "for", "race", ",", "it", "is", "important", "to", "note", "that", "not", "all", "African", "-", "Americans", "use", "AAE", "and", "that", "not", "all", "AAE", "users", "are", "African", "-", "American", ",", "although", "use", "of", "the", "AAE", "dialect", "suggests", "a", "social", "proximity", "to", "or", "affinity", "for", "African", "-", "American", "communities", "(", "Blodgett", "et", "al", ".", ",", "2016", ")", "the", "fact", "that", "they", "contain", "language", "associated", "with", "either", "demographic", "category", "but", "which", "may", "not", "all", "be", "produced", "by", "members", "of", "these", "categories", ".", "We", "now", "describe", "how", "we", "use", "these", "data", "in", "our", "experiments", ".", "We", "examine", "whether", "the", "probability", "that", "a", "tweet", "is", "predicted", "to", "belong", "to", "a", "particular", "class", "varies", "in", "relation", "to", "the", "racial", "alignment", "of", "the", "language", "it", "uses", ".", "The", "null", "hypothesis", "of", "no", "racial", "bias", "is", "that", "the", "probability", "a", "tweet", "will", "belong", "to", "a", "negative", "class", "is", "independent", "of", "the", "racial", "group", "the", "tweet", "'s", "author", "is", "a", "member", "of", ".", "Formally", ",", "for", "class", "c", "i", ",", "where", "c", "i", "=", "1", "denotes", "membership", "in", "the", "class", "and", "c", "i", "=", "0", "the", "opposite", ",", "we", "aim", "to", "test", "H", "N", ":", ")", "and", "the", "difference", "is", "statistically", "significant", "then", "we", "can", "reject", "the", "null", "hypothesis", "H", "N", "in", "favor", "of", "the", "alternative", "hypothesis", "H", "A", "that", "black", "-", "aligned", "tweets", "are", "classified", "into", "c", "i", "at", "a", "higher", "rate", "than", "white", "-", "aligned", "tweets", ".", "Conversely", ",", "if", "P", "(", "c", "i", "=", "1|black", ")", "<", "P", "(", "c", "i", "=", "1|white", ")", "we", "can", "conclude", "that", "the", 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"rate", "than", "whitealigned", "tweets", ".", "We", "also", "conduct", "a", "second", "experiment", ",", "where", "we", "assess", "whether", "there", "is", "racial", "bias", "conditional", "upon", "a", "tweet", "containing", "a", "keyword", "likely", "to", "be", "associated", "with", "a", "negative", "class", ".", "While", "differences", "in", "language", "will", "undoubtedly", "remain", ",", "this", "should", "help", "to", "account", "for", "the", "possibility", "that", "results", "in", "Experiment", "1", "are", "driven", "by", "differences", "in", "the", "true", "distribution", "of", "the", "different", "classes", "of", "interest", ",", "or", "of", "words", "associated", "with", "these", "classes", ",", "in", "the", "two", "corpora", ".", "For", "classifier", "c", "and", "category", "i", ",", "we", "evaluate", "H", "N", ":", "P", "(", "c", "i", "=", "1|black", ",", "t", ")", "=", "P", "(", "c", "i", "=", "1|white", ",", "t", ")", "for", "a", "given", "term", "t.", "We", "conduct", 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"1", "may", "be", "driven", "by", "differences", "in", "the", "frequencies", "of", "words", "associated", "with", "negative", "classes", "in", "the", "training", "datasets", ".", "Since", "we", "are", "using", "a", "subsample", "of", "the", "available", "data", ",", "we", "use", "smaller", "bootstrap", "samples", ",", "drawing", "k", "=", "100", "tweets", "each", "time", ".", "The", "results", "of", "Experiment", "1", "are", "shown", "in", "Table", "2.", "We", "observe", "substantial", "racial", "disparities", "in", "the", "performance", "of", "all", "classifiers", ".", "In", "all", "but", "one", "of", "the", "comparisons", ",", "there", "are", "statistically", "significant", "(", "p", "<", "0.", "001", ")", "differences", "and", "in", "all", "but", "one", "of", "these", "we", "see", "that", "tweets", "in", "the", "black", "-", "aligned", "corpus", "are", "assigned", "negative", "labels", "more", "frequently", "than", "those", "by", "whites", ".", "The", "only", "case", "where", 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"compared", "to", "6", "%", "and", "8", "%", "of", "white", "-", "aligned", "tweets", "respectively", ".", "It", "also", "classifies", "black", "-", "aligned", "tweets", "as", "spam", "1.", "8", "times", "as", "frequently", ".", "The", "results", "of", "Experiment", "2", "are", "consistent", "with", "the", "previous", "results", ",", "although", "there", "are", "some", "notable", "differences", ".", "In", "most", "cases", "the", "racial", "disparities", "persist", ",", "although", "they", "are", "generally", "smaller", "in", "magnitude", "and", "in", "some", "cases", "the", "direction", "even", "changes", ".", "Table", "3", "shows", "that", "for", "tweets", "containing", "the", "word", "\"", "n*gga", "\"", ",", "classifiers", "trained", "on", "Waseem", "and", "Hovy", "(", "2016", ")", "and", "Waseem", "(", "2016", ")", "are", "both", "predict", "black", "-", "aligned", "tweets", "to", "be", "instances", "of", "sexism", "approximately", "1.", "5", "times", "as", "often", "as", "white", "-", "aligned", "tweets", ".", "The", "classifier", "trained", "on", "the", "Davidson", "et", "al", ".", "(", "2017", ")", "data", "is", "significantly", "less", "likely", "to", "classify", "black", "-", "aligned", "tweets", "as", "hate", "speech", ",", "although", "it", "is", "more", "likely", "to", "classify", "them", "as", "offensive", ".", " ", "Golbeck", "et", "al", ".", "(", "2017", ")", "classifies", "black", "-", "aligned", "tweets", "as", "harassment", "at", "a", "higher", "rate", "for", "both", "groups", "than", "in", "the", "previous", "experiment", ",", "although", "the", "disparity", "is", "narrower", ".", "For", "the", "Founta", "et", "al", ".", "(", "2018", ")", "classifier", "we", "see", "that", "black", "-", "aligned", "tweets", "are", "slightly", "less", "frequently", "considered", "to", "be", "hate", "speech", "but", "are", "much", "more", "frequently", "classified", "as", "abusive", ".", "The", "results", "for", "the", "second", "variation", "of", "Experiment", "2", "where", "we", "conditioned", "on", "the", "word", "\"", "b*tch", "\"", "are", "shown", "in", "Table", "4.", "We", "see", "similar", "results", "for", "Waseem", "and", "Hovy", "(", "2016", ")", "and", "Waseem", "(", "2016", ")", ".", "In", "both", "cases", "the", "classifiers", "trained", "upon", "their", "data", "are", "still", "more", "likely", "to", "flag", "black", "-", "aligned", "tweets", "as", "sexism", ".", "The", "Waseem", "and", "Hovy", "(", "2016", ")", "classifier", "is", "particularly", "sensitive", "to", "the", "word", "\"", "b*tch", "\"", "with", "96", "%", "of", "black", "-", "aligned", "and", "94", "%", "of", "white", "-", "aligned", "tweets", "predicted", "to", "belong", "to", "this", "class", ".", "For", "Davidson", "et", "al", ".", "(", "2017", ")", "almost", "all", "of", "these", "tweets", "are", "classified", "as", "offensive", ",", "however", "those", "in", "the", "blackaligned", "corpus", "are", "1.", "15", "times", "as", "frequently", "classified", "as", "hate", "speech", ".", "We", "see", "a", "very", "similar", "result", "for", "Golbeck", "et", "al", ".", "(", "2017", ")", "compared", "to", "the", "previous", "experiment", ",", "with", "black", "-", "aligned", "tweets", "flagged", "as", "harassment", "at", "1.", "1", "times", "the", "rate", "of", "those", "in", "the", "white", "-", "aligned", "corpus", ".", "Finally", ",", "for", "the", "Founta", "et", "al", ".", "(", "2018", ")", "classifier", "we", "see", "a", "substantial", "racial", "disparity", ",", "with", "black", "-", "aligned", "tweets", "classified", "as", "hate", "speech", "at", "2.", "7", "times", "the", "rate", "of", "white", "aligned", "ones", ",", "a", "higher", "rate", "than", "in", "Experiment", "1.", "Our", "results", "demonstrate", "consistent", ",", "systematic", "and", "substantial", "racial", "biases", "in", "classifiers", "trained", "on", "all", "five", "datasets", ".", "In", "almost", "every", "case", ",", "black", "-", "aligned", "tweets", "are", "classified", "as", "sexism", ",", "hate", "speech", ",", "harassment", ",", "and", "abuse", "at", "higher", "rates", "than", "whitealigned", "tweets", ".", "To", "some", "extent", ",", "the", "results", "in", "the", "first", "experiment", "may", "be", "driven", "by", "underlying", "differences", "in", "the", "rates", "at", "which", "speakers", "of", "different", "dialects", "use", "particular", "words", "and", "phrases", "associated", "with", "these", "negative", "classes", "in", "the", "training", "data", ".", "For", "example", ",", "the", "word", "\"", "n*gga", "\"", "appears", "fifteen", "times", "as", "frequently", "in", "the", "black", "-", "aligned", "corpus", "compared", "to", "the", "white", "-", "aligned", "corpus", ".", "7", "owever", ",", "the", "second", "experiment", "shows", "that", "these", "disparities", "tend", "to", "persist", "even", "when", "comparing", "tweets", "containing", "keywords", "likely", "to", "be", "associated", "with", "negative", "classes", ".", "While", "some", "of", "the", "remaining", "disparities", "are", "likely", "due", "to", "differences", "in", "the", "distributions", "of", "other", "keywords", "we", "did", "not", "condition", "on", ",", "we", "expect", "that", "other", "more", "innocuous", "aspects", "of", "black", "-", "aligned", "language", "may", "be", "associated", "with", "negative", "labels", "in", "the", "training", "data", ",", "leading", "classifiers", "to", "disproportionately", "predict", "that", "tweets", "by", "African", "-", "Americans", "belong", "to", "negative", "classes", ".", "We", "now", "discuss", "the", "results", "as", "they", "pertain", "to", "each", "of", "the", "datasets", "used", ".", "Classifiers", "trained", "on", "data", "from", "Waseem", "and", "Hovy", "(", "2016", ")", "and", "Waseem", "(", "2016", ")", "only", "predicted", "a", "small", "fraction", "of", "the", "tweets", "to", "be", "racism", ".", "We", "suspect", "that", "this", "is", "due", "to", "the", "composition", "of", "their", "dataset", ",", "since", "the", "majority", "of", "the", "racist", "training", "examples", "consist", "of", "anti", "-", "Muslim", "rather", "than", "anti", "-", "  ", "black", "language", ".", "Across", "both", "datasets", "the", "words", "\"", "n*gger", "\"", "and", "\"", "n*gga", "\"", "appear", "in", "4", "and", "10", "tweets", "respectively", ".", "Looking", "at", "the", "sexism", "class", "on", "the", "other", "hand", ",", "we", "see", "that", "both", "models", "were", "consistently", "classifying", "tweets", "in", "the", "black", "-", "aligned", "corpus", "as", "sexism", "at", "a", "substantially", "higher", "rate", "than", "those", "in", "the", "white", "-", "aligned", "corpus", ".", "Given", "this", "result", ",", "and", "the", "gender", "biases", "identified", "in", "these", "data", "by", "Park", "et", "al", ".", "(", "2018", ")", ",", "it", "not", "apparent", "that", "the", "purportedly", "expert", "annotators", "were", "any", "less", "biased", "than", "amateur", "annotators", "(", "Waseem", ",", "2016", ")", ".", "The", "classifier", "trained", "on", "Davidson", "et", "al", ".", "(", "2017", ")", "shows", "the", "largest", "disparities", "in", "Experiment", "1", ",", "with", "tweets", "in", "the", "black", "-", "aligned", "corpus", "classified", "as", "hate", "speech", "and", "offensive", "language", "at", "substantially", "higher", "rates", "than", "white", "-", "aligned", "tweets", ".", "We", "expect", "that", "this", "result", "occurred", "for", "two", "reasons", ".", "First", ",", "the", "dataset", "contains", "a", "large", "number", "of", "cases", "where", "AAE", "is", "used", "(", "Waseem", "et", "al", ".", ",", "2018", ")", ".", "Second", ",", "many", "of", "the", "AAE", "tweets", "also", "use", "words", "like", "\"", "n*gga", "\"", "and", "\"", "b*tch", "\"", ",", "and", "are", "thus", "frequently", "associated", "with", "the", "hate", "speech", "and", "offensive", "classes", ",", "resulting", "in", "\"", "false", "positive", "bias", "\"", "(", "Dixon", "et", "al", ".", ",", "2018", ")", ".", "On", "the", "other", "hand", ",", "the", "distinction", "between", "hate", "speech", "and", "offensive", "language", "appears", "to", "hold", "up", "to", "scrutiny", ":", "while", "a", "large", "proportion", "of", "tweets", "in", "Experiment", "2", "containing", "the", "word", "\"", "n*gga", "\"", "are", "classified", "as", "hate", "speech", ",", "the", "rate", "is", "substantially", "higher", "for", "white", "-", "aligned", "tweets", ".", "Without", "this", "category", "we", "expect", "that", "many", "of", "the", "tweets", "classified", "as", "offensive", "would", "instead", "be", "mistakenly", "classified", "as", "hate", "speech", ".", "Turning", "to", "the", "Golbeck", "et", "al", ".", "(", "2017", ")", "classifer", "we", "found", "that", "tweets", "in", "the", "black", "-", "aligned", "dataset", "were", "significantly", "more", "likely", "to", "be", "classified", "as", "harassment", "in", "all", "experiments", ",", "although", "the", "disparity", "decreased", "substantially", "after", "conditioning", "on", "certain", "keywords", ".", "It", "seems", "likely", "that", "their", "simple", "binary", "labelling", "scheme", "may", "not", "be", "sufficient", "to", "capture", "the", "variation", "in", "language", "used", ",", "resulting", "in", "high", "rates", "of", "false", "positives", ".", "Finally", ",", "Founta", "et", "al", ".", "(", "2018", ")", "is", "the", "largest", "and", "perhaps", "the", "most", "comprehensive", "of", "the", "available", "datasets", ".", "In", "Experiment", "1", "we", "see", "that", "this", "clas", "-", "sifier", "has", "the", "second", "highest", "rates", "of", "racial", "disparities", ",", "classifying", "black", "-", "aligned", "tweets", "as", "hate", "speech", ",", "abusive", ",", "and", "spam", "at", "substantially", "higher", "rates", "than", "white", "-", "aligned", "tweets", ".", "In", "Experiment", "2", "the", "classifier", "is", "slightly", "less", "likely", "to", "classify", "black", "-", "aligned", "tweets", "containing", "the", "word", "\"", "n*gga", "\"", "as", "hate", "speech", "but", "is", "2.", "7", "times", "more", "likely", "to", "predict", "that", "black", "-", "aligned", "tweets", "using", "\"", "b*tch", "\"", "belong", "to", "this", "category", ".", "Our", "study", "is", "the", "first", "to", "measure", "racial", "bias", "in", "hate", "speech", "and", "abusive", "language", "detection", "datasets", ".", "We", "find", "evidence", "of", "substantial", "racial", "bias", "in", "all", "of", "the", "datasets", "tested", ".", "This", "bias", "tends", "to", "persist", "even", "when", "comparing", "tweets", "containing", "certain", "relevant", "keywords", ".", "While", "these", "datasets", "are", "still", "valuable", "for", "academic", "research", ",", "we", "caution", "against", "using", "them", "in", "the", "field", "to", "detect", "and", "particularly", "to", "take", "enforcement", "action", "against", "different", "types", "of", "abusive", "language", ".", "If", "they", "are", "used", "in", "this", "way", "we", "expect", "that", "they", "will", "systematically", "penalize", "African", "-", "Americans", "more", "than", "whites", ",", "resulting", "in", "racial", "discrimination", ".", "We", "have", "not", "evaluated", "these", "datasets", "for", "bias", "related", "to", "other", "ethnic", "and", "racial", "groups", ",", "nor", "other", "protected", "categories", "like", "gender", "and", "sexuality", ",", "but", "expect", "that", "such", "bias", "is", "also", "likely", "to", "exist", ".", "We", "recommend", "that", "efforts", "to", "measure", "and", "mitigate", "bias", "should", "start", "by", "focusing", "on", "how", "bias", "enters", "into", "datasets", "as", "they", "are", "collected", "and", "labeled", ".", "In", "particular", ",", "future", "work", "should", "focus", "on", "the", "following", "three", "areas", ".", "First", ",", "we", "expect", "that", "some", "biases", "emerge", "at", "the", "point", "of", "data", "collection", ".", "Some", "studies", "sampled", "tweets", "using", "small", ",", "ad", "hoc", "sets", "of", "keywords", "created", "by", "the", "authors", "(", "Waseem", "and", "Hovy", ",", "2016", ";", "Waseem", ",", "2016", ";", "Golbeck", "et", "al", ".", ",", "2017", ")", ",", "an", "approach", "demonstrated", "to", "produce", "poor", "results", "(", "King", "et", "al", ".", ",", "2017", ")", ".", "Others", "start", "with", "large", "crowdsourced", "dictionaries", "of", "keywords", ",", "which", "tend", "to", "include", "many", "irrelevant", "terms", ",", "resulting", "in", "high", "rates", "of", "false", "positives", "(", "Davidson", "et", "al", ".", ",", "2017", ";", "Founta", "et", "al", ".", ",", "2018", ")", ".", "In", "both", "cases", ",", "by", "using", "keywords", "to", "identify", "relevant", "tweets", "we", "are", "likely", "to", "get", "non", "-", "representative", "samples", "of", "training", "data", "that", "may", "over", "-", "or", "under", "-", "represent", "certain", "communities", ".", "In", "particular", ",", "we", "need", "to", "consider", "whether", "the", "linguistic", "markers", "we", "use", "to", "identify", "potentially", "abusive", "language", "may", "be", "associated", "with", "language", "used", "by", "members", "of", "protected", "categories", ".", "For", "example", ",", "although", "Davidson", "et", "al", ".", "(", "2017", ")", "started", "with", "thousands", "of", "terms", "from", "the", "Hatebase", "lexicon", ",", "AAE", "is", "over", "-", "represented", "in", "the", "dataset", "(", "Waseem", "et", "al", ".", ",", "2018", ")", "because", "some", "keywords", "associated", "with", "this", "speech", "community", "were", "used", "more", "frequently", "on", "Twitter", "than", "other", "keywords", "in", "the", "lexicon", "and", "were", "consequentially", "over", "-", "sampled", ".", "Second", ",", "we", "expect", "that", "the", "people", "who", "annotate", "data", "have", "their", "own", "biases", ".", "Since", "individual", "biases", "in", "reflect", "societal", "prejudices", ",", "they", "aggregate", "into", "systematic", "biases", "in", "training", "data", ".", "The", "datasets", "considered", "here", "relied", "upon", "a", "range", "of", "different", "annotators", ",", "from", "the", "authors", "(", "Golbeck", "et", "al", ".", ",", "2017", ";", "Waseem", "and", "Hovy", ",", "2016", ")", "and", "crowdworkers", "(", "Davidson", "et", "al", ".", ",", "2017", ";", "Founta", "et", "al", ".", ",", "2018", ")", "to", "activists", "(", "Waseem", ",", "2016", ")", ".", "Even", "the", "classifier", "trained", "on", "expert", "-", "labeled", "data", "(", "Waseem", ",", "2016", ")", "flags", "black", "-", "aligned", "tweets", "as", "sexist", "at", "almost", "twice", "the", "rate", "of", "white", "-", "aligned", "tweets", ".", "While", "we", "agree", "that", "there", "is", "value", "in", "working", "with", "domain", "-", "experts", "to", "annotate", "data", ",", "these", "results", "suggest", "that", "activists", "may", "be", "prone", "to", "similar", "biases", "as", "academics", "and", "crowdworkers", ".", "Further", "work", "is", "therefore", "necessary", "to", "better", "understand", "how", "to", "integrate", "expertise", "into", "the", "process", "and", "how", "training", "can", "be", "used", "to", "help", "to", "mitigate", "bias", ".", "We", "also", "need", "to", "consider", "how", "sociocultural", "context", "influences", "annotators", "'", "decisions", ".", "For", "example", ",", "48", "%", "of", "the", "workers", "employed", "by", "Founta", "et", "al", ".", "(", "2018", ")", "were", "located", "in", "Venezuela", "but", "the", "authors", "did", "not", "consider", "whether", "this", "affected", "their", "results", "(", "or", "if", "the", "annotators", "understood", "English", "sufficiently", "for", "the", "task", ")", ".", "Third", ",", "we", "observed", "substantial", "variation", "in", "the", "rates", "of", "class", "membership", "across", "classifiers", "and", "datasets", ".", "In", "Experiment", "1", "the", "rate", "at", "which", "tweets", "were", "assigned", "to", "negative", "classes", "varied", "from", "1", "%", "to", "18", "%", ".", "Some", "of", "the", "low", "proportions", "may", "indicate", "a", "preponderance", "of", "false", "negatives", "due", "to", "a", "lack", "of", "training", "data", ",", "suggesting", "that", "these", "models", "may", "not", "be", "able", "to", "sufficiently", "generalize", "beyond", "the", "data", "they", "were", "trained", "on", ".", "The", "high", "proportions", "may", "signal", "too", "many", "false", "positives", ",", "which", "may", "a", "result", "of", "the", "over", "-", "sampling", "of", "abusive", "language", "in", "labeled", "datasets", ".", " ", "Founta", "et", "al", ".", "(", "2018", ")", "claim", "that", ",", "on", "average", ",", "between", "0.", "1", "%", "and", "3", "%", "of", "tweets", "are", "abusive", ",", "depending", "upon", "the", "category", "of", "abuse", ".", "Identifying", "such", "content", "is", "therefore", "a", "highly", "imbalanced", "classification", "problem", ".", "When", "labeling", "datasets", "and", "evaluating", "our", "models", "we", "must", "pay", "more", "attention", "to", "the", "baseline", "rates", "of", "usage", "of", "different", "types", "of", "abusive", "language", "and", "how", "they", "may", "vary", "across", "populations", "(", "Silva", "et", "al", ".", ",", "2016", ")", ".", "Finally", ",", "we", "need", "to", "more", "carefully", "consider", "how", "contextual", "factors", "interact", "with", "linguistic", "subtleties", "and", "our", "definitions", "of", "abuse", ".", "The", "\"", "n", "-", "word", "\"", "is", "a", "particularly", "useful", "illustration", "of", "this", "issue", ".", "It", "exhibits", "polysemy", ",", "as", "it", "can", "be", "extremely", "racist", "or", "quotidian", ",", "depending", "on", "the", "speaker", ",", "the", "context", ",", "and", "the", "spelling", ".", "While", "the", "history", "of", "the", "word", "and", "its", "usages", "is", "too", "complex", "to", "be", "summarized", "here", "(", "Neal", ",", "2013", ")", ",", "when", "used", "with", "the", "\"", "er", "\"", "suffix", "it", "is", "generally", "considered", "to", "be", "a", "racist", "ephiphet", ",", "associated", "with", "white", "supremacy", ".", "Prior", "work", "has", "confirmed", "that", "the", "use", "of", "this", "variant", "online", "is", "generally", "considered", "to", "be", "hateful", "(", "Kwok", "and", "Wang", ",", "2013", ")", ",", "although", "not", "always", "the", "case", ",", "for", "example", "when", "a", "victim", "of", "abuse", "shares", "an", "insult", "they", "have", "received", ".", "However", "the", "variant", "with", "the", "\"", "-", "a", "\"", "suffix", "is", "typically", "used", "innocuously", "by", "African", "-", "Americans", "(", "Kwok", "and", "Wang", ",", "2013", ")", ",", "indeed", "our", "results", "indicate", "that", "it", "is", "used", "far", "more", "frequently", "in", "black", "-", "aligned", "tweets", "(", "although", "it", "is", "still", "used", "by", "many", "white", "people", ")", ".", "8", "Despite", "this", "distinction", ",", "some", "studies", "have", "considered", "this", "variant", "to", "be", "hateful", "(", "Silva", "et", "al", ".", ",", "2016", ";", "Alorainy", "et", "al", ".", ",", "2018", ")", ".", "This", "approach", "results", "in", "high", "rates", "of", "false", "positive", "cases", "of", "hate", "speech", ",", "thus", "Davidson", "et", "al", ".", "(", "2017", ")", "included", "a", "class", "for", "offensive", "language", "which", "does", "not", "appear", "to", "be", "hateful", "and", "let", "annotators", "decide", "which", "class", "tweets", "belonged", "to", "based", "upon", "their", "interpretation", "of", "the", "context", ",", "many", "of", "whom", "labeled", "tweets", "containing", "the", "term", "as", "offensive", ".", " ", "Waseem", "et", "al", ".", "(", "2018", ")", "criticized", "this", "decision", ",", "claiming", "that", "it", "is", "problematic", "to", "ever", "consider", "the", "word", "to", "be", "offensive", "due", "to", "its", "widespread", "use", "among", "AAE", "speakers", ".", "This", "critique", "appears", "to", "be", "reasonable", "in", "the", "sense", "that", "we", "should", "not", "penalize", "African", "-", "Americans", "for", "using", "the", "word", ",", "but", "it", "avoids", "grappling", "with", "how", "to", "act", "when", "the", "word", "is", "used", "by", "other", "speakers", "and", "in", "other", "contexts", ".", "What", "should", "be", "done", "if", "it", "is", "used", "by", "a", "white", "social", "media", "user", "in", "reference", "to", "a", "black", "user", "?", "How", "should", "the", "context", "of", "their", "interaction", "and", "the", "nature", "of", "their", "relationship", "affect", "our", "decision", "?", "A", "\"", "one", "-", "size", "-", "fits", "-", "all", "\"", ",", "context", "-", "independent", "approach", "to", "defining", "and", "detecting", "abusive", "language", "is", "clearly", "inappropriate", ".", "Different", "communities", "have", "different", "speech", "norms", ",", "such", "that", "a", "model", "suitable", "for", "one", "community", "may", "discriminate", "against", "another", ".", "However", "there", "is", "no", "con", "-", "sensus", "in", "the", "field", "on", "how", "and", "if", "we", "can", "develop", "detection", "systems", "sensitive", "to", "different", "social", "and", "cultural", "contexts", ".", "In", "addition", "to", "our", "recommendations", "for", "improving", "training", "data", ",", "we", "emphasize", "the", "necessity", "of", "considering", "how", "context", "matters", "and", "how", "detection", "systems", "will", "have", "uneven", "effects", "across", "different", "communities", ".", "First", ",", "while", "the", "Blodgett", "et", "al", ".", "(", "2016", ")", "dataset", "is", "the", "best", "available", "source", "of", "tweets", "labeled", "as", "AAE", ",", "we", "do", "not", "have", "ground", "truth", "labels", "for", "the", "racial", 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"NIL"], [1924, 1930, 0.01648663729429245, "NIL"], [1919, 1930, 0.016146600246429443, "NIL"], [1905, 1905, 0.016042916104197502, "NIL"], [1911, 1911, 0.015434318222105503, "NIL"], [1919, 1919, 0.015420758165419102, "NIL"], [1903, 1903, 0.01531846821308136, "NIL"], [1919, 1922, 0.012878482230007648, "NIL"], [1903, 1905, 0.012766409665346146, "NIL"], [1920, 1921, 0.012238173745572567, "NIL"], [1920, 1931, 0.011694165877997875, "NIL"], [1931, 1932, 0.011585211381316185, "NIL"], [1922, 1931, 0.011317775584757328, "NIL"], [1924, 1926, 0.01060314942151308, "NIL"], [1929, 1932, 0.010317012667655945, "NIL"], [1926, 1927, 0.010278478264808655, "NIL"], [1910, 1915, 0.009764505550265312, "NIL"], [1921, 1926, 0.009409143589437008, "NIL"], [1925, 1925, 0.009207482449710369, "NIL"], [1922, 1926, 0.007937753573060036, "NIL"], [1932, 1932, 0.007833776995539665, "NIL"]], [[1951, 1956, 0.9668217897415161, "ReferenceLink"], [1975, 1980, 0.9616677761077881, "ReferenceLink"], [1966, 1967, 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0.037621401250362396, "NIL"], [1962, 1973, 0.035648163408041, "NIL"], [1961, 1962, 0.03515494242310524, "NIL"], [1962, 1963, 0.031980372965335846, "NIL"], [1962, 1967, 0.03075534664094448, "NIL"], [1965, 1967, 0.028417464345693588, "NIL"], [1961, 1961, 0.027920439839363098, "NIL"], [1970, 1980, 0.02741851471364498, "NIL"], [1956, 1956, 0.026730990037322044, "NIL"], [1937, 1937, 0.026447873562574387, "NIL"], [1963, 1973, 0.026358431205153465, "NIL"], [1975, 1981, 0.025152936577796936, "NIL"], [1961, 1964, 0.02507573552429676, "NIL"], [1949, 1949, 0.02439138852059841, "NIL"], [1940, 1941, 0.024012411013245583, "NIL"], [1973, 1981, 0.024007359519600868, "NIL"], [1960, 1961, 0.023458043113350868, "NIL"], [1980, 1980, 0.022578638046979904, "NIL"], [1951, 1959, 0.021881330758333206, "NIL"], [1967, 1973, 0.021433763206005096, "NIL"], [1959, 1959, 0.020871996879577637, "NIL"], [1950, 1957, 0.02087179198861122, "NIL"], [1969, 1972, 0.02046455815434456, "NIL"], [1945, 1946, 0.02022850513458252, "NIL"], [1951, 1954, 0.01889893412590027, "NIL"], [1951, 1962, 0.018837474286556244, "NIL"], [1969, 1978, 0.018539391458034515, "NIL"], [1939, 1943, 0.01785295270383358, "NIL"], [1974, 1980, 0.017630022019147873, "NIL"], [1948, 1956, 0.017486613243818283, "NIL"], [1945, 1945, 0.017194991931319237, "NIL"], [1970, 1978, 0.017036428675055504, "NIL"], [1974, 1981, 0.01648837700486183, "NIL"], [1962, 1972, 0.016449209302663803, "NIL"], [1967, 1978, 0.01615719310939312, "NIL"]], [[1987, 1988, 0.2782766819000244, "DatasetGeneric"], [1997, 1997, 0.2527446746826172, "NIL"], [1999, 1999, 0.24894139170646667, "NIL"], [1991, 1994, 0.240813747048378, "NIL"], [1984, 1986, 0.23064346611499786, "NIL"], [1990, 1994, 0.1984080672264099, "NIL"], [2001, 2001, 0.1556701362133026, "NIL"], [1997, 1999, 0.13726592063903809, "NIL"], [1996, 1997, 0.122630774974823, "NIL"], [1988, 1988, 0.11422339081764221, "NIL"], [1992, 1994, 0.09962058812379837, "NIL"], [1990, 1990, 0.09023415297269821, "NIL"], [1987, 1994, 0.08460770547389984, "NIL"], [1988, 1994, 0.07744303345680237, "NIL"], [1987, 1987, 0.06861506402492523, "NIL"], [1996, 1996, 0.06387962400913239, "NIL"], [1984, 1994, 0.0637880265712738, "NIL"], [1996, 1999, 0.060241080820560455, "NIL"], [1990, 1997, 0.05565395951271057, "NIL"], [1990, 1999, 0.05295726656913757, "NIL"], [1997, 2001, 0.05268856883049011, "NIL"], [1999, 2001, 0.05248750373721123, "NIL"], [1988, 1999, 0.0522734709084034, "NIL"], [1988, 1997, 0.05195869505405426, "NIL"], [1987, 1997, 0.050962019711732864, "NIL"], [1990, 1992, 0.044507190585136414, "NIL"], [1991, 1997, 0.04404444247484207, "NIL"], [1990, 2001, 0.04323926940560341, "NIL"], [1990, 1991, 0.04236530512571335, "NIL"], [1991, 1999, 0.04105597361922264, "NIL"], [1990, 1996, 0.039898939430713654, "NIL"], [1988, 1996, 0.03943720832467079, "NIL"], [1988, 1990, 0.038713496178388596, "NIL"], [1984, 1987, 0.03419351205229759, "NIL"], [1984, 1990, 0.0338013619184494, "NIL"], [1984, 1988, 0.03366287425160408, "NIL"], [1996, 2001, 0.0334259532392025, "NIL"], [1987, 1990, 0.030131354928016663, "NIL"], [1991, 2001, 0.029053837060928345, "NIL"], [1987, 1996, 0.028509989380836487, "NIL"], [1992, 1997, 0.0228219386190176, "NIL"], [1997, 2002, 0.021561669185757637, "NIL"], [2001, 2002, 0.021353766322135925, "NIL"], [1993, 1994, 0.0212511345744133, "NIL"], [1994, 1994, 0.021244868636131287, "NIL"], [1991, 1996, 0.02107413113117218, "NIL"], [1988, 1991, 0.02090091072022915, "NIL"], [1992, 1999, 0.02057088166475296, "NIL"], [1996, 2002, 0.020281817764043808, "NIL"], [1984, 1991, 0.01967121846973896, "NIL"], [1999, 2002, 0.019665507599711418, "NIL"], [1988, 1992, 0.018031399697065353, "NIL"], [1992, 2001, 0.016905194148421288, "NIL"], [1992, 1996, 0.015238049440085888, "NIL"], [1991, 1992, 0.01511294487863779, "NIL"], [1984, 1992, 0.014934776350855827, "NIL"], [1991, 1991, 0.01460693683475256, "NIL"], [1992, 1992, 0.01302170380949974, "NIL"], [1994, 1997, 0.011299265548586845, "NIL"], [1991, 2002, 0.011182116344571114, "NIL"]], [[2014, 2016, 0.448972225189209, "NIL"], [2006, 2006, 0.2480025291442871, "NIL"], [2005, 2005, 0.20210014283657074, "NIL"], [2005, 2006, 0.14223012328147888, "NIL"], [2013, 2016, 0.12278416007757187, "NIL"], [2008, 2008, 0.11983145028352737, "NIL"], [2008, 2010, 0.08953404426574707, "NIL"], [2009, 2010, 0.08426528424024582, "NIL"], [2005, 2008, 0.08370161801576614, "NIL"], [2008, 2009, 0.06934823095798492, "NIL"], [2018, 2020, 0.06426264345645905, "NIL"], [2010, 2010, 0.06363867968320847, "NIL"], [2008, 2016, 0.0626416802406311, "NIL"], [2006, 2016, 0.058009061962366104, "NIL"], [2018, 2022, 0.057726360857486725, "NIL"], [2005, 2016, 0.05504261329770088, "NIL"], [2005, 2010, 0.05149753764271736, "NIL"], [2005, 2009, 0.051410023123025894, "NIL"], [2009, 2016, 0.05113295465707779, "NIL"], [2022, 2022, 0.0486886166036129, "NIL"], [2006, 2010, 0.04509764909744263, "NIL"], [2006, 2008, 0.044921088963747025, "NIL"], [2004, 2005, 0.040372084826231, "NIL"], [2013, 2013, 0.036333583295345306, "NIL"], [2016, 2016, 0.03347112610936165, "NIL"], [2005, 2013, 0.03330010920763016, "NIL"], [2019, 2020, 0.03271365165710449, "NIL"], [2019, 2022, 0.03262114152312279, "NIL"], [2006, 2009, 0.031658824533224106, "NIL"], [2008, 2013, 0.03002726100385189, "NIL"], [2005, 2014, 0.029964629560709, "NIL"], [2014, 2022, 0.029746901243925095, "NIL"], [2008, 2014, 0.02603219263255596, "NIL"], [2018, 2021, 0.024944422766566277, "NIL"], [2015, 2016, 0.024486606940627098, "NIL"], [2014, 2020, 0.023376889526844025, "NIL"], [2009, 2009, 0.023243825882673264, "NIL"], [2004, 2004, 0.02200801484286785, "NIL"], [2008, 2019, 0.02152552828192711, "NIL"], [2018, 2018, 0.019566385075449944, "NIL"], [2008, 2018, 0.019543059170246124, "NIL"], [2014, 2014, 0.01940150558948517, "NIL"], [2010, 2016, 0.019373008981347084, "NIL"], [2006, 2013, 0.019301563501358032, "NIL"], [2013, 2020, 0.01744009181857109, "NIL"], [2004, 2006, 0.01714354194700718, "NIL"], [2014, 2023, 0.016810746863484383, "NIL"], [2018, 2019, 0.016157889738678932, "NIL"], [2009, 2020, 0.015877561643719673, "NIL"], [2006, 2014, 0.015682635828852654, "NIL"], [2020, 2022, 0.015601740218698978, "NIL"], [2013, 2022, 0.015566912479698658, "NIL"], [2004, 2008, 0.01543894037604332, "NIL"], [2020, 2020, 0.015085404738783836, "NIL"], [2022, 2023, 0.014976016245782375, "NIL"], [2013, 2014, 0.0138408113270998, "NIL"], [2019, 2019, 0.013295293785631657, "NIL"], [2014, 2018, 0.012667078524827957, "NIL"], [2018, 2023, 0.012640300206840038, "NIL"], [2014, 2019, 0.012343766167759895, "NIL"]], [[2027, 2028, 0.7578819990158081, "DatasetGeneric"], [2030, 2034, 0.4214409291744232, "Method"], [2040, 2043, 0.31272652745246887, "NIL"], [2031, 2033, 0.28484028577804565, "NIL"], [2037, 2043, 0.2299204170703888, "NIL"], [2031, 2034, 0.206915482878685, "NIL"], [2027, 2034, 0.14096681773662567, "NIL"], [2028, 2028, 0.09719949215650558, "NIL"], [2027, 2027, 0.07342204451560974, "NIL"], [2040, 2042, 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"it", "contains", "examples", "of", "high", "-", "quality", "scientific", "writing", ".", "Hacker", "News", "9", "is", "a", "link", "aggregator", "operated", "by", "Y", "Combinator", ",", "a", "startup", "incubator", "and", "investment", "fund", ".", "Users", "submit", "articles", "defined", "as", "\"", "anything", "that", "gratifies", "one", "'s", "intellectual", "curiosity", ",", "\"", "but", "submitted", "articles", "tend", "to", "focus", "on", "topics", "in", "computer", "science", "and", "entrepreneurship", ".", "Users", "can", "comment", "on", "submitted", "stories", ",", "resulting", "in", "comment", "trees", "discussing", "and", "critiquing", "submitted", "stories", ".", "We", "scrape", ",", "parse", ",", "and", "include", "these", "comment", "trees", "since", "we", "believe", "they", "provide", "high", "quality", "dialogue", "and", "debate", "on", "niche", "topics", ".", "The", "Enron", "Emails", "dataset", "(", "Klimt", "and", "Yang", ",", "2004", ")", "is", "a", "valuable", "corpus", "commonly", "used", "for", "research", "about", "the", "usage", "patterns", "of", "email", ".", "We", "included", "Enron", "Emails", "to", "aid", "in", "understanding", "the", "modality", "of", "email", "communications", ",", "which", "is", "typically", "not", "found", "in", "any", "of", "our", "other", "datasets", ".", "3", "Benchmarking", "Language", "Models", "with", "the", "Pile", "While", "the", "Pile", "was", "conceived", "as", "a", "training", "dataset", "for", "large", "-", "scale", "language", "models", ",", "its", "coverage", "of", "multiple", "disparate", "domains", "makes", "it", "also", "suitable", "as", "an", "evaluation", "dataset", ".", "In", "this", "section", ",", "we", "describe", "how", "the", "Pile", "can", "be", "used", "as", "a", "broad", "-", "coverage", "dataset", "for", "benchmarking", "language", "models", ".", "The", "Pile", "is", "provided", "as", "train", ",", "validation", ",", "and", "testing", "splits", ".", "The", "validation", "and", "testing", "components", "each", "contain", "0.", "1", "%", "of", "the", "data", ",", "sampled", "uniformly", "at", "random", ".", "While", "this", "is", "a", "far", "smaller", "percentage", "than", "most", "datasets", ",", "the", "sheer", "size", "of", "the", "dataset", "results", "in", "over", "1", "GiB", "of", "validation", "and", "testing", "data", "each", ".", "We", "highlight", "that", "while", "we", "have", "made", "efforts", "to", "deduplicate", "documents", "within", "the", "Pile", "(", "See", ":", "Section", "D.2", ")", ",", "it", "is", "still", "possible", "that", "some", "documents", "are", "duplicated", "across", "the", "train", "/", "validation", "/", "test", "splits", ".", "Our", "preferred", "metric", "is", "bits", "per", "UTF-8", "encoded", "byte", "(", "BPB", ")", ".", "Bits", "per", "byte", "is", "preferred", "over", "bits", "per", "character", "or", "perplexity", "when", "using", "Pile", "as", "a", "metric", "due", "to", "its", "invariance", "to", "different", "tokenization", "schemes", "and", "the", "ambiguity", "of", "measuring", "characters", "in", "Unicode", ".", "To", "compute", "bits", "per", "byte", "from", "a", "given", "negative", "log", "likelihood", "loss", ",", "we", "compute", ",", "where", "L", "T", "is", "the", "length", "of", "the", "dataset", "in", "tokens", "and", "L", "B", "is", "the", "length", "of", "the", "dataset", "in", "UTF-8", "encoded", "bytes", ".", "We", "find", "that", "L", "T", "/L", "B", "is", "0.", "29335", "GPT-2tokens", "/", "byte", "across", "the", "Pile", ";", "dataset", "-", "specific", "values", "of", "L", "T", "/L", "B", "can", "be", "found", "in", "Table", "7.", "We", "compute", "the", "test", "perplexity", "of", "the", "constituent", "datasets", "of", "the", "Pile", "using", "GPT-2", "(", "Radford", "et", "al", ".", ",", "2019", ")", "and", "GPT-3", "(", "Brown", "et", "al", ".", ",", "2020", ")", ",", "shown", "in", "Figure", "2.", "We", "use", "all", "available", "versions", "of", "GPT-2", ",", "and", "all", "four", "versions", "of", "GPT-3", "available", "via", "the", "OpenAI", "API", ".", "Because", "of", "the", "cost", "associated", "with", "using", "the", "OpenAI", "API", ",", "we", "evaluate", "on", "one", "-", "tenth", "of", "the", "respective", "test", "sets", "for", "most", "of", "the", "constituent", "datasets", ".", "We", "report", "the", "perplexity", "converted", "to", "bits", "per", "UTF-8", "encoded", "byte", "(", "BPB", ")", ".", "Importantly", ",", "we", "compute", "perplexity", "by", "evaluating", "each", "document", "independently", "within", "each", "dataset", ",", "as", "opposed", "to", "concatenating", "all", "documents", "as", "is", "common", "practice", "for", "computing", "perplexity", "on", "large", "corpora", ".", "Full", "details", "of", "the", "perplexity", "computation", "can", "be", "found", "in", "Appendix", "E.2", ".", "Unsurprisingly", ",", "larger", "language", "models", "generally", "attain", "lower", "perplexity", "compared", "to", "smaller", "models", ".", "Recent", "work", "has", "shown", "an", "increased", "focus", "on", "the", "empirical", "scaling", "laws", "of", "language", "models", "(", "Kaplan", "et", "al", ".", ",", "2020", ";", "Henighan", "et", "al", ".", ",", "2020", ")", ".", "As", "such", ",", "we", "investigate", "the", "scaling", "law", "for", "the", "GPT-2", "and", "GPT-3", "families", "of", "models", "on", "perplexity", "evaluation", "on", "the", "Pile", ".", "The", "scaling", "law", "relation", "for", "the", "GPT-3", "family", "of", "models", "is", "shown", "in", "Figure", "2.", "10", "The", "line", "of", "best", "fit", "shown", "in", "the", "figure", "has", "a", "coefficient", "of", "-", "0.", "1674", "and", "an", "intercept", "of", "2.", "5516", ".", "Interestingly", ",", "while", "GPT-2", "and", "GPT-3", "were", "not", "trained", "on", "the", "Pile", ",", "there", "still", "appears", "to", "be", "a", "clear", "scaling", "law", "without", "diminishing", "returns", ".", "We", "hypothesize", "that", "this", "is", "due", "to", "the", "inherent", "generalization", "capability", "of", "these", "models", ".", "We", "leave", "a", "more", "rigorous", "analysis", "of", "zero", "-", "shot", "scaling", "laws", "to", "future", "work", ".", "Determining", "which", "components", "GPT-3", "underperforms", "on", "provides", "information", "about", "which", "Pile", "components", "are", "most", "dissimilar", "to", "the", "distribution", "of", "text", "(", "web", "pages", "and", "books", ")", "that", "GPT-3", "was", "trained", "on", ".", "These", "components", "would", "thus", "make", "especially", "good", "candidates", "for", "supplementing", "GPT-3", "training", "data", ".", "These", "results", "are", "also", "valuable", "for", "determining", "which", "types", "of", "datasets", "to", "emphasize", "for", "future", "iterations", "of", "the", "Pile", ".", "Due", "to", "the", "difference", "in", "entropy", "of", "different", "datasets", ",", "directly", "comparing", "perplexity", "of", "GPT-3", "on", "different", "Pile", "components", "is", "not", "an", "accurate", "indication", "of", "relative", "performance", ".", "Ideally", "we", "would", "train", "a", "GPT-3", "model", "from", "scratch", "on", "the", "Pile", "and", "compare", "the", "difference", "in", "loss", "per", "dataset", "with", "that", "of", "the", "original", "GPT-3", ".", "Because", "of", "resource", "constraints", ",", "we", "instead", "use", "a", "GPT-2", "model", "trained", "from", "scratch", "on", "the", "Pile", "(", "see", "Section", "4", ")", "to", "construct", "a", "proxy", "measure", ".", "To", "construct", "our", "proxy", ",", "we", "first", "measure", "the", "improvement", "from", "the", "GPT-2", "-", "Pile", "model", "to", "GPT-3", "on", "each", "component", ".", "Then", ",", "we", "normalize", "our", "results", "by", "setting", "the", "change", "on", "OpenWebText2", "to", "be", "zero", ".", "This", "computation", "is", "shown", "in", "the", "equation", "below", ":", "Since", "GPT2", "-", "Pile", "was", "trained", "on", "both", "OWT2", "and", "the", "dataset", "we", "are", "evaluating", ",", "we", "expect", "the", "second", "term", "in", "\u2206", "set", "to", "reflect", "the", "difference", "in", "the", "intrinsic", "difficulty", "of", "the", "two", "datasets", ".", "Thus", "the", "total", "value", "of", "\u2206", "set", "reflects", "how", "much", "harder", "the", "dataset", "we", "are", "evaluating", "was", "for", "GPT-3", "than", "OWT2", ",", "minus", "the", "relative", "difficulty", "of", "the", "two", "tasks", ".", "As", "GPT-3", "was", "trained", "on", "data", "very", "similar", "to", "OWT2", ",", "this", "gives", "us", "a", "proxy", "for", "how", "much", "better", "GPT-3", "would", "do", "if", "it", "were", "trained", "on", "the", "Pile", ".", "The", "results", "are", "shown", "in", "Figure", "3.", "As", "a", "sanity", "check", ",", "we", "observe", "that", "datasets", "that", "are", "contained", "in", ",", "or", "are", "extremely", "similar", "to", ",", "GPT-3", "'s", "training", "set", "(", "Books3", ",", "Wikipedia", "(", "en", ")", ",", "Pile", "-", "CC", "and", "Project", "Gutenberg", ")", "score", "close", "to", "zero", "on", "our", "metric", ".", "GPT-3", "appears", "to", "perform", "poorly", "on", "datasets", "pertaining", "to", "research", "or", "academic", "writing", "like", "PubMed", "Central", ",", "PubMed", "Abstracts", ",", "and", "ArXiv", ";", "domain", "-", "specific", "datasets", "like", "FreeLaw", ",", "Hack", "-", "erNews", ",", "and", "USPTO", "Backgrounds", ";", "and", "on", "datasets", "containing", "predominantly", "text", "distinct", "from", "natural", "language", ",", "like", "GitHub", "and", "DM", "Mathematics", ".", "In", "addition", ",", "the", "majority", "of", "datasets", "see", "less", "of", "an", "improvement", "than", "OpenWebText2", ".", "As", "such", ",", "we", "expect", "a", "GPT-3", "sized", "model", "trained", "on", "Pile", "to", "perform", "significantly", "better", "on", "research", "related", "tasks", ",", "software", "tasks", ",", "and", "symbol", "manipulation", "tasks", "than", "the", "base", "model", ".", "Additionally", ",", "this", "experiment", "provides", "evidence", "that", "the", "majority", "of", "Pile", "components", "are", "not", "redundant", "with", "the", "predominantly", "web", "-", "based", "GPT-3", "training", "data", ".", "We", "note", "that", "this", "metric", "is", "only", "a", "proxy", "for", "similarity", ",", "and", "that", "it", "could", "be", "confounded", "by", "dataset", "specific", "scaling", "effects", ".", "Although", "our", "results", "largely", "accord", "with", "expectations", ",", "there", "are", "some", "puzzling", "results", ",", "like", "the", "datasets", "on", "which", "GPT-3", "outperformed", "GPT-2", "Pile", ".", "We", "hypothesize", "that", "GPT-3", "learns", "to", "be", "so", "good", "at", "these", "datasets", "that", "training", "on", "them", "explicitly", "does", "not", "notably", "benefit", "the", "model", "'s", "performance", ".", "We", "leave", "a", "more", "rigorous", "analysis", "of", "these", "effects", "for", "future", "work", ".", "To", "confirm", "the", "effectiveness", "of", "the", "Pile", "for", "improving", "language", "modeling", "quality", ",", "we", "train", "architecturally", "-", "identical", "1.", "3", "billion", "parameter", "models", "based", "on", "those", "in", "Brown", "et", "al", ".", "(", "2020", ")", "on", "different", "datasets", "and", "evaluate", "on", "the", "WikiText", "and", "LAMBADA", "tasks", "as", "benchmarks", "of", "language", "modeling", "ability", ".", "We", "also", "report", "results", "on", "the", "Pile", "as", "a", "measure", "of", "more", "cross", "-", "domain", "generalization", ".", "To", "ensure", "a", "fair", "comparison", "across", "datasets", "of", "different", "sizes", ",", "we", "decontaminate", "any", "instances", "of", "the", "evaluation", "sets", "using", "the", "same", "13", "-", "gram", "overlap", "filtering", "as", "in", "Brown", "et", "al", ".", "(", "2020", ")", "and", "downsample", "to", "40", "GB", "to", "control", "for", "dataset", "size", ".", "As", "we", "control", "for", "dataset", "size", ",", "we", "emphasize", "that", "our", "evaluation", "is", "generous", "to", "CC-100", "(", "en", ")", ",", "which", "is", "about", "1", "/", "3", "the", "size", "of", "the", "Pile", "in", "reality", ".", "On", "traditional", "language", "modeling", "benchmarks", ",", "the", "Pile", "improves", "significantly", "on", "WikiText", "and", "shows", "negligible", "changes", "in", "LAMBADA", ".", "However", ",", "models", "trained", "on", "Pile", "improve", "significantly", "over", "both", "Raw", "CC", "and", "CC-100", "on", "all", "components", "of", "the", "Pile", ",", "as", "shown", "in", "We", "hypothesize", "that", "this", "is", "due", "to", "the", "perplexity", "based", "filtering", "used", "in", "CC-100", ",", "where", "a", "language", "model", "is", "trained", "on", "Wikipedia", "and", "all", "data", "with", "a", "perplexity", "too", "high", "or", "too", "low", "is", "discarded", ".", "This", "effectively", "discards", "any", "data", "too", "similar", "to", "or", "too", "different", "from", "Wikipedia", ",", "which", "severely", "limits", "the", "diversity", "of", "the", "collected", "data", ".", "This", "result", "suggests", "that", "future", "work", "using", "Common", "Crawl", "should", "take", "caution", "with", "filtering", "to", "preserve", "its", "diversity", ".", "In", "this", "section", ",", "we", "cover", "the", "Structural", "Statistics", "of", "the", "dataset", ",", "which", "provide", "more", "coarse", "-", "grained", "and", "statistical", "information", "about", "the", "Pile", ".", "In", "Sec", "-", "  ", "tion", "6", ",", "we", "provide", "a", "closer", "investigation", "and", "documentation", "of", "the", "textual", "content", "within", "the", "Pile", "datasets", ".", "Each", "dataset", "consists", "of", "a", "large", "number", "of", "documents", ".", "We", "analyze", "the", "distribution", "of", "document", "lengths", ",", "as", "well", "as", "the", "number", "of", "bytes", "-", "per", "-", "token", "using", "the", "GPT-2", "tokenizer", "in", "order", "to", "put", "our", "ablations", "in", "context", ".", "While", "the", "majority", "of", "documents", "in", "the", "Pile", "are", "short", ",", "there", "is", "a", "long", "tail", "of", "very", "long", "documents", "(", "Figure", "5", ")", ".", "While", "only", "13", "%", "of", "the", "world", "'s", "population", "speaks", "English", ",", "the", "vast", "majority", "of", "NLP", "research", "is", "done", "on", "English", ".", "For", "the", "Pile", ",", "we", "took", "a", "similar", "approach", "to", "the", "dataset", "used", "by", "Brown", "et", "al", ".", "(", "2020", ")", "and", "focused", "predominantly", "on", "English", ",", "while", "also", "not", "explicitly", "filtering", "out", "other", "languages", "when", "collecting", "our", "own", "data", ".", "When", "evaluating", "a", "multilingual", "dataset", ",", "our", "main", "criteria", "for", "inclusion", "was", "whether", "the", "English", "component", "of", "the", "dataset", "merited", "inclusion", "alone", ".", "We", "plan", "to", "create", "a", "fully", "multi", "-", "  ", "lingual", "expansion", "of", "the", "Pile", "as", "future", "work", ".", "Using", "fasttext", "(", "Su\u00e1rez", "et", "al", ".", ",", "2019a", ")", ",", "we", "determine", "that", "the", "Pile", "is", "97.4", "%", "English", ".", "We", "note", "that", "due", "to", "issues", "with", "language", "identification", ",", "particularly", "with", "rare", "languages", "Caswell", "et", "al", ".", "(", "2020", ")", ",", "this", "methodology", "provides", "only", "a", "rough", "estimate", "for", "English", "content", "and", "no", "reliable", "conclusions", "for", "low", "-", "resource", "languages", "can", "be", "drawn", ".", "As", "the", "scale", "of", "machine", "learning", "research", "has", "grown", ",", "scrutiny", "has", "been", "placed", "on", "the", "ever", "larger", "datasets", "that", "models", "are", "trained", "on", "(", "Prabhu", "and", "Birhane", ",", "2020", ";", "Biderman", "and", "Scheirer", ",", "2020", ")", "While", "this", "issue", "has", "been", "raised", "within", "AI", "ethics", "and", "bias", "research", "(", "Hovy", "and", "Spruit", ",", "2016", ";", "Hutchinson", "et", "al", ".", ",", "2020", ";", "Blodgett", "et", "al", ".", ",", "2020", ")", ",", "it", "has", "not", "been", "a", "focal", "point", "of", "concern", "within", "the", "language", "modeling", "community", ".", "Despite", "the", "proliferation", "of", "work", "exploring", "and", "documenting", "issues", "with", "datasets", "(", "Gebru", "et", "al", ".", ",", "2018", ";", "Bender", "and", "Friedman", ",", "2018", ";", "Jo", "and", "Gebru", ",", "2020", ")", ",", "no", "dataset", "intended", "to", "train", "massive", "language", "models", "has", "been", "seriously", "documented", "by", "its", "creators", "12", ".", "Therefore", ",", "our", "analyses", "serve", "two", "goals", ":", "to", "address", "ethical", "concerns", "about", "the", "Pile", ",", "and", "to", "promote", "and", "normalize", "the", "practice", "of", "engaging", "with", "the", "AI", "ethics", "literature", ".", "Natural", "language", "processing", "technologies", "are", "widely", "applicable", "and", "can", "be", "used", "in", "extremely", "different", "contexts", ".", "What", "is", "and", "is", "not", "appropriate", "data", "to", "train", "on", "can", "therefore", "vary", "wildly", "with", "the", "application", "context", ".", "In", "our", "view", ",", "the", "best", "approach", "is", "to", "document", "rather", "than", "eliminate", "potentially", "concerning", "aspects", "of", "datasets", "13", ",", "particularly", "since", "the", "purpose", "of", "the", "Pile", "is", "to", "train", "general", "-", "purpose", "language", "models", ".", "The", "primary", "goal", "of", "our", "documentation", ",", "therefore", ",", "is", "to", "empower", "NLP", "researchers", "to", "make", "informed", "decisions", ".", "To", "document", "the", "Pile", ",", "we", "chose", "to", "implement", "two", "frameworks", "that", "have", "been", "proposed", "by", "methodologists", "and", "ethics", "researchers", ".", "The", "first", ",", "the", "datasheets", "methodology", "(", "Gebru", "et", "al", ".", ",", "2018", ")", ",", "is", "a", "general", "purpose", "methodology", "that", "is", "recommended", "by", "several", "methodologists", "(", "Raji", "and", "Yang", ",", "2019", ";", "Biderman", "and", "Scheirer", ",", "2020", ")", "and", "appears", "to", "be", "used", "more", "frequently", "by", "practitioners", "than", "alterna", "-", "tives", "(", "Seck", "et", "al", ".", ",", "2018", ";", "Costa", "-", "juss\u00e0", "et", "al", ".", ",", "2020", ";", "Thieme", "et", "al", ".", ",", "2020", ")", ".", "The", "second", ",", "the", "data", "statements", "methodology", "(", "Bender", "and", "Friedman", ",", "2018", ")", ",", "was", "proposed", "specifically", "for", "natural", "language", "processing", "and", "has", "been", "well", "received", "by", "the", "NLP", "community", ".", "Our", "datasheet", "and", "data", "statement", "will", "be", "featured", "in", "the", "GitHub", "repository", "where", "the", "code", "for", "the", "Pile", "is", "stored", "and", "will", "also", "be", "available", "as", "separate", "documents", "on", "arXiv", "(", "Biderman", "et", "al", ".", ",", "2021", ";", "Biderman", ",", "2021", ")", ".", "In", "addition", "to", "the", "datasheet", "and", "data", "statement", ",", "there", "is", "additional", "information", "that", "may", "be", "helpful", "to", "people", "training", "language", "models", "that", "these", "documents", "do", "not", "cover", ".", "In", "the", "rest", "of", "this", "section", "we", "investigate", "and", "document", "in", "greater", "detail", "some", "of", "this", "additional", "contextual", "information", ".", "In", "order", "to", "better", "understand", "the", "specific", "subject", "matter", "covered", "by", "the", "Pile", ",", "we", "performed", "a", "topic", "modeling", "analysis", "on", "its", "components", ".", "Using", "Gensim", "(", "Rehurek", "et", "al", ".", ",", "2011", ")", ",", "we", "trained", "16", "-", "topic", "Latent", "Dirichlet", "Allocation", "(", "Blei", "et", "al", ".", ",", "2003", ")", "models", "on", "each", "component", "of", "the", "validation", "set", "of", "the", "Pile", "concurrently", ",", "in", "an", "online", "fashion", "(", "Hoffman", "et", "al", ".", ",", "2010", ")", ".", "We", "filtered", "the", "Pile", "for", "English", "only", "for", "this", "analysis", ".", "Afterwards", ",", "we", "computed", "the", "perplexity", "of", "the", "Common", "Crawl", "-", "derived", "(", "Pile", "-", "CC", ")", "topic", "model", "on", "the", "document", "sets", "of", "the", "other", "components", ".", "In", "this", "way", ",", "we", "provide", "a", "rough", "measure", "of", "the", "degree", "to", "which", "parts", "of", "the", "Pile", "contain", "topics", "not", "well", "covered", "within", "Common", "Crawl", ".", "In", "Figure", "7", ",", "these", "cross", "-", "component", "perplexities", "are", "shown", ",", "with", "a", "vertical", "line", "indicating", "the", "perplexity", "of", "the", "Pile", "-", "CC", "topic", "model", "evaluated", "on", "the", "documents", "of", "OpenWebText2", ".", "This", "component", "was", "chosen", "as", "a", "baseline", "of", "comparison", "for", "similar", "reasons", "as", "in", "the", "previous", "evaluation", ":", "it", "is", "derived", "in", "a", "similar", "manner", "(", "filtered", "crawls", "of", "the", "open", "web", ")", "as", "the", "Common", "Crawl", ",", "and", "thus", "is", "expected", "to", "contain", "a", "similar", "distribution", "of", "topics", ".", "Although", "Pile", "-", "CC", "is", "somewhat", "diverse", "in", "its", "content", ",", "several", "of", "the", "Pile", "'s", "other", "components", "deviate", "from", "it", "strongly", "in", "their", "topical", "focus", ",", "as", "evidenced", "by", "higher", "perplexity", "on", "Github", ",", "PhilPapers", ",", "and", "EuroParl", ".", "We", "also", "documented", "the", "topical", "clusters", "inferred", "from", "our", "LDA", "models", "for", "each", "component", ",", "which", "we", "provide", "in", "Appendix", "C", ".", "As", "expected", ",", "though", "the", "larger", "CC", "-", "derived", "component", "itself", "represents", "a", "diversity", "of", "content", "-", "including", "politics", ",", "education", ",", "sports", "and", "entertainment", "-", "the", "content", "clusters", "it", "misses", "become", "apparent", "when", "compared", "qualitatively", "to", "other", "components", "of", "the", "Pile", ".", "Notably", ",", "the", "data", "modes", "covering", "programming", ",", "logic", ",", "physics", ",", "and", "legal", "knowledge", "appear", "largely", "absent", ".", "Due", "to", "the", "wide", "diversity", "in", "origins", ",", "it", "is", "possible", "for", "the", "Pile", "to", "contain", "pejorative", ",", "sexually", "explicit", ",", "or", "otherwise", "objectionable", "content", ".", "As", "this", "content", "may", "not", "be", "desirable", "for", "some", "use", "cases", ",", "we", "break", "down", "profanity", "on", "a", "per", "-", "dataset", "level", ".", "We", "used", "the", "profanity", "-", "checker", "Python", "package", "(", "Zhou", ",", "2019", ")", ".", "This", "package", "includes", "a", "\"", "toxicity", "model", "\"", "trained", "on", "multiple", "profanity", "lists", "as", "well", "as", "the", "Wikidetox", "Toxic", "Comment", "Dataset", "(", "Wulczyn", "et", "al", ".", ",", "2016", ")", "and", "classifies", "a", "given", "string", "as", "being", "profane", "or", "not", "profane", ".", "We", "considered", "only", "the", "English", "sentences", "in", "each", "dataset", "using", "the", "same", "language", "classifier", "from", "Section", "3.", "7", ".", "We", "did", "this", "since", "profanity", "-", "checker", "is", "built", "for", "English", "and", "other", "languages", "may", "improperly", "impact", "the", "results", ".", "For", "instance", ",", "the", "German", "nominative", "/", "accusative", "feminine", "/", "plural", "definite", "article", "\"", "die", "\"", "is", "flagged", "as", "being", "profane", "regardless", "of", "context", ".", "We", "split", "each", "sentence", "into", "words", "and", "computed", "the", "percentage", "of", "words", "that", "are", "flagged", "as", "profane", "for", "each", "component", "of", "the", "Pile", ".", "We", "emphasize", "that", "this", "methodology", "is", "only", "a", "proxy", "for", "profanity", ",", "given", "the", "complexity", "of", "determining", "whether", "a", "given", "word", "or", "phrase", "is", "profane", "in", "context", ".", "As", "shown", "in", "Figure", "8", ",", "the", "Pile", "as", "a", "whole", "appears", "less", "profane", "than", "Pile", "-", "CC", ".", "Further", ",", "the", "majority", "of", "Pile", "components", "appear", "less", "profane", "than", "Pile", "-", "CC", "as", "well", ".", "We", "also", "broke", "each", "dataset", "down", "on", "a", "sentence", "level", ",", "to", "allow", "profanity", "-", "checker", "to", "check", "entire", "sentences", ".", "Splitting", "datasets", "by", "sentence", "allows", "for", "additional", "context", "to", "be", "considered", "when", "determining", "whether", "content", "is", "pejorative", ".", "Our", "results", "are", "shown", "in", "Figure", "12", ".", "As", "language", "models", "may", "pick", "up", "unexpected", "biases", "from", "the", "training", "data", ",", "we", "performed", "a", "preliminary", "analysis", "of", "the", "different", "components", "that", "make", "up", "the", "Pile", ".", "Because", "models", "with", "different", "characteristics", "may", "be", "trained", "on", "the", "Pile", ",", "we", "aimed", "to", "document", "the", "biases", "of", "the", "data", "and", "not", "a", "specific", "model", ".", "We", "primarily", "focus", "on", "co", "-", "occurrence", "tests", ",", "where", "we", "analyzed", "what", "words", "occur", "in", "the", "same", "sentence", "as", "other", "specific", "words", ".", "Using", "this", "information", ",", "we", "can", "estimate", "what", "words", "strongly", "bias", "towards", "a", "category", "word", ",", "as", "well", "as", "calculate", "the", "general", "sentiment", "of", "surrounding", "words", ".", "We", "focused", "our", "analysis", "on", "gender", ",", "religion", ",", "and", "race", ".", "Our", "goal", "is", "to", "provide", "users", "of", "this", "dataset", "with", "preliminary", "guidance", "on", "how", "the", "different", "components", "are", "biased", "so", "that", "they", "can", "make", "decisions", "on", "which", "components", "to", "train", "on", ".", "All", "tables", "and", "figures", "in", "this", "section", "can", "be", "found", "in", "the", "Appendix", ".", "We", "computed", "gender", "associations", "by", "computing", "cooccurrences", "for", "binary", "pronouns", ".", "For", "each", "word", ",", "we", "computed", "the", "difference", "in", "the", "rate", "it", "co", "-", "occurs", "with", "\"", "he", "\"", "and", "\"", "she", "\"", "14", "and", "weighed", "it", "by", "the", "square", "root", "of", "its", "frequency", ".", "We", "report", "the", "top", "15", "most", "biased", "adjectives", "or", "adverbs", "(", "Loper", "and", "Bird", ",", "2002", ")", "for", "each", "in", "Table", "10", ".", "We", "see", "that", "words", "like", "\"", "military", "\"", ",", "\"", "criminal", "\"", ",", "and", "\"", "offensive", "\"", "strongly", "bias", "towards", "men", ",", "while", "\"", "little", "\"", ",", "\"", "married", "\"", ",", "\"", "sexual", "\"", ",", "and", "\"", "happy", "\"", "bias", "towards", "women", ".", "In", "addition", ",", "we", "computed", "the", "average", "sentiment", "(", "Baccianella", "et", "al", ".", ",", "2010", ")", "of", "words", "cooccurring", "with", "the", "gendered", "pronouns", "across", "each", "dataset", "in", "Figure", "13", ".", "Generally", ",", "we", "find", "no", "significant", "sentiment", "bias", "towards", "men", "or", "women", ".", "This", ",", "of", "course", ",", "does", "not", "mean", "that", "the", "dataset", "is", "free", "of", "gender", "bias", "(", "as", "our", "co", "-", "occurrence", "tests", "show", ")", ".", "We", "computed", "a", "similar", "co", "-", "occurrence", "analysis", "for", "religion", ",", "which", "can", "be", "found", "in", "Table", "11", ".", "Like", "gender", ",", "we", "find", "that", "these", "co", "-", "occurrences", "reflect", "how", "these", "terms", "are", "used", "in", "pockets", "of", "online", "discourse", ".", "For", "example", ",", "\"", "radical", "\"", "co", "-", "occurs", "with", "\"", "muslim", "\"", "at", "a", "high", "rate", ",", "while", "\"", "rational", "\"", "often", "co", "-", "occurs", "with", "\"", "atheist", "\"", ".", "This", "analysis", "also", "demonstrates", "some", "of", "the", "limitations", "of", "a", "purely", "co", "-", "occurrence", "based", "analysis", ".", "For", "example", ",", "\"", "religious", "\"", "often", "co", "-", "occurs", "with", "\"", "atheist", "\"", ",", "which", "likely", "reflects", "the", "type", "of", "conversations", "in", "which", "the", "word", "\"", "atheist", "\"", "is", "likely", "to", "occur", "as", "opposed", "to", "a", "descriptor", "of", "\"", "atheist", "\"", ".", "In", "addition", ",", "we", "computed", "the", "average", "sentiment", "of", "co", "-", "occurrences", "across", "each", "of", "the", "constituent", "datasets", "in", "Figure", "14", ".", "Over", "the", "entire", "dataset", ",", "we", "find", "that", "\"", "Buddhist", "\"", "has", "the", "highest", "sentiment", ",", "followed", "by", "\"", "Hindu", "\"", ",", "\"", "Christian", "\"", ",", "\"", "Atheist", "\"", ",", "and", "\"", "Muslim", "\"", ".", "Notably", ",", "\"", "Jew", "\"", "is", "the", "lowest", ",", "perhaps", "reflecting", "its", "historical", "use", "as", "a", "pejorative", ".", "Finally", ",", "we", "ran", "the", "same", "analysis", "for", "racial", "groups", ".", "Here", ",", "as", "identifiers", "like", "\"", "black", "\"", "or", "\"", "white", "\"", "often", "do", "not", "indicate", "race", ",", "we", "instead", "compute", "co", "-", "occurences", "with", "phrases", "like", "\"", "black", "man", "\"", "or", "\"", "white", "woman", "\"", ".", "We", "show", "the", "top", "15", "most", "biased", "words", "for", "each", "demographic", "in", "Table", "12", ".", "Once", "again", ",", "we", "found", "that", "the", "co", "-", "occurrences", "reflect", "the", "context", "in", "which", "these", "terms", "are", "used", ".", "For", "example", ",", "the", "4", "most", "biased", "words", "for", "\"", "black", "\"", "are", "\"", "unarmed", "\"", ",", "\"", "civil", "\"", ",", "\"", "criminal", "\"", ",", "and", "\"", "scary", "\"", ".", "Similar", "to", "above", ",", "we", "compute", "the", "average", "sentiment", "of", "co", "-", "occurring", "words", ".", "We", "report", "the", "average", "sentiment", "numbers", "in", "Table", "13", ".", "We", "find", "that", "\"", "hispanic", "/", "latino", "\"", "narrowly", "edges", "out", "\"", "asian", "\"", "for", "the", "highest", "sentiment", ",", "followed", "by", "\"", "white", "\"", ".", "On", "the", "other", "hand", ",", "\"", "black", "\"", "had", "the", "lowest", "sentiment", ",", "at", "-", "0.", "15", ".", "We", "note", "that", "for", "all", "demographics", ",", "the", "average", "sentiment", "is", "negative", ".", "We", "hypothesize", "that", "this", "is", "due", "to", "the", "specific", "context", "for", "which", "the", "phrases", "we", "use", "to", "compute", "co", "-", "occurrences", "appear", ".", "For", "example", ",", "it", "is", "often", "quite", "common", "for", "news", "articles", "to", "describe", "suspects", "as", "an", "\"", "asian", "man", "\"", ".", "Another", "issue", "with", "the", "use", "of", "texts", "in", "natural", "language", "processing", "research", "is", "consent", ".", "Although", "one", "is", "typically", "not", "legally", "obligated", "to", "receive", "the", "permission", "of", "an", "author", "to", "train", "a", "NLP", "algorithm", "on", "their", "work", "15", ",", "many", "consider", "doing", "so", "a", "moral", "obli", "-", "gation", "or", "a", "good", "measure", "to", "guard", "against", "misuse", "(", "Obar", ",", "2020", ";", "Prabhu", "and", "Birhane", ",", "2020", ")", ".", "On", "the", "other", "hand", ",", "there", "is", "significant", "disagreement", "surrounding", "the", "ethics", "of", "repurposing", "data", "protected", "by", "terms", "of", "service", "in", "research", "contexts", "(", "Vitak", "et", "al", ".", ",", "2016", ";", "Fiesler", "et", "al", ".", ",", "2020", ")", ",", "particularly", "given", "the", "power", "asymmetries", "inherent", "in", "digital", "platforms", ",", "which", "often", "close", "off", "independent", "researchers", "from", "investigating", "public", "data", "while", "simultaneously", "compelling", "users", "to", "consent", "to", "its", "private", "use", "(", "Halavais", ",", "2019", ")", ".", "While", "much", "of", "the", "Pile", "'s", "data", "comes", "from", "sources", "that", "have", "expressly", "consented", "to", "its", "wider", "dissemination", "and", "use", "in", "research", ",", "researchers", "often", "fail", "to", "clearly", "document", "where", "their", "data", "came", "from", "and", "under", "what", "terms", "its", "use", "was", "consented", "to", ".", "In", "light", "of", "this", ",", "we", "felt", "it", "appropriate", "to", "release", "the", "Pile", "with", "transparency", "around", "how", "the", "authors", "of", "its", "data", "have", "indicated", "that", "that", "data", "can", "be", "used", ".", "To", "provide", "needed", "nuance", "to", "our", "discussion", "of", "consent", ",", "we", "identified", "three", "tiers", "of", "availability", "for", "public", "use", ".", "Public", "data", "is", "data", "which", "is", "freely", "and", "readily", "available", "on", "the", "internet", ".", "This", "primarily", "excludes", "data", "which", "is", "pay", "-", "walled", "(", "regardless", "of", "how", "easy", "that", "paywall", "is", "to", "bypass", ")", "and", "data", "which", "can", "not", "be", "easily", "obtained", "but", "can", "be", "obtained", ",", "e.g.", "through", "a", "torrent", "or", "on", "the", "dark", "web", ".", "Terms", "of", "Service", "(", "ToS", ")", "compliant", "data", "is", "data", "which", "is", "obtained", "and", "used", "in", "a", "fashion", "that", "is", "known", "to", "be", "consistent", "with", "the", "terms", "of", "service", "of", "the", "data", "host", ".", "Data", "with", "authorial", "consent", "is", "data", "for", "which", "the", "original", "authors", "of", "the", "work", "consented", "to", "the", "use", "of", "their", "data", ",", "or", "where", "a", "reasonable", "person", "could", "not", "assume", "that", "their", "data", "would", "not", "be", "used", "for", "purposes", "such", "as", "research", ".", "ToS", "compliant", "data", "and", "authorial", "consented", "data", "differ", "in", "two", "main", "ways", ":", "It", "is", "important", "to", "keep", "in", "mind", "that", "people", "typically", "do", "not", "read", "Terms", "of", "Service", ",", "and", "additionally", "that", "being", "ToS", "-", "compliant", "does", "not", "entail", "authorial", "consent", ".", "We", "adopted", "a", "strict", "model", "of", "consent", ",", "where", "ambiguous", "or", "unknown", "consent", "is", "treated", "as", "nonconsensual", ".", "Table", "5", "summarizes", "our", "understanding", "of", "the", "status", "of", "each", "of", "the", "datasets", "within", "the", "Pile", ".", "Datasets", "marked", "with", "a", "are", "compliant", "in", "the", "relevant", "respects", ",", "though", "a", "couple", "datasets", "are", "worth", "remarking", "on", "in", "particular", ".", "Book3", "and", "OpenSubtitles", "are", "being", "used", "in", "a", "fashion", "that", "is", "consistent", "with", "the", "terms", "of", "service", "of", "the", "data", "host", ".", "However", ",", "this", "is", "somewhat", "misleading", "in", "that", "the", "data", "host", "is", "not", "authorized", "to", "post", "the", "data", "online", "by", "the", "parties", "that", "own", "it", ".", "The", "Enron", "Emails", "dataset", "was", "not", "collected", "with", "the", "permission", "of", "the", "authors", ",", "but", "was", "collected", "by", "the", "U.S", ".", "government", "as", "part", "of", "a", "criminal", "investigation", ".", "While", "the", "people", "whose", "emails", "are", "in", "the", "Enron", "dataset", "are", "aware", "of", "this", "fact", ",", "they", "were", "not", "given", "the", "ability", "to", "consent", "to", "its", "inclusion", "in", "any", "way", ".", "There", "are", "five", "datasets", "included", "in", "the", "Pile", "that", "were", "not", "collected", "and", "distributed", "in", "a", "ToS", "compliant", "fashion", "and", "for", "which", "the", "authors", "had", "no", "ability", "to", "consent", "to", "their", "data", "being", "used", ".", "Each", "of", "these", "datasets", "are", "widely", "used", ",", "both", "in", "the", "NLP", "literature", "and", "the", "world", "at", "large", ".", "With", "the", "exception", "of", "the", "YouTube", "Subtitles", "dataset", ",", "each", "of", "these", "datasets", "were", "published", "by", "researchers", "and", "are", "passed", "around", "freely", "on", "the", "internet", ".", "The", "YouTube", "Subtitles", "dataset", "was", "created", "by", "us", "for", "this", "project", ",", "using", "a", "very", "popular", "unofficial", "API", "that", "is", "both", "widely", "used", "and", "easily", "obtainable", "on", "Pip", ",", "Conda", ",", "and", "GitHub", ",", "among", "other", "places", ".", "Given", "the", "processing", "applied", "and", "the", "difficulty", "of", "identifying", "particular", "files", "in", "the", "Pile", ",", "we", "feel", "that", "our", "use", "of", "these", "datasets", "does", "not", "constitute", "significantly", "increased", "harm", "beyond", "that", "which", "has", "already", "been", "done", "by", "the", "widespread", "publication", "of", "these", "datasets", ".", "The", "Pile", "represents", "yet", "another", "stepping", "stone", "along", "the", "path", "of", "scaling", "models", "and", "datasets", "to", "ever", "larger", "sizes", "and", "capabilities", ".", "There", "are", "many", "serious", "concerns", "about", "how", "the", "emergence", "of", "progressively", "stronger", "AI", "systems", "will", "influence", "the", "wider", "world", "(", "Brundage", "et", "al", ".", ",", "2018", ";", "Amodei", "et", "al", ".", ",", "2016", ";", "Bostrom", "and", "Yudkowsky", ",", "2014", ";", "Bostrom", ",", "2014", ";", "Critch", "and", "Krueger", ",", "2020", ")", ",", "and", "we", "believe", "that", "they", "merit", "serious", "thought", ".", "In", "this", "section", "we", "discuss", "the", "legal", "ramifications", "of", "the", "Pile", ",", "and", "then", "consider", "the", "impact", "of", "the", "Pile", "to", "AI", "alignment", "from", "two", "angles", ":", "accelerating", "AI", "timelines", "and", "the", "dangers", "posed", "by", "unaligned", "language", "models", ".", "While", "the", "machine", "learning", "community", "has", "begun", "to", "discuss", "the", "issue", "of", "the", "legality", "of", "training", "models", "on", "copyright", "data", ",", "there", "is", "little", "acknowledgment", "of", "the", "fact", "that", "the", "processing", "and", "distribution", "of", "data", "owned", "by", "others", "may", "also", "be", "a", "violation", "of", "copyright", "law", ".", "As", "a", "step", "in", "that", "direc", "-", "tion", ",", "we", "discuss", "the", "reasons", "we", "believe", "that", "our", "use", "of", "copyright", "data", "is", "in", "compliance", "with", "US", "copyright", "law", ".", "16", "Under", "pre", "(", "1984", ")", "(", "and", "affirmed", "in", "subsequent", "rulings", "such", "as", "aff", "(", "2013", ")", ";", "Google", "(", "2015", ")", ")", ",", "noncommercial", ",", "not", "-", "for", "-", "profit", "use", "of", "copyright", "media", "is", "preemptively", "fair", "use", ".", "Additionally", ",", "our", "use", "is", "transformative", ",", "in", "the", "sense", "that", "the", "original", "form", "of", "the", "data", "is", "ineffective", "for", "our", "purposes", "and", "our", "form", "of", "the", "data", "is", "ineffective", "for", "the", "purposes", "of", "the", "original", "documents", ".", "Although", "we", "use", "the", "full", "text", "of", "copyright", "works", ",", "this", "is", "not", "necessarily", "disqualifying", "when", "the", "full", "work", "is", "necessary", "(", "ful", ",", "2003", ")", ".", "In", "our", "case", ",", "the", "long", "-", "term", "dependencies", "in", "natural", "language", "require", "that", "the", "full", "text", "be", "used", "in", "order", "to", "produce", "the", "best", "results", "(", "Dai", "et", "al", ".", ",", "2019", ";", "Rae", "et", "al", ".", ",", "2019", ";", "Henighan", "et", "al", ".", ",", "2020", ";", "Liu", "et", "al", ".", ",", "2018", ")", ".", "Copyright", "law", "varies", "by", "country", ",", "and", "there", "may", "be", "16", "This", "discussion", "does", "not", ",", "and", "is", "not", "intended", "to", ",", "constitute", "legal", "advice", ";", "rather", ",", "it", "is", "a", "general", "discussion", "of", "law", ".", "Only", "your", "attorney", "can", "provide", "assurances", "that", "the", "information", "contained", "herein", "is", "applicable", "or", "appropriate", "to", "a", "particular", "situation", ".", "If", "in", "doubt", ",", "it", "is", "always", "advisable", "to", "speak", "to", "an", "intellectual", "property", "attorney", ".", "additional", "restrictions", "on", "some", "of", "these", "works", "in", "particular", "jurisdictions", ".", "To", "enable", "easier", "compliance", "with", "local", "laws", ",", "the", "Pile", "reproduction", "code", "is", "available", "and", "can", "be", "used", "to", "exclude", "certain", "components", "of", "the", "Pile", "which", "are", "inappropriate", "for", "the", "user", ".", "Unfortunately", ",", "we", "do", "not", "have", "the", "metadata", "necessary", "to", "determine", "exactly", "which", "texts", "are", "copyrighted", ",", "and", "so", "this", "can", "only", "be", "undertaken", "at", "the", "component", "level", ".", "Thus", ",", "this", "should", "be", "be", "taken", "to", "be", "a", "heuristic", "rather", "than", "a", "precise", "determination", ".", "There", "is", "serious", "concern", "that", "AI", "systems", "may", "soon", "be", "meaningfully", "more", "capable", "than", "humans", "in", "all", "relevant", "economic", "tasks", "(", "Grace", "et", "al", ".", ",", "2018", ";", "Yudkowsky", ",", "2013", ")", ".", "Relatedly", ",", "there", "are", "serious", "unresolved", "questions", "surrounding", "how", "to", "properly", "align", "such", "powerful", "AI", "systems", "with", "human", "interests", "(", "Bostrom", "and", "Yudkowsky", ",", "2014", ";", "Russell", ",", "2019", ";", "Bostrom", ",", "2014", ";", "Amodei", "et", "al", ".", ",", "2016", ")", "and", "generally", "avoid", "morally", "catastrophic", "outcomes", "(", "Sotala", "and", "Gloor", ",", "2017", ";", "Shulman", "and", "Bostrom", ",", "2020", ")", ".", "As", "such", ",", "it", "has", "been", "argued", "that", "accelerating", "the", "development", "of", "such", "powerful", "AI", "systems", "may", "be", "undesirable", "before", "these", "concerns", "have", "been", "more", "adequately", "addressed", "(", "Bostrom", ",", "2014", ")", ".", "There", "are", "several", "pragmatic", "responses", "to", "this", "view", ":", "1.", "Due", "to", "human", "competition", ",", "curiosity", ",", "and", "cultural", "diversity", ",", "halting", "technological", "development", "is", "incredibly", "difficult", ",", "if", "not", "impossible", ".", "(", "Russell", ",", "2019", ")", "(", "Critch", "and", "Krueger", ",", "2020", ")", "The", "alignment", "problem", "can", "only", "be", "solved", "through", "development", ",", "testing", "and", "(", "hopefully", "non", "-", "existential", ")", "failure", ".", "3.", "High", "powered", "language", "models", ",", "along", "with", "their", "more", "general", "successors", ",", "must", "be", "capable", "of", "viewing", "morally", "problematic", "content", "without", "adopting", "it", "in", "their", "output", ".", "We", "elaborate", "on", "this", "in", "the", "following", "section", ".", "With", "this", "in", "mind", ",", "we", "accept", "the", "reality", "that", "the", "Pile", "could", "potentially", "accelerate", "AI", "timelines", ".", "However", ",", "we", "hope", "our", "efforts", "to", "establish", "best", "practices", ",", "such", "as", "thoroughly", "documenting", "the", "contents", "of", "our", "data", ",", "will", "help", "encourage", "diligence", "for", "downstream", "researchers", "on", "alignment", "problems", ".", "There", "has", "been", "much", "discussion", "about", "the", "possible", "negative", "effects", "of", "powerful", "language", "models", "in", "the", "world", "(", "Brown", "et", "al", ".", ",", "2020", ";", "Brundage", "et", "al", ".", ",", "2018", ")", ".", "Some", "of", "these", "possible", "problems", ",", "such", "as", "the", "ability", "to", "mass", "produce", "low", "quality", "content", "for", "the", "purpose", "of", "Search", "Engine", "Optimization", ",", "are", "inherent", "problems", "to", "the", "way", "online", "content", "is", "distributed", ",", "and", "can", "not", "be", "stopped", "by", "those", "developing", "language", "models", "alone", ".", "Directly", "solving", "these", "problems", "would", "require", "sweeping", "changes", "to", "the", "architecture", "of", "the", "Internet", ",", "such", "as", "vastly", "expanded", "Public", "Key", "Infrastructure", "and", "distributed", "authentication", "of", "identity", "(", "Ferguson", "and", "Schneier", ",", "2003", ")", ".", "Another", "concern", "is", "that", "training", "such", "models", "on", "huge", "datasets", "will", "almost", "inevitably", "require", "them", "to", "have", "undesirable", "content", "in", "their", "training", "sets", ",", "such", "as", "that", "promoting", "hateful", "stereotypes", "(", "Christian", ",", "2020", ")", ".", "Having", "models", "output", "undesirable", "content", "is", ",", "by", "definition", ",", "undesirable", ",", "but", "we", "believe", "that", "attacking", "this", "problem", "from", "the", "training", "set", "side", "is", "unproductive", "and", "ultimately", "leads", "us", "away", "from", "optimal", "solutions", ".", "If", "a", "person", "reads", "a", "racist", "piece", "of", "content", ",", "they", "do", "not", "then", "immediately", "adopt", "its", "racist", "views", "-", "they", "may", "be", "capable", "of", "doing", "so", ",", "but", "can", "decide", "not", "to", ".", "This", "capacity", "to", "understand", "undesirable", "content", "and", "then", "decide", "to", "ignore", "it", "is", "an", "essential", "future", "research", "direction", ".", "Not", "only", "would", "this", "allow", "models", "to", "use", "\"", "dirtier", "\"", "data", "with", "less", "concern", ",", "but", "also", "to", "use", "their", "gained", "knowledge", "to", "better", "understand", "what", "not", "to", "do", ".", "We", "recognize", "that", ",", "despite", "recent", "progress", "in", "human", "-", "guided", "learning", "(", "Stiennon", "et", "al", ".", ",", "2020", ")", ",", "the", "technology", "is", "not", "yet", "at", "this", "stage", ",", "and", "have", "thus", "made", "a", "number", "of", "editorial", "decisions", "as", "described", "in", "this", "paper", ".", "However", ",", "this", "approach", "seems", "essential", "to", "the", "future", "of", "these", "models", "and", "AI", "more", "broadly", ",", "and", "more", "research", "is", "needed", ".", "Self", "-", "supervised", "training", "of", "natural", "language", "processing", "models", "on", "large", ",", "unlabeled", "text", "corpora", ",", "has", "seen", "widespread", "adoption", "in", "the", "field", ".", "Word", "representation", "models", "such", "as", "GloVe", "(", "Pennington", "et", "al", ".", ",", "2014", ")", "and", "word2vec", "(", "Mikolov", "et", "al", ".", ",", "2013", ")", "were", "trained", "on", "datasets", "such", "as", "Wikipedia", ",", "Gigaword", "(", "Graff", "et", "al", ".", ",", "2003", ")", ",", "or", "a", "non", "-", "public", "Google", "News", "corpus", ".", "More", "recently", ",", "language", "models", "(", "Radford", "et", "al", ".", ",", "2018", "(", "Radford", "et", "al", ".", ",", ",", "2019", ";", ";", "Brown", "et", "al", ".", ",", "2020", ";", "Rosset", ",", "2019", ";", "Shoeybi", "et", "al", ".", ",", "2019", ")", "and", "masked", "language", "models", "(", "Devlin", "et", "al", ".", ",", "2019", ";", "Liu", "et", "al", ".", ",", "2019", ";", "Raffel", "et", "al", ".", ",", "2019", ")", ",", "2019", ")", ".", "C4", "is", "comparably", "-", "sized", "to", "the", "Pile", ",", "while", "mC4", "and", "CC-100", "are", "larger", ",", "multilingual", "datasets", ".", "However", ",", "C4", "/", "mC4", "require", "immense", "computational", "resources", "to", "preprocess", "the", "data", ",", "with", "its", "maintainers", "even", "recommending", "the", "use", "of", "a", "distributed", "cloud", "service", ",", "17", "setting", "a", "high", "bar", "of", "entry", "to", "using", "these", "datasets", ".", "CC-100", "is", "directly", "downloadable", "and", "pre", "-", "cleaned", ";", "however", ",", "its", "English", "portion", "is", "much", "smaller", "than", "the", "Pile", ".", "Importantly", ",", "these", "three", "datasets", "are", "all", "derived", "entirely", "from", "Common", "Crawl", "-", "as", "discussed", "above", ",", "the", "current", "best", "practice", "in", "training", "largescale", "language", "models", "involve", "using", "both", "large", "web", "scrapes", "and", "more", "targeted", ",", "higher", "-", "quality", "datasets", ",", "which", "the", "Pile", "directly", "addresses", ".", "Leo", "Gao", "led", "the", "project", ",", "implemented", "the", "main", "Pile", "codebase", ",", "contributed", "to", "the", "model", "training", "code", ",", "performed", "the", "evaluations", "and", "the", "language", "analysis", ",", "interpreted", "the", "perplexity", "analysis", "results", ",", "implemented", "the", "processing", "to", "create", "the", "final", "data", ",", "and", "processed", "Pile", "-", "CC", ",", "PubMed", "Central", ",", "ArXiv", ",", "and", "Ubuntu", "IRC", ".", "Stella", "Biderman", "led", "the", "data", "analysis", ",", "the", "broader", "impact", "analysis", ",", "and", "the", "data", "documentation", ",", "and", "coordinated", "the", "project", ".", "She", "also", "wrote", "the", "analysis", "of", "structural", "statistics", ",", "authorial", "consent", ",", "and", "copyright", "law", ".", "Sid", "Black", "implemented", "the", "model", "training", "and", "evaluation", "code", "and", "processed", "YouTube", "Subtitles", ",", "Stack", "Exchange", ",", "and", "GitHub", ".", "Laurence", "Golding", "implemented", "deduplication", ",", "performed", "the", "n", "-", "gram", "analysis", ",", "and", "processed", "OpenWebText2", ".", "Travis", "Hoppe", "processed", "FreeLaw", ",", "Pubmed", "Abstracts", ",", "ExPorter", ",", "and", "PhilPapers", ".", "Charles", "Foster", "performed", "the", "topic", "modeling", "analysis", ",", "contributed", "to", "the", "discussion", "of", "authorial", "consent", ",", "and", "processed", "USPTO", "Backgrounds", ".", "Jason", "Phang", "implemented", "and", "performed", "the", "GPT-2", "/", "3", "perplexity", "analysis", "and", "advised", "the", "project", ".", "Horace", "He", "performed", "the", "bias", "and", "sentiment", "analysis", ".", "Anish", "Thite", "implemented", "and", "performed", "the", "profanity", "analysis", "and", "processed", "Hacker", "News", ".", "Noa", "Nabeshima", "processed", "GitHub", ".", "Shawn", "Presser", "processed", "BookCorpus2", ".", "Connor", "Leahy", "wrote", "the", "alignment", "implication", "analysis", "and", "the", "model", "training", "code", ".", "In", "the", "course", "of", "building", "the", "Pile", ",", "we", "considered", "including", "and", "ultimately", "decided", "to", "not", "use", "several", "datasets", ".", "We", "excluded", "several", "datasets", "on", "the", "grounds", "that", "they", "were", "too", "small", "to", "be", "worth", "spending", "time", "on", "or", "because", "the", "English", "component", "of", "the", "data", "did", "not", "merit", "inclusion", "on", "its", "own", ".", "However", "we", "also", "decided", "to", "exclude", "several", "data", "sets", "for", "other", "reasons", ",", "which", "we", "document", "here", "for", "transparency", ":", "1.", "US", "Congressional", "Record", ".", "The", "official", "record", "of", "the", "United", "States", "Congress", "(", "1800", "-", "today", ")", "records", "important", "points", "of", "debate", "at", "the", "highest", "levels", "of", "American", "government", ".", "It", "reflects", "the", "opinions", "and", "biases", "of", "the", "political", "class", "over", "the", "past", "200", "years", ",", "including", "segregationism", "and", "xenophobia", ".", "In", "particular", ",", "we", "found", "a", "large", "quantity", "of", "extremely", "racist", "content", "that", "we", "did", "not", "feel", "appropriate", "for", "a", "dataset", "intended", "for", "general", "-", "purpose", "language", "modeling", ".", "2.", "Fanfiction", ".", "Hundreds", "of", "GiB", "of", "fanfiction", "has", "been", "written", "and", "put", "online", ",", "primarily", "on", "the", "websites", "www.fanfiction.net", "and", "www.https", ":/", "/", "archiveofourown", ".", "org", "/", ".", "This", "represents", "a", "significant", "untapped", "resource", "for", "language", "modeling", "as", "it", "is", "almost", "exclusively", "short", "-", "form", "fiction", ",", "a", "writing", "style", "that", "is", "not", "represented", "in", "most", "language", "modeling", "datasets", ".", "We", "ultimately", "decided", "to", "exclude", "fanfiction", "on", "logistical", "grounds", ":", "we", "found", "other", "sources", "of", "data", "that", "were", "easier", "to", "obtain", ".", "3.", "Literotica", ".", "Literotica", "is", "a", "website", "where", "users", "can", "upload", "short", "-", "form", "erotic", "fiction", ".", "We", "had", "originally", "planned", "on", "including", "it", "in", "the", "Pile", "and", "even", "went", "as", "far", "as", "scraping", "and", "processing", "it", ".", "However", "we", "decided", "to", "not", "include", "it", "for", "several", "reasons", ".", "Firstly", ",", "once", "we", "decided", "to", "exclude", "fanfiction", ",", "Literotica", "represented", "our", "sole", "source", "of", "short", "-", "form", "fiction", ",", "which", "would", "likely", "lead", "to", "undesirable", "biases", "in", "the", "trained", "model", ".", "Secondly", ",", "Literotica", "would", "require", "significantly", "more", "investigation", ",", "assessment", ",", "and", "care", "than", "we", "spent", "on", "the", "other", "datasets", ".", "Thirdly", ",", "Literotica", "contains", "a", "significant", "amount", "of", "stereotyping", ",", "including", "racial", "fetishes", ".", "While", "Literotica", "is", "likely", "usable", "for", "some", "tasks", ",", "we", "are", "not", "comfortable", "including", "it", "in", "the", "Pile", ".", "This", "section", "contains", "additional", "information", "about", "each", "dataset", "listed", "in", "Section", "2", ",", "including", "how", "it", "was", "obtained", ",", "how", "it", "was", "processed", ",", "and", "any", "other", "details", "relevant", "for", "replication", ".", "The", "intent", "of", "this", "section", "is", "to", "provide", "as", "much", "detail", "as", "possible", ",", "so", "that", "Pile", "can", "be", "replicated", "in", "the", "future", "if", "necessary", ",", "and", "so", "that", "any", "future", "processing", "of", "these", "and", "similar", "datasets", "can", "use", "or", "improve", "on", "our", "methods", ".", "As", "such", ",", "all", "code", "created", "for", "processing", "has", "been", "made", "publicly", "available", "under", "permissive", "open", "source", "licenses", "and", "is", "referenced", "in", "footnotes", "where", "applicable", ".", "We", "extract", "Common", "Crawl", "using", "jusText", "(", "Endr\u00e9dy", "and", "Nov\u00e1k", ",", "2013", ")", "We", "do", "not", "believe", "that", "document", "level", "filtering", "is", "sufficient", "for", "WET", "files", "because", "many", "of", "the", "issues", "with", "WET", "files", "stem", "from", "intra", "-", "document", "boilerplate", ".", "We", "also", "find", "many", "of", "the", "heuristics", "used", "in", "Raffel", "et", "al", ".", "(", "2019", ")", ",", "such", "as", "the", "removal", "of", "all", "lines", "without", "terminal", "punctuation", ",", "the", "word", "\"", "javascript", "\"", ",", "and", "3", "-", "sentence", "deduplication", "to", "be", "too", "aggressive", ".", "In", "addition", "to", "jusText", ",", "we", "also", "considered", "Trafilatura", ",", "Newspaper", ",", "Goose3", ",", "and", "DragNet", ".", "While", "we", "were", "originally", "intending", "on", "creating", "an", "extraction", "benchmark", ",", "this", "proved", "infeasible", "given", "our", "available", "resources", ",", "and", "we", "chose", "jusText", "based", "on", "visual", "inspection", "of", "the", "output", ".", "In", "inspection", ",", "we", "noticed", "that", "jusText", "has", "the", "characteristic", "that", "it", "discards", "more", "data", "than", "many", "other", "extractors", ",", "which", "is", "not", "a", "major", "drawback", "given", "the", "large", "volume", "of", "CC", "data", "available", ".", "This", "was", "as", "expected", ",", "given", "jusText", "'s", "intended", "application", "for", "text", "corpora", "creation", ".", "In", "contrast", ",", "trafilatura", "is", ",", "for", "instance", ",", "better", "at", "preserving", "the", "structure", "of", "the", "website", "faithfully", ",", "often", "correctly", "extracting", "elements", "such", "as", "tables", ",", "but", "it", "kept", "too", "much", "unnecessary", "boilerplate", ".", "Had", "we", "used", "trafilatura", ",", "we", "would", "have", "required", "an", "additional", "intra", "-", "page", "filtering", "step", "to", "remove", "boilerplate", "from", "the", "page", ".", "While", "jusText", "does", "technically", "support", "several", "other", "languages", ",", "the", "quality", "on", "those", "languages", "is", "worse", "than", "on", "English", "as", "many", "constants", "in", "the", "algorithm", "are", "specifically", "tuned", "for", "English", ".", "Additionally", ",", "jusText", "is", "completely", "unable", "to", "handle", "languages", "such", "as", "Chinese", "and", "Japanese", ",", "which", "do", "not", "use", "spaces", "to", "delimit", "words", ".", "Due", "to", "the", "difficulty", "of", "maintaining", "an", "acceptable", "level", "of", "extraction", "quality", "across", "all", "languages", ",", "we", "decided", "to", "restrict", "the", "scope", "of", "the", "CC", "dataset", "to", "only", "English", "and", "leave", "a", "high", "-", "quality", ",", "fully", "multilingual", ",", "WARC", "-", "based", "CC", "-", "based", "dataset", "to", "future", "work", ".", "To", "filter", "for", "only", "English", ",", "we", "use", "the", "py", "-", "cld2", "library", "and", "only", "attempt", "to", "extract", "text", "from", "documents", "where", "English", "is", "the", "most", "common", "language", ".", "We", "use", "pycld2", "instead", "of", "fasttext", "because", "it", "is", "capable", "of", "classifying", "the", "language", "from", "the", "HTML", "directly", ",", "and", "since", "jusText", "requires", "knowledge", "of", "the", "language", "of", "the", "webpage", "before", "extraction", ".", "Additionally", ",", "pycld2", "was", "significantly", "faster", "than", "jus", "-", "Text", ",", "and", "by", "only", "processing", "with", "jusText", "documents", "classified", "as", "English", "by", "pycld2", ",", "we", "reduced", "the", "required", "computation", "by", "approximately", "half", ".", "Extracting", "text", "from", "websites", "for", "language", "modeling", ",", "especially", "for", "multilingual", "corpora", ",", "is", "highly", "nontrivial", ",", "and", "we", "leave", "the", "refinement", "of", "such", "extraction", "to", "future", "work", ".", "To", "filter", "CC", "for", "quality", ",", "we", "follow", "Brown", "et", "al", ".", "(", "2020", ")", "2020", ")", ",", "with", "\u03b1", "=", "3.", "Our", "choice", "of", "\u03b1", "targets", "the", "filtering", "ratio", "necessary", "to", "filter", "our", "subset", "of", "CC", "to", "the", "size", "we", "needed", ".", "The", "impact", "of", "\u03b1", "on", "the", "filtering", "ratio", "is", "shown", "in", "Table", "6.", "We", "use", "pandoc", "1.", "19.2.4", "(", "MacFarlane", ",", "2006", "19.2.4", "(", "MacFarlane", ",", "-", "2020", ")", ")", "to", "convert", "the", "JATS", "format", "data", "provided", "by", "PMC", "to", "markdown", ".", "Afterwards", ",", "we", "remove", "any", "line", "beginning", "with", ":", ":", ":", ",", "which", "is", "used", "by", "pandoc", "to", "indicate", "html", "classes", "in", "markdown", ".", "No", "additional", "details", ".", "To", "produce", "the", "dataset", ",", "URLs", "and", "their", "associated", "metadata", "were", "first", "extracted", "from", "all", "Reddit", "submissions", "up", "to", "April", "2020", ".", "URLs", "were", "deduplicated", ",", "with", "each", "unique", "URL", "featuring", "a", "list", "of", "associated", "submissions", "metadata", ",", "and", "an", "aggregate", "score", ".", "URLs", "with", "an", "aggregate", "score", "of", "less", "then", "3", "were", "removed", ".", "The", "links", "were", "then", "scraped", "and", "processed", "with", "Newspaper", "scraper", ".", "Deduplication", "was", "performed", "at", "the", "document", "level", "using", "in", "memory", "MinHashLSH", "through", "the", "DataSketch", "library", ".", "Both", "We", "chose", "to", "use", "Newspaper", "instead", "of", "jusText", "for", "OpenWebText2", "for", "consistency", "with", "OpenWeb", "-", "TextCorpus", ".", "Additionally", ",", "by", "using", "multiple", "different", "html", "extractors", "for", "different", "components", "of", "the", "Pile", ",", "we", "reduce", "the", "potential", "impact", "of", "systematic", "biases", "from", "any", "one", "extractor", "negatively", "impacting", "the", "dataset", ".", "We", "downloaded", "the", "T", "E", "X", "sources", "of", "all", "papers", "on", "arXiv", "up", "to", "the", "July", "2020", "dump", "(", "the", "last", "file", "included", "in", "our", "data", "is", "arXiv_src_2007_068.tar", ")", "via", "arXiv", "'s", "S3", "Bulk", "Source", "File", "Access", "18", ",", "and", "used", "pandoc", "1.", "19.2.4", "to", "convert", "these", "source", "files", "to", "Markdown", ",", "discarding", "any", "papers", "which", "had", "errors", "during", "the", "conversion", "process", ".", "This", "yielded", "a", "total", "of", "1", ",", "264", ",", "405", "papers", ".", "We", "remove", "any", "line", "beginning", "with", ":", ":", ":", ",", "which", "is", "used", "by", "pandoc", "to", "indicate", "html", "classes", "in", "markdown", ".", "We", "separate", "the", "data", "gathering", "process", "into", "two", "steps", ":", "1.", "Gathering", "a", "list", "of", "the", "desired", "repositories", "and", "their", "metadata", "2.", "Extracting", "all", "text", "data", "useful", "for", "language", "modeling", "from", "each", "repository", "For", "the", "first", "step", ",", "mirroring", "the", "approach", "of", "the", "WebText", "dataset", ",", "we", "use", "GitHub", "'", "stars", "'", "as", "a", "proxy", "for", "quality", ",", "and", "choose", "to", "gather", "only", "repositories", "with", "more", "than", "100", "stars", ".", "For", "practical", "reasons", ",", "we", "also", "limit", "the", "list", "of", "repositories", "gathered", "to", "repositories", "with", "less", "than", "1", "GB", "of", "files", ".", "Since", "Github", "'s", "API", "limits", "the", "number", "of", "search", "results", "to", "1000", ",", "in", "order", "to", "comprehensively", "gather", "all", "repositories", "we", "need", "to", "create", "many", "small", "queries", "that", "each", "return", "fewer", "than", "1000", "results", "in", "such", "a", "way", "that", "every", "repository", "of", "interest", "will", "be", "returned", "by", "at", "least", "one", "of", "our", "queries", ".", "To", "achieve", "this", ",", "we", "bound", "our", "initial", "search", "by", "size", "to", "return", "only", "repositories", "between", "a", "lower", "bound", "of", "0", "and", "5", "bytes", ".", "At", "the", "time", "of", "writing", ",", "this", "returns", "965", "results", ".", "For", "the", "next", "step", ",", "we", "set", "our", "lower", "bound", "one", "above", "our", "previous", "upper", "bound", ",", "and", "decide", "on", "a", "new", "upper", "bound", "that", "should", "also", "return", "fewer", "than", "1000", "results", "by", "  ", "This", "tends", "not", "to", "overshoot", ",", "because", "Github", "repositories", "follow", "a", "power", "distribution", "with", "respect", "to", "size", ",", "but", "if", "it", "does", ",", "we", "simply", "use", "the", "amount", "of", "repositories", "our", "new", "query", "returned", "in", "order", "to", "construct", "a", "new", "upper", "bound", "estimate", ".", "Using", "the", "gathered", "list", "of", "repositories", ",", "we", "clone", "each", "one", ",", "extract", "any", "text", "-", "based", "files", ",", "and", "discard", "the", "rest", ".", "Because", "some", "repositories", "took", "an", "impractical", "amount", "of", "time", "to", "clone", "and/or", "extract", ",", "we", "set", "a", "hard", "time", "limit", "of", "300", "seconds", "for", "both", "the", "git", "cloning", "and", "text", "extraction", "steps", ".", "As", "such", ",", "some", "larger", "repositories", "may", "only", "be", "partially", "extracted", ".", "We", "also", "impose", "a", "file", "size", "limit", "of", "100kB", "on", "extracted", "files", ",", "as", "we", "found", "that", "the", "majority", "of", "files", "over", "that", "size", "were", "typically", "very", "repetitive", "autogenerated", "source", "files", "or", "data", "files", ",", "and", "that", "setting", "this", "file", "size", "limit", "was", "an", "effective", "cleaning", "step", "to", "limit", "the", "data", "to", "code", ".", "Because", "we", "wanted", "to", "limit", "the", "size", "of", "the", "overall", "Pile", ",", "we", "randomly", "sampled", "95.0", "GiB", "of", "the", "630.64", "GiB", "of", "Github", "data", "we", "collected", "in", "total", "and", "leave", "quality", "filtering", "to", "future", "work", ".", "However", ",", "we", "believe", "code", "generation", "will", "be", "an", "increasingly", "important", "component", "of", "language", "models", "as", "they", "continue", "to", "scale", "up", "and", "increase", "in", "their", "ability", "to", "generalize", ".", "As", "such", ",", "we", "hope", "to", "extend", "this", "dataset", "in", "future", "work", ".", "We", "download", "the", "court", "opinions", "data", "in", "bulk", "from", "CourtListener", ",", "19", "and", "extract", "the", "raw", "text", "using", "BeautifulSoup", ".", "To", "construct", "the", "dataset", ",", "we", "download", "and", "parse", "every", "Stack", "Exchange", "database", "dump", "to", "plaintext", "files", ".", "We", "opt", "to", "extract", "the", "top", "three", "answers", "with", "at", "least", "three", "upvotes", ",", "discarding", "all", "other", "responses", ".", "We", "only", "include", "the", "plain", "text", "question", "and", "response", "and", "do", "not", "incorporate", "any", "metadata", ".", "Motivated", "by", "large", "-", "scale", "language", "models", "'", "few", "-", "shot", "ability", "(", "Brown", "et", "al", ".", ",", "2020", ")", ",", "we", "provide", "context", "by", "prepending", "all", "questions", "and", "answers", "with", "Q", ":", "\\n\\n", "and", "A", ":", "\\n\\n", "respectively", ".", "The", "resulting", "dataset", "contains", "a", "total", "of", "15", ",", "622", ",", "475", "documents", "across", "a", "total", "of", "365", "Stack", "Exchanges", "and", "Meta", "-", "Stack", "Exchanges", ",", "the", "bulk", "of", "which", "is", "from", "StackOverflow", ".", "The", "United", "States", "Patent", "and", "Trademark", "Office", "(", "USPTO", ")", "has", "published", "bulk", "archives", "of", "the", "full", "text", "of", "all", "patents", "granted", "in", "the", "US", "from", "1976", "to", "September", "2020", ".", "From", "these", "archives", ",", "we", "extract", "the", "Background", "sections", ",", "along", "with", "key", "grantspecific", "metadata", ",", "such", "as", "the", "inventor", ",", "assignee", ",", "and", "classification", "information", ".", "The", "file", "format", "used", "for", "storing", "bulk", "text", "US", "patents", "has", "changed", "over", "time", ".", "Prior", "to", "2002", ",", "all", "of", "the", "datasets", "are", "in", "a", "specialized", "format", "called", "APS", "(", "Automated", "Patent", "System", ")", ".", "Since", "2002", ",", "the", "data", "is", "XML", "encoded", ".", "Partially", "as", "a", "function", "of", "this", "change", ",", "the", "location", "of", "the", "\"", "Background", "\"", "section", "has", "also", "shifted", ".", "Our", "converter", "accounts", "for", "these", "structural", "shifts", "and", "extracts", "the", "raw", "text", "from", "each", "patent", "'s", "Background", ".", "About", "one", "-", "third", "of", "the", "articles", "in", "the", "dataset", "were", "missing", "or", "contained", "a", "malformed", "title", "or", "abstract", "and", "were", "excluded", ".", "Additionally", ",", "PubMed", "Central", "(", "see", "Section", "2.", "2", ")", "contains", "full", "-", "text", "resources", "to", "many", "recent", "publications", ";", "any", "publications", "which", "already", "appear", "in", "PMC", "are", "excluded", "from", "this", "set", ".", "To", "process", "the", "data", ",", "we", "concatenated", "the", "title", "and", "abstract", "and", "removed", "any", "copyright", "information", ".", "The", "remaining", "dataset", "contains", "15", ",", "518", ",", "009", "titles", "and", "abstracts", ".", "No", "additional", "details", ".", "To", "create", "the", "text", "dataset", ",", "we", "simply", "extract", "the", "subtitle", "text", "from", "each", "XML", "file", "in", "the", "English", "language", "dataset", "provided", "by", "Tiedemann", "(", "2016", ")", ",", "discarding", "any", "provided", "metadata", ".", "We", "use", "the", "wikipedia", "/", "20200301.en", "dataset", "from", "TensorFlow", "Datasets", ".", "20", "We", "prepend", "the", "title", "to", "the", "body", "of", "each", "article", ",", "separated", "by", "two", "newlines", ".", "We", "include", "instances", "from", "the", "Easy", ",", "Medium", ",", "and", "Hard", "components", "of", "DeepMind", "Mathematics", ",", "breaking", "each", "curriculum", "item", "(", "such", "as", "algebra__polynomial_roots", ")", "into", "8", "KiB", "chunks", ".", "20", "https", ":/", "/", "www.tensorflow.org", "/", "datasets", "/", "catalog", "/", "wikipedia#wikipedia20200301en", "We", "processed", "all", "logs", "from", "July", "5", ",", "2004", "through", "September", "1", ",", "2020", ".", "To", "process", "the", "data", ",", "all", "system", "messages", ",", "such", "as", "joins", ",", "disconnects", ",", "nick", "changes", ",", "etc", ".", "were", "discarded", ",", "but", "actions", "(", "i.e", "using", "/me", ")", "were", "kept", ".", "Timestamps", "were", "removed", ",", "and", "all", "logs", "for", "the", "same", "channel", "in", "a", "given", "week", "were", "concatenated", "into", "a", "single", "document", ",", "with", "each", "the", "logs", "for", "each", "day", "prepended", "with", "the", "date", "if", "that", "day", "'s", "log", "is", "non", "-", "empty", ".", "The", "original", "BookCorpus", "consists", "of", "11", ",", "038", "books", ".", "However", ",", "due", "to", "issues", "with", "availability", "of", "the", "original", "BookCorpus", ",", "as", "well", "as", "the", "possibility", "of", "collecting", "a", "larger", "version", ",", "we", "decided", "to", "collect", "our", "own", "version", "of", "BookCorpus", "using", "a", "similar", "methodology", "as", "Kobayashi", "(", "2018", ")", ".", "Our", "version", "of", "BookCorpus", "contains", "17", ",", "868", "books", "instead", ".", "We", "create", "and", "use", "a", "modified", "version", "of", "the", "epubto", "-", "text", "converter", "in", "Kobayashi", "(", "2018", ")", "that", ":", "\u2022", "Correctly", "preserves", "the", "document", "structure", "across", "chapters", ",", "matching", "the", "table", "of", "contents", "very", "closely", ";", "\u2022", "Correctly", "renders", "tables", "of", "data", ",", "whereas", "by", "default", "html2txt", "produces", "poor", "-", "quality", "results", "for", "tables", ",", "\u2022", "Correctly", "preserves", "code", "structure", ",", "so", "that", "source", "code", "is", "visually", "coherent", ",", "\u2022", "Converts", "numbered", "lists", "from", "\"", "1\\", ".", "\"", "to", "\"", "1.", "\"", "\u2022", "Runs", "the", "full", "text", "through", "ftfy.fix_text", "(", ")", "(", "Speer", ",", "2019", ")", ",", "replacing", "Unicode", "apostrophes", "with", "ascii", "apostrophes", "and", "expanding", "Unicode", "ellipses", "to", "\"", "...", "\"", "(", "three", "separate", "ascii", "characters", ")", ".", "We", "download", "the", "data", "in", "bulk", "from", "21", ".", "We", "remove", "all", "basic", "tag", "information", "and", "only", "retain", "the", "name", "of", "each", "document", "as", "a", "title", ".", "For", "example", ",", "<", "SPEAKER", "ID", "=", "77", "LANGUAGE", "=", "\"NL", "\"", "NAME", "=", "\"Pronk", "\"", ">", "becomes", "Pronk", ",", "and", "then", "extract", "the", "body", "of", "each", "document", ",", "discarding", "those", "that", "are", "shorter", "than", "200", "characters", ".", "We", "first", "use", "the", "Hackernews", "BigQuery", "dataset", "to", "obtain", "a", "list", "of", "all", "story", "ids", "in", "our", "date", "range", ".", "For", "the", "Pile", "we", "use", "the", "first", "Hacker", "News", "post", "(", "1", ")", "to", "post", "number", "24531712", ".", "This", "corresponds", "to", "a", "date", "range", "of", "approximately", "10", "/", "09", "/", "2006", "to", "09", "/", "20", "/", "2020", ".", "We", "use", "the", "BigQuery", "dataset", "to", "gather", "story", "ids", "for", "efficiency", "purposes", ".", "However", ",", "the", "BigQuery", "dataset", "was", "lacking", "some", "information", "for", "stories", ",", "so", "we", "used", "the", "official", "Hacker", "News", "API", "for", "story", "and", "comment", "text", "retrieval", ".", "Hacker", "News", "displays", "and", "stores", "comments", "in", "a", "tree", "-", "like", "manner", ",", "with", "children", "comments", "replying", "to", "parent", "comments", ".", "However", ",", "most", "language", "models", "require", "input", "data", "to", "be", "in", "a", "sequential", "form", ".", "Considering", "each", "path", "through", "the", "comment", "tree", "as", "a", "sequence", "could", "be", "detrimental", ",", "since", "there", "will", "be", "a", "large", "amount", "of", "near", "-", "duplicate", "comment", "sequences", ".", "In", "addition", ",", "only", "taking", "one", "path", "through", "the", "comment", "tree", "for", "each", "story", "leaves", "out", "a", "large", "portion", "of", "the", "comment", "data", ".", "Therefore", ",", "we", "parsed", "comments", "in", "a", "hybrid", "form", ".", "For", "every", "top", "-", "level", "comment", "(", "comments", "that", "have", "no", "parent", "comment", ")", ",", "we", "create", "a", "sequence", "of", "comments", "by", "traversing", "down", "the", "comment", "tree", "from", "the", "top", "-", "level", "comment", ".", "We", "choose", "the", "next", "comment", "by", "taking", "the", "child", "comment", "with", "the", "highest", "number", "of", "children", "comments", "(", "a", "cheap", "attempt", "at", "taking", "a", "long", "path", "through", "the", "comment", "tree", ",", "note", "that", "it", "does", "not", "take", "the", "longest", "possible", "path", ")", ".", "We", "consider", "all", "stories", "that", "have", "at", "least", "one", "comment", "and", "are", "not", "flagged", "by", "the", "moderators", "for", "potential", "conduct", "violations", ".", "Since", "comments", "are", "stored", "in", "HTML", ",", "we", "use", "the", "html2text", "package", "to", "extract", "the", "text", "from", "the", "post", ".", "We", "order", "each", "document", "by", "listing", "the", "title", ",", "url", ",", "sub", "-", "title", ",", "and", "author", "at", "the", "top", ".", "Top", "-", "level", "comments", "are", "delimited", "by", "\"", "\\n----\\n", "\"", "and", "sub", "-", "comment", "chains", "are", "delimited", "by", "\"", "\\n~~~\\n", "\"", ".", "We", "include", "author", "and", "extracted", "text", "for", "each", "comment", ".", "We", "construct", "the", "dataset", "in", "three", "stages", ":", "1.", "We", "build", "a", "large", "list", "of", "search", "terms", "by", "prompting", "a", "GPT-3", "model", "with", "a", "manually", "selected", "list", "of", "queries", ",", "manually", "filtering", "the", "responses", ",", "and", "repeating", "this", "process", "iteratively", "until", "a", "suitable", "size", "is", "reached", ".", "The", "list", "of", "terms", "is", "centred", "around", ",", "but", "not", "limited", "to", ",", "educational", "topics", ".", "2.", "We", "use", "requests", "-", "html", "to", "gather", "a", "list", "of", "1000", "Youtube", "video", "IDs", "for", "each", "search", "term", ",", "and", "deduplicate", "the", "resulting", "video", "ids", "across", "search", "terms", ".", "3.", "We", "use", "YoutubeTranscriptApi", "22", "to", "gather", "all", "human", "generated", "closed", "captions", "for", "every", "available", "language", "for", "each", "video", ".", "To", "align", "each", "language", "in", "parallel", ",", "we", "split", "the", "captions", "for", "each", "language", "into", "parallel", "minute", "-", "long", "sections", "by", "timestamp", ",", "and", "arrange", "each", "language", "in", "a", "random", "order", "within", "these", "sections", ",", "appending", "the", "language", "as", "a", "header", "to", "each", "minute", "-", "long", "section", "to", "provide", "context", ".", "If", "only", "a", "single", "language", "is", "available", ",", "the", "output", "is", "just", "the", "subtitles", ",", "with", "no", "header", "appended", ".", "In", "total", ",", "subtitles", "for", "173", ",", "651", "videos", "were", "gathered", ".", "The", "PhilPapers", "(", "PP", ")", "are", "indexed", "using", "OAI", "-", "MPH", ",", "the", "Open", "Archives", "Initiative", "Protocol", "for", "Metadata", "Harvesting", ".", "As", "such", ",", "the", "first", "step", "to", "collect", "the", "data", "is", "to", "get", "the", "XML", "for", "all", "links", ".", "This", "was", "done", "using", "pyoaiharvester", ".", "23", "rom", "that", ",", "each", "publication", "is", "downloaded", ".", "Some", "entries", "do", "not", "exist", ",", "or", "have", "been", "removed", "by", "the", "authors", ".", "Papers", "with", "text", "are", "extracted", "using", "pdfbox", ",", "and", "papers", "with", "non", "-", "machine", "readable", "text", "are", "ignored", ".", "Non", "-", "English", "language", "publications", "are", "kept", ",", "and", "the", "metadata", "reflects", "the", "language", "reported", "by", "the", "OAI", "-", "MPH", "XML", ".", "The", "text", "is", "filtered", "with", "pdf_filter.py", "from", "PDFextract", ",", "and", "we", "discard", "any", "papers", "with", "less", "than", "1000", "characters", ".", "24", "The", "NIH", "provides", "a", "bulk", "-", "data", "repository", "for", "awarded", "applications", "through", "the", "ExPORTER", "service", "covering", "the", "fiscal", "years", "1985", "-", "present", ".", "These", "data", "come", "from", "the", "NIH", ",", "but", "also", "other", "other", "Health", "and", "Human", "Services", "agencies", "(", "ACF", ",", "AHRQ", ",", "CDC", ",", "HRSA", ",", "FDA", ")", ",", "and", "the", "VA", ".", "Additionally", ",", "the", "NIH", "provides", "a", "legacy", "data", "format", "named", "CRISP", "for", "awarded", "applications", "during", "the", "fiscal", "years", "1970", "-", "2009", ".", "We", "merged", "both", "the", "ExPORTER", "and", "CRISP", "data", "to", "form", "a", "consolidated", "dataset", "of", "awarded", "applications", ".", "Entries", "were", "deduplicated", "based", "off", "their", "application", "ID", ",", "and", "excluded", "if", "their", "abstract", "text", "was", "missing", "or", "too", "short", ".", "Small", "grants", ",", "especially", "administrative", "ones", ",", "consisted", "solely", "of", "short", "boilerplate", ".", "For", "this", "reason", ",", "we", "further", "deduplicated", "on", "abstract", "text", ".", "All", "grants", "types", "were", "considered", ",", "including", "new", "applications", "(", "Application", "Type", "Code", "1", ")", "and", "renewals", "(", "Application", "Type", "Code", "2", ")", "as", "the", "text", "differed", "enough", "to", "provide", "novel", "input", ".", "The", "text", "was", "then", "minimally", "parsed", "to", "remove", "administrative", "boilerplate", ",", "(", "ex", ".", "most", "old", "awards", "contain", "some", "variation", "of", "\"", "description", ":", "(", "provided", "by", "applicant", ")", "\"", ")", ".", "In", "total", ",", "there", "were", "939", ",", "668", "grant", "application", "abstracts", "added", ".", "To", "extract", "the", "data", ",", "we", "used", "the", "mailparser", "package", "25", "to", "extract", "the", "body", "of", "each", "email", "as", "a", "document", ".", "This", "section", "discusses", "any", "processes", "applied", "across", "multiple", "datasets", ".", "To", "combine", "the", "constituent", "datasets", ",", "we", "iterate", "until", "the", "size", "of", "the", "output", "dataset", "is", "the", "desired", "size", ",", "drawing", "documents", "from", "datasets", "at", "random", ",", "weighted", "by", "the", "number", "of", "documents", "in", "each", "dataset", "times", "the", "number", "of", "epochs", "desired", "on", "that", "dataset", ".", "Because", "the", "number", "of", "documents", "involved", "is", "high", ",", "by", "the", "law", "of", "large", "numbers", ",", "the", "number", "of", "copies", "of", "each", "dataset", "present", "in", "the", "Pile", "is", "approximately", "equal", "to", "its", "epoch", "count", ".", "Shuffling", "a", "dataset", "posed", "a", "major", "problem", "due", "to", "our", "limited", "memory", "and", "computational", "budget", ".", "We", "follow", "Hardin", "(", "2018", ")", ",", "a", "method", "descended", "from", "Rao", "(", "1961", ")", ",", "and", "interleave", "our", "output", "to", "produce", "30", "output", "piles", ".", "We", "hold", "out", "approximately", "10GiB", "of", "data", "from", "the", "Pile", ",", "of", "which", "2GiB", "are", "used", "to", "create", "the", "validation", "and", "test", "splits", ",", "and", "the", "remainder", "is", "held", "in", "reserve", ".", "From", "the", "training", "set", ",", "we", "remove", "any", "25", "https", ":/", "/", "github.com", "/", "SpamScope", "/", "mail", "-", "parser", "elements", "that", "are", "also", "present", "verbatim", "in", "any", "of", "the", "held", "out", "data", ",", "to", "prevent", "leakage", ".", "Similar", "to", "Brown", "et", "al", ".", "(", "2020", ")", ",", "we", "increase", "the", "weight", "of", "certain", "components", "such", "that", "the", "number", "of", "epochs", "elapsed", "on", "data", "we", "consider", "high", "quality", "is", "greater", "than", "one", ".", "Our", "choice", "of", "weights", "was", "primarily", "informed", "by", "the", "source", "of", "the", "data", "and", "the", "size", "of", "the", "dataset", ";", "we", "attempted", "to", "upweight", "academic", "texts", "the", "most", ",", "which", "we", "felt", "provided", "the", "highest", "quality", "data", ",", "as", "well", "as", "smaller", "sets", ",", "such", "that", "they", "would", "have", "a", "more", "pronounced", "impact", "on", "the", "data", ".", "We", "strictly", "disallowed", "any", "data", "more", "than", "3", "epochs", "and", "avoided", "having", "any", "data", "with", "more", "than", "2", "epochs", ".", "Due", "to", "memory", "constraints", "we", "did", "not", "perform", "Pile", "wide", "de", "-", "duplication", ".", "Instead", ",", "de", "-", "duplication", "was", "performed", "at", "the", "document", "level", "within", "Open", "-", "WebText2", "and", "Pile", "-", "CC", "as", "those", "sets", "were", "the", "most", "likely", "to", "contain", "duplicate", "documents", ".", "We", "used", "10", "hash", "functions", "for", "each", "Minhash", "and", "an", "approximate", "Jaccard", "similarity", "of", "0.", "5", ".", "This", "produced", "a", "duplicate", "rate", "of", "28", "%", "in", "OpenWebText2", "and", "26", "%", "for", "Common", "Crawl", ".", "The", "main", "challenge", "here", "was", "computational", ",", "leading", "us", "on", "a", "journey", "through", "the", "various", "LSH", "persistence", "options", ".", "A", "simple", "quadratic", "Minhash", "comparison", "of", "all", "documents", "would", "have", "taken", "several", "hundred", "thousand", "years", ",", "motivating", "the", "use", "of", "LSH", ".", "Initially", ",", "we", "did", "not", "have", "sufficient", "RAM", "for", "inmemory", "LSH", "and", "chose", "to", "use", "the", "Cassandra", "backend", "when", "de", "-", "duplicating", "OpenWebText2", ".", "This", "was", "reasonably", "fast", ",", "but", "the", "same", "method", "resulted", "in", "a", "corrupted", "database", "about", "3", "4", "of", "the", "way", "through", "processing", "Common", "Crawl", ".", "After", "the", "Cassandra", "corruption", ",", "we", "briefly", "tested", "the", "experimental", "Mongo", "implementation", ";", "however", "this", "was", "quite", "slow", "due", "to", "the", "nature", "of", "Mongo", "itself", ".", "In", "the", "end", ",", "we", "ran", "in", "-", "memory", "LSH", "on", "a", "machine", "with", "enough", "RAM", "for", "Common", "Crawl", ",", "taking", "several", "days", ".", "To", "avoid", "leakage", "of", "data", "from", "downstream", "evaluations", ",", "recent", "work", "(", "Radford", "et", "al", ".", ",", "2019", ";", "Brown", "et", "al", ".", ",", "2020", ";", "Shoeybi", "et", "al", ".", ",", "2019", ")", "has", "removed", "any", "data", "in", "the", "training", "set", "that", "may", "overlap", "with", "the", "evaluation", "metrics", ".", "We", "decided", "not", "to", "perform", "any", "such", "removal", ",", "because", "it", "is", "impossible", "to", "anticipate", "all", "potential", "downstream", "evaluation", "metrics", ",", "and", "so", "any", "particular", "selection", "of", "metrics", "would", "inevitably", "either", "become", "obsolete", "as", "the", "choice", "of", "benchmarks", "in", "the", "field", "changes", ",", "or", "potentially", "hinder", "the", "development", "of", "new", "benchmarks", "for", "models", "trained", "on", "Pile", ".", "For", "models", "trained", "on", "Pile", "and", "evaluated", "on", "metrics", "other", "than", "Pile", "'s", "own", "validation", "and", "test", "sets", ",", "we", "encourage", "authors", "to", "remove", "overlaps", "between", "Pile", "and", "the", "validation", "data", "of", "these", "additional", "downstream", "evaluations", ".", "We", "do", "not", "anticipate", "that", "such", "leakage", "removal", "will", "hurt", "model", "performance", ",", "as", "the", "validation", "sets", "of", "most", "benchmarks", "are", "very", "small", "in", "relation", "to", "the", "size", "of", "the", "Pile", ",", "and", "so", "choosing", "to", "evaluate", "on", "more", "metrics", "will", "not", "be", "a", "disadvantage", "for", "any", "model", ".", "As", "part", "of", "our", "exploratory", "analysis", ",", "we", "calculated", "the", "counts", "of", "all", "13", "-", "grams", "across", "Common", "Crawl", ".", "We", "chose", "n", "=", "13", "due", "to", "its", "use", "in", "prior", "work", "(", "Brown", "et", "al", ".", ",", "2020", ")", ".", "There", "were", "a", "total", "of", "40", ",", "216", ",", "231", ",", "078", "different", "13", "-", "grams", "in", "this", "dataset", ".", "The", "1000", "most", "common", "range", "from", "11", "million", "occurrences", "down", "to", "20k", ".", "The", "most", "frequently", "occurring", "13", "-", "grams", "were", "character", "repetitions", "used", "for", "styling", "such", "as", "\"", "-", "-", "-", "-", "\"", ",", "\"", "*", "*", "*", "*", "\"", ",", "\"", "!", "!", "!", "!", "\"", ",", "at", "11", "million", ",", "5.", "8", "million", "and", "1.", "1", "million", "respectively", ".", "Other", "characters", "used", "in", "this", "manner", "include", "the", "following", ":", "\"", "#", ".", ">", "?", "\"", ".", "In", "the", "264k", "count", "range", ",", "we", "see", "repetitions", "of", "badly", "formatted", "HTML", "escape", "characters", "\"", ";", "&", "nbsp", "\"", ",", "\"", ";", "amp", "\"", ".", "Boilerplate", "from", "standard", "forum", "software", "appears", "around", "the", "180k", "occurrences", "range", ",", "such", "as", "the", "following", ":", "\"", "select", "the", "forum", "that", "you", "want", "to", "visit", "from", "the", "selection", "below", "\"", ".", "Overall", ",", "a", "large", "amount", "of", "common", "HTML", "and", "CSS", "is", "included", "in", "the", "top", "1000", ",", "along", "with", "boilerplate", "text", "from", "Amazon", "Affiliate", "Advertising", ",", "Tokens", "TripAdvisor", ",", "SimplyHired", ",", "Associated", "Press", ",", "Post", "-", "Media", ",", "The", "FCC", "etc", ".", "PHP", "error", "messages", "and", "password", "login", "prompts", "also", "made", "an", "appearance", ".", "It", "may", "be", "of", "interest", "to", "fans", "of", "Portal", "that", "repetitions", "of", "\"", "the", "cake", "is", "a", "lie", ".", "\"", "achieved", "a", "high", "count", ".", "To", "compute", "the", "perplexity", "for", "a", "given", "dataset", ",", "we", "tokenize", "each", "document", "separately", ",", "divide", "the", "document", "into", "segments", "of", "up", "to", "the", "maximum", "sequence", "length", "of", "the", "model", "(", "1024", "tokens", "for", "GPT-2", ",", "2048", "for", "GPT-3", ")", ",", "and", "predict", "the", "logits", "of", "the", "each", "segment", ".", "The", "inputs", "to", "the", "model", "are", "the", "immediate", "prior", "tokens", "the", "e.g.", "for", "scoring", "tokens", "1", "to", "1024", ",", "we", "provide", "tokens", "0", "to", "1023", "at", "the", "input", "context", ".", "The", "respective", "language", "model", "implementations", "handle", "the", "causal", "attention", "masking", ".", "This", "ensures", "that", "every", "token", "in", "the", "dataset", "is", "scored", "exactly", "once", ".", "This", "also", "means", "that", "some", "tokens", "will", "have", "more", "input", "context", "than", "others", ".", "We", "then", "aggregate", "over", "the", "whole", "dataset", "and", "compute", "the", "final", "per", "-", "plexity", "score", ".", "The", "perplexity", "for", "the", "whole", "Pile", "is", "computed", "by", "aggregating", "over", "the", "constituent", "datasets", "(", "i.e.", "weighted", "by", "dataset", "size", ",", "not", "a", "simple", "average", "of", "dataset", "perplexities", ")", ".", "Both", "GPT-2", "and", "GPT-3", "share", "the", "same", "tokenizer", "and", "vocabulary", ",", "making", "the", "perplexity", "scores", "directly", "comparable", ".", "We", "use", "the", "Hugging", "Face", "(", "Wolf", "et", "al", ".", ",", "2020", ")", "implementation", "of", "GPT-2", ",", "and", "the", "OpenAI", "API", "for", "GPT-3", ".", "The", "davinci", "model", "in", "the", "OpenAI", "API", "is", "presumed", "to", "correspond", "to", "a", "175B", "parameter", "version", "of", "GPT-3", ".", "In", "Table", "8", "we", "show", "the", "test", "set", "perplexities", "(", "i.e.", "not", "normalized", "by", "UTF-8", "length", ",", "as", "in", "Table", "2", ")", ".", "Because", "of", "the", "costs", "associated", "with", "using", "the", "OpenAI", "API", ",", "we", "compute", "test", "perplexities", "on", "only", "one", "-", "tenth", "of", "the", "test", "set", "in", "Tables", "8", "and", "Table", "2.", "Specifically", ",", "we", "randomly", "sample", "one", "-", "tenth", "of", "the", "documents", "of", "each", "dataset", "except", "for", "three", ":", "Ubuntu", "IRC", ",", "Book", "-", "Corpus2", ",", "and", "PhilPapers", ".", "In", "Table", "9", ",", "we", "show", "test", "perplexity", "computed", "on", "the", "full", "test", "set", "on", "all", "GPT-2", "models", ".", "Initially", "we", "decided", "on", "separating", "pejorative", "content", "into", "4", "groups", ":", "sex", "-", "related", "terminology", ",", "slurs", ",", "neither", "of", "these", "categories", ",", "and", "both", "of", "these", "categories", ".", "We", "adapted", "a", "public", "\"", "naughty", "words", "\"", "list", "and", "broke", "them", "into", "these", "categories", "with", "the", "intern", "of", "looking", "at", "the", "proportion", "of", "each", "category", "in", "each", "dataset", ".", "However", ",", "this", "provided", "many", "issues", ".", "First", ",", "any", "blacklist", "of", "words", "would", "be", "hard", "-", "pressed", "to", "catch", "all", "the", "instances", "of", "pejorative", "content", ",", "since", "purposeful", "misspellings", "of", "words", "could", "evade", "the", "censor", "and", "still", "have", "the", "intended", "effect", ".", "Furthermore", ",", "words", "and", "their", "intents", "are", "always", "evolving", ",", "therefore", "any", "list", "created", "would", "likely", "be", "always", "outdated", ".", "Another", "issue", "pertains", "to", "sorting", "the", "words", "into", "the", "categories", ".", "Words", "are", "highly", "dependent", "on", "their", "context", ",", "so", "a", "word", "would", "change", "categories", "with", "different", "contexts", ".", "The", "following", "consists", "of", "two", "random", ",", "noncherrypicked", "512", "-", "byte", "samples", "from", "each", "constituent", "dataset", "of", "the", "Pile", ",", "sampled", "from", "the", "validation", "split", ".", "pot", "trending", "topics", "and", "the", "coverage", "around", "them", ".", "First", "up", ",", "there", "'s", "a", "bit", "of", "a", "visual", "redesign", ".", "Previously", ",", "clicking", "on", "a", "trending", "topic", "would", "highlight", "a", "story", "from", "one", "publication", ",", "and", "you", "'d", "have", "to", "scroll", "down", "past", "a", "live", "video", "section", "to", "view", "related", "stories", ".", "Facebook", "is", "replacing", "that", "system", "with", "a", "simple", "carousel", ",", "which", "does", "a", "better", "job", "of", "showing", "you", "different", "coverage", "options", ".", "To", "be", "clear", ",", "the", "change", "does", "n't", "affect", "how", "stories", "are", "sourced", ",", "according", "to", "Facebook", ".", "It", "'s", "still", "the", "same", "algorithm", "pickin", "e", "public", "safety", ".", "He", "said", "the", "bridge", "saves", "commuters", "two", "or", "three", "minutes", "when", "trains", "pass", "-", "and", "those", "minutes", "could", "be", "vital", ".", "\"", "Two", "to", "three", "minutes", "may", "not", "mean", "much", "if", "you", "'re", "just", "driving", "home", "from", "work", ",", "but", "if", "you", "'re", "the", "one", "waiting", "for", "an", "ambulance", "to", "get", "to", "your", "home", ",", "if", "you", "'re", "the", "one", "waiting", "for", "a", "fire", "truck", "to", "get", "to", "your", "home", ",", "if", "you", "'re", "the", "one", "waiting", "for", "a", "police", "car", "to", "get", "to", "your", "home", ",", "those", "two", "to", "three", "minutes", "could", "mean", "the", "difference", "between", "life", "or", "death", ",", "\"", "Sharp", "said", ".", "\"", "That", "'s", "what", "this", "pro", "Introduction", "=", "=", "=", "=", "=", "=", "=", "=", "=", "=", "=", "=", "Total", "knee", "arthroplasty", "(", "TKA", ")", "is", "a", "promising", "treatment", "for", "endstage", "osteoarthritis", "(", "OA", ")", "of", "the", "knee", "for", "alleviating", "pain", "and", "restoring", "the", "function", "of", "the", "knee", ".", "Some", "of", "the", "cases", "with", "bilateral", "TKA", "are", "symptomatic", ",", "necessitating", "revision", "arthroplasty", "in", "both", "the", "knees", ".", "A", "bilateral", "revision", "TKA", "can", "be", "done", "ei", "ent\\", "'s", "ability", "to", "make", "judgements", "and", "decisions", "about", "their", "work", "experiences", "and", "learning", "that", "will", "position", "them", "as", "future", "critical", "thinkers", ",", "life", "longer", "enquirers", "and", "learners", ".", "Identification", "of", "the", "core", "capabilities", "that", "our", "stakeholder", "community", "rate", "highly", "has", "proved", "informative", "in", "assisting", "us", "to", "describe", "a", "\"", "work", "ready", "*", "plus", "\"", "*", "medical", "imaging", "graduate", "for", "the", "New", "Zealand", "context", ".", "The", "results", "have", "provided", "data", "to", "the", "curriculum", "development", "team", "allowing", "them", "cept", "of", "_", "for\u00e7age", "_", ",", "'", "a", "forcing", "of", "language", "enacted", "by", "the", "advent", "of", "an", "\"", "other", "\"", "language", "that", "is", "at", "once", "immanent", "and", "created", "'", ",", "44as", "Badiou", "puts", "it", ":", "this", "opens", "up", "vistas", "of", "a", "truly", "syntactic", "analysis", "of", "the", "poem", ",", "in", "which", ",", "again", ",", "Badiou", "would", "be", "close", "to", "his", "philosophical", "other", ",", "Deleuze", ",", "who", ",", "as", "we", "just", "saw", ",", "defines", "style", "through", "a", "-", "grammaticality", "and", "who", "tries", "to", "define", "what", "he", "calls", "an", "'", "intensive", "line", "of", "syntax'.45", "Nevertheless", ",", "the", "insistence", "on", "syntax", "as", "guarantee", "involves", "a", "_", "seventh", "paradox", "_", ",", "the", "parad", "rnment", ",", "before", "the", "Second", "World", "War", "there", "were", "5", ",", "300", "communities", "and", "two", "million", "burakumin", ".", "The", "BLL", "thinks", "there", "must", "be", "at", "least", "three", "million", "burakumin", "living", "in", "Japan", "today", ".", "We", "visited", "a", "hall", "in", "Osaka", "where", "a", "taiko", "drum", "group", ",", "made", "up", "exclusively", "of", "young", "burakumin", ",", "were", "about", "to", "start", "their", "weekly", "rehearsal", ".", "The", "small", "gymnasium", "was", "filled", "with", "taiko", "drums", "of", "all", "sizes", ".", "The", "smallest", "was", "about", "the", "size", "of", "a", "snare", "drum", ",", "the", "largest", "about", "the", "size", "of", "a", "compact", "car", ".", "The", "Japanese", "drum", "group", "Kodo", "have", "made", "th", "prime", "minister", "to", "repatriate", "all", "the", "police", "sent", "to", "Catalonia", "before", "the", "referendum", ".", "What", "were", "the", "results", "?", "With", "nearly", "all", "votes", "counted", ",", "the", "pro", "-", "independence", "parties", 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0.7116782665252686, "DataSource"], [1937, 1937, 0.7078099846839905, "DataSource"], [1949, 1950, 0.512004017829895, "NIL"], [1952, 1952, 0.18480396270751953, "NIL"], [1949, 1949, 0.12661324441432953, "NIL"], [1949, 1952, 0.09030238538980484, "NIL"], [1946, 1947, 0.0865073949098587, "NIL"], [1946, 1950, 0.07362862676382065, "NIL"], [1945, 1947, 0.06935033947229385, "NIL"], [1950, 1950, 0.06848718971014023, "NIL"], [1947, 1950, 0.06299960613250732, "NIL"], [1945, 1950, 0.05181035399436951, "NIL"], [1945, 1945, 0.04461408779025078, "NIL"], [1947, 1947, 0.043506525456905365, "NIL"], [1945, 1946, 0.03948592767119408, "NIL"], [1942, 1942, 0.038528699427843094, "NIL"], [1955, 1955, 0.03697676584124565, "NIL"], [1947, 1949, 0.03531822934746742, "NIL"], [1945, 1948, 0.03381757810711861, "NIL"], [1939, 1942, 0.03293076530098915, "NIL"], [1946, 1948, 0.03284827992320061, "NIL"], [1941, 1942, 0.03149618208408356, "NIL"], [1947, 1948, 0.030324988067150116, "NIL"], [1951, 1952, 0.03020811825990677, "NIL"], [1940, 1940, 0.028621505945920944, "NIL"], [1945, 1949, 0.02409990318119526, "NIL"], [1950, 1952, 0.023675154894590378, "NIL"], [1945, 1952, 0.02342708222568035, "NIL"], [1939, 1939, 0.01863974891602993, "NIL"], [1946, 1949, 0.017397090792655945, "NIL"], [1946, 1952, 0.017071638256311417, "NIL"], [1947, 1952, 0.015385857783257961, "NIL"], [1939, 1940, 0.014609134756028652, "NIL"], [1955, 1956, 0.013884308747947216, "NIL"]], [[1960, 1961, 0.6399005055427551, "NIL"], [1957, 1958, 0.5870948433876038, "Dataset"], [1958, 1958, 0.30976083874702454, "NIL"], [1963, 1965, 0.26884907484054565, "NIL"], [1960, 1965, 0.20417536795139313, "DatasetGeneric"], [1961, 1961, 0.10528851300477982, "NIL"], [1964, 1965, 0.10463795810937881, "NIL"], [1957, 1957, 0.10035639256238937, "NIL"], [1964, 1964, 0.06985437870025635, "NIL"], [1960, 1962, 0.05669686198234558, "NIL"], [1960, 1960, 0.050440628081560135, "NIL"], [1961, 1962, 0.04481598734855652, "NIL"], [1961, 1965, 0.043755318969488144, "NIL"], [1963, 1964, 0.04026767611503601, "NIL"], [1961, 1964, 0.03607910871505737, "NIL"], [1960, 1964, 0.03592444956302643, "NIL"], [1960, 1966, 0.03218541666865349, "NIL"], [1961, 1963, 0.03196077421307564, "NIL"], [1960, 1963, 0.03126811608672142, "NIL"], [1965, 1965, 0.031107541173696518, "NIL"], [1963, 1966, 0.02234051749110222, "NIL"], [1961, 1966, 0.021929746493697166, "NIL"], [1963, 1963, 0.02107866108417511, "NIL"], [1964, 1966, 0.01566968485713005, "NIL"], [1965, 1966, 0.010045979171991348, "NIL"]], [[1987, 1992, 0.9442926645278931, "ReferenceLink"], [1976, 1976, 0.8839545845985413, "Dataset"], [2005, 2005, 0.6424814462661743, "Dataset"], [1967, 1972, 0.624325156211853, "DatasetGeneric"], [1980, 1982, 0.6168519854545593, "NIL"], [2000, 2005, 0.2178530991077423, "NIL"], [2000, 2003, 0.19597643613815308, "NIL"], [1969, 1971, 0.19341374933719635, "NIL"], [1980, 1981, 0.18958139419555664, "NIL"], [1969, 1970, 0.16660217940807343, "Dataset"], [1969, 1972, 0.15901222825050354, "NIL"], [1976, 1982, 0.153213769197464, "NIL"], [1997, 1998, 0.1430748850107193, "NIL"], [2003, 2003, 0.13890142738819122, "Dataset"], [1985, 1985, 0.1271466761827469, "NIL"], [1984, 1985, 0.122630774974823, "NIL"], [1970, 1971, 0.12191884964704514, "NIL"], [1978, 1982, 0.10873617231845856, "NIL"], [1982, 1982, 0.1057797223329544, "NIL"], [1981, 1982, 0.10176895558834076, "NIL"], [1986, 1992, 0.0966976061463356, "NIL"], [1970, 1970, 0.09266604483127594, "NIL"], [2001, 2003, 0.08271109312772751, "NIL"], [1980, 1985, 0.08233188092708588, "DatasetGeneric"], [1968, 1972, 0.07670767605304718, "NIL"], [1981, 1981, 0.07397778332233429, "NIL"], [1971, 1971, 0.07255389541387558, "NIL"], [1996, 1998, 0.06702346354722977, "NIL"], [1976, 1985, 0.06140264868736267, "NIL"], [1967, 1971, 0.059626255184412, "NIL"], [1970, 1972, 0.05914758890867233, "NIL"], [1978, 1978, 0.05784083530306816, "NIL"], [1998, 1998, 0.05523254722356796, "NIL"], [1976, 1981, 0.054375577718019485, "NIL"], [2003, 2005, 0.04970323294401169, "NIL"], [2002, 2003, 0.04907121881842613, "NIL"], [1980, 1980, 0.04852583631873131, "NIL"], [1969, 1969, 0.04839737340807915, "NIL"], [1967, 1976, 0.04736776649951935, "NIL"], [1969, 1976, 0.04529260843992233, "NIL"], [1983, 1985, 0.04412579536437988, "NIL"], [1997, 2005, 0.04233593866229057, "NIL"], [1972, 1972, 0.040806885808706284, "NIL"], [2001, 2005, 0.03974190726876259, "NIL"], [1972, 1982, 0.03958096355199814, "NIL"], [1987, 1993, 0.03919883444905281, "NIL"], [1967, 1970, 0.03730066493153572, "NIL"], [1984, 1993, 0.036876384168863297, "NIL"], [1997, 2003, 0.03673091530799866, "NIL"], [1968, 1971, 0.03620287403464317, "NIL"], [1971, 1982, 0.03536355122923851, "NIL"], [1971, 1972, 0.03512243553996086, "NIL"], [2000, 2002, 0.03387201949954033, "NIL"], [1978, 1979, 0.032801758497953415, "NIL"], [1981, 1985, 0.032133374363183975, "NIL"], [1981, 1992, 0.0316346250474453, "NIL"], [1982, 1985, 0.029486631974577904, "NIL"], [1967, 1978, 0.028356237336993217, "NIL"], [2001, 2002, 0.028226787224411964, "NIL"], [1996, 2005, 0.02799960784614086, "NIL"]], [[2017, 2021, 0.6845365762710571, "Task"], [2010, 2010, 0.6695597767829895, "Dataset"], [2009, 2011, 0.3868768811225891, "NIL"], [2017, 2020, 0.11666309088468552, "NIL"], [2010, 2011, 0.08602307736873627, "NIL"], [2020, 2021, 0.0758335292339325, "NIL"], [2010, 2021, 0.05970177799463272, "NIL"], [2017, 2019, 0.05576162040233612, "NIL"], [2009, 2010, 0.048090022057294846, "NIL"], [2009, 2020, 0.0413120873272419, "NIL"], [2010, 2020, 0.03982362896203995, "NIL"], [2020, 2020, 0.037677351385354996, "NIL"], [2021, 2021, 0.03625686094164848, "NIL"], [2007, 2007, 0.03217678144574165, "NIL"], [2011, 2011, 0.030165696516633034, "NIL"], [2014, 2014, 0.029556777328252792, "NIL"], [2019, 2021, 0.029075924307107925, "NIL"], [2010, 2019, 0.028835304081439972, "NIL"], [2013, 2014, 0.022587411105632782, "NIL"], [2011, 2020, 0.021813878789544106, "NIL"], [2013, 2021, 0.020911280065774918, "NIL"], [2014, 2020, 0.0197798740118742, "NIL"], [2017, 2022, 0.019572386518120766, "NIL"], [2014, 2021, 0.01751090958714485, "NIL"], [2013, 2013, 0.017465446144342422, "NIL"], [2019, 2020, 0.017128605395555496, "NIL"], [2009, 2019, 0.016485486179590225, "NIL"], [2013, 2020, 0.015932103618979454, "NIL"], [2011, 2021, 0.015341285616159439, "NIL"], [2010, 2014, 0.014751695096492767, "NIL"], [2011, 2019, 0.014080562628805637, "NIL"], [2018, 2021, 0.013481884263455868, "NIL"], [2009, 2014, 0.013416919857263565, "NIL"], [2018, 2020, 0.012506413273513317, "NIL"], [2019, 2019, 0.012019649147987366, "NIL"], [2017, 2017, 0.011977942660450935, "NIL"], [2009, 2013, 0.01162679959088564, "NIL"], [2014, 2019, 0.010653134435415268, "NIL"], [2018, 2019, 0.010643900372087955, "NIL"], [2011, 2014, 0.010477590374648571, "NIL"], [2010, 2013, 0.009462179616093636, "NIL"], [2010, 2017, 0.008609757758677006, "NIL"], [2014, 2022, 0.008550044149160385, "NIL"], [2021, 2022, 0.008499789983034134, "NIL"], [2011, 2022, 0.007956039160490036, "NIL"], [2013, 2019, 0.007686200086027384, "NIL"], [2020, 2022, 0.007213038392364979, "NIL"], [2011, 2013, 0.006891246419399977, "NIL"], [2011, 2017, 0.0064871604554355145, "NIL"], [2013, 2022, 0.005963320843875408, "NIL"], [2009, 2017, 0.005842879880219698, "NIL"], [2014, 2017, 0.00537825096398592, "NIL"], [2018, 2022, 0.004930736962705851, "NIL"], [2019, 2022, 0.004554440267384052, "NIL"], [2013, 2017, 0.0033820918761193752, "NIL"]], [[2040, 2043, 0.731701672077179, "NIL"], [2024, 2024, 0.6794072389602661, "Dataset"], [2027, 2030, 0.6190181970596313, "DatasetGeneric"], [2032, 2032, 0.5402227640151978, "NIL"], [2034, 2034, 0.37170544266700745, "NIL"], [2023, 2025, 0.35424554347991943, "NIL"], [2027, 2032, 0.22673898935317993, "NIL"], [2028, 2030, 0.21492312848567963, "NIL"], [2024, 2032, 0.1458851546049118, "NIL"], [2028, 2032, 0.14435815811157227, "NIL"], [2040, 2042, 0.14041690528392792, "ReferenceLink"], [2024, 2025, 0.11464683711528778, "NIL"], [2032, 2034, 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"and", "then", "cover", "their", "corresponding", "image", "regions", "on", "the", "document", "image", ".", "The", "model", "needs", "to", "predict", "a", "binary", "label", "for", "each", "token", "based", "on", "whether", "it", "is", "covered", "or", "not", ".", "Text", "-", "Image", "Matching", "For", "Text", "-", "Image", "Matching", "(", "TIM", ")", ",", "we", "aim", "to", "align", "the", "high", "-", "level", "semantic", "representation", "between", "text", "and", "image", ".", "To", "this", "end", ",", "we", "require", "the", "model", "to", "predict", "whether", "the", "text", "and", "image", "come", "from", "the", "same", "document", "page", ".", "The", "LayoutXLM", "model", "is", "pre", "-", "trained", "with", "documents", "in", "53", "languages", ".", "Figure", "2", "shows", "the", "distribution", "of", "pre", "-", "training", "languages", ".", "In", "this", "section", ",", "we", "briefly", "describe", "the", "pipeline", "for", "preparing", "the", "large", "-", "scale", "multilingual", "document", "collection", ".", "To", "collect", "a", "large", "-", "scale", "multilingual", "visually", "-", "rich", "document", "collection", ",", "we", "download", "and", "process", "publicly", "available", "multilingual", "digital", "-", "born", "PDF", "documents", "following", "the", "principles", "and", "policies", "of", "Common", "Crawl", "1.", "Using", "digital", "-", "born", "PDF", "documents", "can", "benefit", "the", "collecting", "and", "pre", "-", "processing", "steps", ".", "On", "the", "one", "hand", ",", "we", "do", "not", "have", "to", "identify", "scanned", "documents", "among", "the", "natural", "images", ".", "On", "the", "other", "hand", ",", "we", "can", "directly", "extract", "accurate", "text", "with", "corresponding", "layout", "information", "with", "off", "-", "the", "-", "shelf", "PDF", "parsers", "and", "save", "time", "for", "running", "expensive", "OCR", "tools", ".", "Pre", "-", "processing", "The", "pre", "-", "processing", "step", "is", "needed", "to", "clean", "the", "dataset", "since", "the", "raw", "multilingual", "PDFs", "are", "often", "noisy", ".", "We", "use", "an", "open", "-", "source", "PDF", "parser", "called", "PyMuPDF", "2", "to", "extract", "text", ",", "layout", ",", "and", "document", "images", "from", "PDF", "documents", ".", "After", "PDF", "parsing", ",", "we", "discard", "the", "documents", "with", "less", "than", "200", "characters", ".", "We", "use", "the", "language", "detector", "from", "the", "BlingFire", "3", "library", "and", "split", "data", "per", "language", ".", "Following", "CCNet", "(", "Wenzek", "et", "al", ".", ",", "2019", ")", ",", "we", "classify", "the", "document", "as", "the", "corresponding", "language", "if", "the", "language", "score", "is", "higher", "than", "0.", "5", ".", "Otherwise", ",", "unclear", "PDF", "files", "with", "a", "language", "score", "of", "less", "than", "0.", "5", "are", "discarded", ".", "Data", "Sampling", "After", "splitting", "the", "data", "per", "language", ",", "we", "use", "the", "same", "sampling", "probability", "p", "l", "\u221d", "(", "n", "l", "/n", ")", "\u03b1", "as", "XLM", "(", "Lample", "and", "Conneau", ",", "2019", ")", "to", "sample", "the", "batches", "from", "different", "languages", ".", "Following", "InfoXLM", "(", "Chi", "et", "al", ".", ",", "2020", ")", ",", "we", "use", "alpha", "=", "0.", "7", "for", "LayoutXLM", "to", "make", "a", "reasonable", "compromise", "between", "performance", "on", "high", "-", "and", "lowresource", "languages", ".", "The", "brief", "language", "distribution", "is", "shown", "in", "Figure", "2.", "Finally", ",", "we", "follow", "this", "distribution", "and", "sample", "a", "multilingual", "document", "dataset", "with", "22", "million", "visually", "rich", "documents", ".", "In", "addition", ",", "we", "also", "sample", "8", "million", "scanned", "English", "documents", "from", "the", "IIT", "-", "CDIP", "dataset", "so", "that", "we", "totally", "use", "30", "million", "documents", "to", "pre", "-", "train", "the", "LayoutXLM", ",", "where", "the", "model", "can", "benefit", "from", "the", "visual", "information", "of", "both", "scanned", "and", "digital", "-", "born", "document", "images", ".", "In", "recent", "years", ",", "many", "evaluation", "datasets", "for", "document", "understanding", "tasks", "have", "been", "proposed", ",", "such", "as", "PublayNet", "(", "Zhong", "et", "al", ".", ",", "2019", ")", ",", "FUNSD", "(", "Jaume", "et", "al", ".", ",", "2019", ")", ",", "SROIE", "4", ",", "TableBank", "(", "Li", "et", "al", ".", ",", "2020a", ")", ",", "DocBank", "(", "Li", "et", "al", ".", ",", "2020b", ")", ",", "DocVQA", "(", "Mathew", "et", "al", ".", ",", "2020", ")", "etc", ".", "They", "have", "successfully", "helped", "to", "evaluate", "the", "proposed", "neural", "network", "models", "and", "show", "the", "performance", "gap", "between", "the", "deep", "learning", "models", "and", "human", "beings", ",", "which", "significantly", "empowers", "the", "development", "of", "document", "understanding", "research", ".", "However", ",", "almost", "all", "of", "these", "evaluations", "and", "benchmarks", "are", "solely", "focused", "on", "English", "documents", ",", "which", "limits", "the", "research", "for", "non", "-", "English", "document", "understanding", "tasks", ".", "To", "this", "end", ",", "we", "introduce", "a", "new", "benchmark", "for", "multilingual", "Form", "Understanding", ",", "or", "XFUND", ",", "by", "extending", "the", "FUNSD", "dataset", "to", "7", "other", "languages", ",", "including", "Chinese", ",", "Japanese", ",", "Spanish", ",", "French", ",", "Italian", ",", "German", ",", "and", "Portuguese", ",", "where", "sampled", "documents", "are", "shown", "in", "Figure", "3.", "Next", ",", "we", "introduce", "the", "key", "-", "value", "extraction", "task", "in", "our", "benchmark", ",", "as", "well", "as", "data", "collection", ",", "labeling", "pipeline", ",", "and", "the", "data", "statistics", ".", "Key", "-", "value", "extraction", "is", "one", "of", "the", "most", "critical", "tasks", "in", "form", "understanding", ".", "Similar", "to", "FUNSD", ",", "we", "define", "this", "task", "with", "two", "sub", "-", "tasks", ",", "which", "are", "semantic", "entity", "recognition", "and", "relation", "extraction", ".", "Semantic", "Entity", "Recognition", "Given", "a", "visuallyrich", "document", "D", ",", "we", "acquire", "discrete", "token", "set", "t", "=", "{", "t", "0", ",", "t", "1", ",", "...", ",", "t", "n", "}", ",", "where", "each", "token", "t", "i", "=", "(", "w", ",", "(", "x", "0", ",", "y", "0", ",", "x", "1", ",", "y", "1", ")", ")", "consists", "of", "a", "word", "w", "and", "its", "bounding", "box", "coordinates", "(", "x", "0", ",", "y", "0", ",", "x", "1", ",", "y", "1", ")", ".", "C", "=", "{", "c", "0", ",", "c", "1", ",", "..", ",", "c", "m", "}", "is", "the", "semantic", "entity", "labels", "where", "the", "tokens", "are", "classified", "into", ".", "Semantic", "entity", "recognition", "is", "the", "task", "of", "extracting", "semantic", "entities", "and", "classifying", "them", "into", "given", "entity", "types", ".", "In", "other", "words", ",", "we", "intend", "to", "find", "a", "function", "F", "SER", ":", "(", "D", ",", "C", ")", "\u2192", "E", ",", "where", "E", "is", "the", "predicted", "semantic", "entity", "set", ":", "where", "head", "i", "and", "tail", "i", "are", "two", "semantic", "entities", ".", "In", "this", "work", ",", "we", "mainly", "focus", "on", "the", "key", "-", "value", "relation", "extraction", ".", "Form", "Templates", "Forms", "are", "usually", "used", "to", "collect", "information", "in", "different", "business", "scenarios", ".", "In", "order", "to", "avoid", "the", "sensitive", "information", "leak", "with", "the", "real", "-", "world", "documents", ",", "we", "collect", "the", "documents", "publicly", "available", "on", "the", "internet", "and", "remove", "the", "content", "within", "the", "documents", "while", "only", "keeping", "the", "templates", "to", "manually", "fill", "in", "synthetic", "information", ".", "We", "collect", "form", "templates", "in", "7", "languages", "from", "the", "internet", ".", "After", "that", ",", "the", "human", "annotators", "manually", "fill", "synthetic", "information", "into", "these", "form", "templates", "following", "corresponding", "requirements", ".", "Each", "template", "is", "allowed", "to", "be", "used", "only", "once", ",", "which", "means", "each", "form", "is", "different", "from", "the", "others", ".", "Besides", ",", "since", "the", "original", "FUNSD", "documents", "contain", "both", "digitally", "filled", "-", "out", "forms", "and", "handwritten", "forms", ",", "we", "also", "ask", "annotators", "to", "fill", "in", "the", "forms", "by", "typing", "or", "handwriting", ".", "The", "completed", "forms", "are", "finally", "scanned", "into", "document", "images", "for", "further", "OCR", "processing", "and", "key", "-", "value", "labeling", ".", "Key", "-", "value", "Pairs", "Key", "-", "value", "pairs", "are", "also", "annotated", "by", "human", "annotators", ".", "Equipped", "with", "the", "synthetic", "forms", ",", "we", "use", "Microsoft", "Read", "API", "5", "to", "generate", "OCR", "tokens", "with", "bounding", "boxes", ".", "With", "a", "GUI", "annotation", "tool", ",", "annotators", "are", "shown", "the", "original", "document", "images", "and", "the", "bounding", "boxes", "visualization", "of", "all", "OCR", "tokens", ".", "The", "annotators", "are", "asked", "to", "group", "the", "discrete", "tokens", "into", "entities", "and", "assign", "pre", "-", "defined", "labels", "to", "the", "entities", ".", "Also", ",", "if", "two", "entities", "are", "related", ",", "they", "should", "be", "linked", "together", "as", "a", "key", "-", "value", "pair", ".", "The", "XFUND", "benchmark", "includes", "7", "languages", "with", "1", ",", "393", "fully", "annotated", "forms", ".", "Each", "language", "includes", "199", "forms", ",", "where", "the", "training", "set", "includes", "149", "forms", ",", "and", "the", "test", "set", "includes", "50", "forms", ".", "Detailed", "information", "is", "shown", "in", "Table", "1.", "Semantic", "Entity", "Recognition", "For", "this", "task", ",", "we", "simply", "follow", "the", "typical", "sequence", "labeling", "paradigm", "with", "BIO", "labeling", "format", "and", "build", "taskspecific", "layers", "over", "the", "text", "part", "of", "LayoutXLM", ".", "Relation", "Extraction", "Following", "Bekoulis", "et", "al", ".", "(", "2018", ")", ",", "we", "first", "incrementally", "construct", "the", "set", "of", "relation", "candidates", "by", "producing", "all", "possible", "pairs", "of", "given", "semantic", "entities", ".", "For", "every", "pair", ",", "the", "representation", "of", "the", "head", "/", "tail", "entity", "is", "the", "concatenation", "of", "the", "first", "token", "vector", "in", "each", "entity", "and", "the", "entity", "type", "embedding", "obtained", "with", "a", "specific", "type", "embedding", "layer", ".", "After", "respectively", "projected", "by", "two", "FFN", "layers", ",", "the", "representations", "of", "head", "and", "tail", "are", "concatenated", "and", "then", "fed", "into", "a", "bi", "-", "affine", "classifier", ".", "In", "this", "we", "introduce", "the", "experiment", "settings", "for", "pre", "-", "training", "LayoutXLM", ".", "To", "verify", "the", "effectiveness", "of", "the", "pre", "-", "trained", "LayoutXLM", "model", ",", "we", "evaluate", "all", "the", "pre", "-", "trained", "models", "on", "our", "human", "-", "labeled", "XFUND", "benchmark", ".", "Pre", "-", "training", "LayoutXLM", "Following", "the", "original", "LayoutLMv2", "recipe", ",", "we", "train", "LayoutXLM", "models", "with", "two", "model", "sizes", ".", "For", "the", "LayoutXLM", "BASE", "model", ",", "we", "use", "a", "12", "-", "layer", "Transformer", "encoder", "with", "12", "heads", "and", "set", "the", "hidden", "size", "to", "d", "=", "768", ".", "For", "the", "LayoutXLM", "LARGE", "model", ",", "we", "increase", "the", "layer", "number", "to", "24", "with", "16", "heads", "and", "hidden", "size", "to", "d", "=", "1", ",", "024", ".", "ResNeXt101", "-", "FPN", "is", "used", "as", "a", "visual", "backbone", "in", "both", "models", ".", "Finally", ",", "the", "number", "of", "parameters", "in", "these", "two", "models", "are", "approximately", "345", "M", "and", "625", "M", ".", "During", "the", "pre", "-", "training", "stage", ",", "we", "first", "initialize", "the", "Transformer", "encoder", "along", "with", "text", "embeddings", "from", "InfoXLM", "and", "initialize", "the", "visual", "embedding", "layer", "with", "a", "Mask", "-", "RCNN", "model", "trained", "on", "PubLayNet", ".", "The", "rest", "of", "the", "parameters", "are", "initialized", "randomly", ".", "Our", "models", "are", "trained", "with", "64", "Nvidia", "V100", "GPUs", ".", "Fine", "-", "tuning", "on", "XFUND", "We", "conduct", "experiments", "on", "the", "XFUND", "benchmark", ".", "Besides", "the", "experiments", "of", "typical", "language", "-", "specific", "fine", "-", "tuning", ",", "we", "also", "design", "two", "additional", "settings", "to", "demonstrate", "the", "ability", "to", "transfer", "knowledge", "among", "different", "languages", ",", "which", "are", "zero", "-", "shot", "transfer", "learning", "and", "multitask", "fine", "-", "tuning", ".", "Specifically", ",", "(", "1", ")", "language", "-", "specific", "fine", "-", "tuning", "refers", "to", "the", "typical", "fine", "-", "tuning", "paradigm", "of", "fine", "-", "tuning", "on", "language", "X", "and", "testing", "on", "language", "X", ".", "(", "2", ")", "Zero", "-", "shot", "transfer", "learning", "means", "the", "models", "are", "trained", "on", "English", "data", "only", "and", "evaluated", "on", "each", "target", "lan", "-", "guage", ".", "(", "3", ")", "Multitask", "fine", "-", "tuning", "requires", "the", "model", "to", "train", "on", "data", "in", "all", "languages", ".", "We", "evaluate", "models", "in", "these", "three", "settings", "over", "two", "sub", "-", "tasks", "in", "XFUND", ":", "semantic", "entity", "recognition", "and", "relation", "extraction", ",", "and", "compare", "LayoutXLM", "to", "two", "strong", "cross", "-", "lingual", "language", "models", ":", "XLM", "-", "R", "and", "In", "-", "foXLM", ".", "We", "evaluate", "the", "LayoutXLM", "model", "on", "languagespecific", "fine", "-", "tuning", "tasks", ",", "and", "the", "results", "are", "shown", "in", "Table", "2.", "Compared", "with", "the", "pre", "-", "trained", "models", "such", "as", "XLM", "-", "R", "and", "InfoXLM", ",", "the", "LayoutXLM", "LARGE", "model", "achieves", "the", "highest", "F1", "scores", "in", "both", "SER", "and", "RE", "tasks", ".", "The", "significant", "improvement", "shows", "LayoutXLM", "'s", "capability", "to", "transfer", "knowledge", "obtained", "from", "pre", "-", "training", "to", "downstream", "tasks", ",", "which", "further", "confirms", "the", "effectiveness", "of", "our", "multilingual", "pre", "-", "training", "framework", ".", "For", "the", "cross", "-", "lingual", "zero", "-", "shot", "transfer", ",", "we", "present", "the", "evaluation", "results", "in", "Table", "3.", "Although", "the", "model", "are", "only", "fine", "-", "tuned", "on", "FUNSD", "dataset", "(", "in", "English", ")", ",", "it", "can", "still", "transfer", "the", "knowledge", "to", "different", "languages", ".", "In", "addition", ",", "it", "is", "observed", "that", "the", "LayoutXLM", "model", "significantly", "outperforms", "the", "other", "text", "-", "based", "models", ".", "This", "verifies", "that", "Lay", "-", "outXLM", "can", "capture", "the", "common", "layout", "invariance", "among", "different", "languages", "and", "transfer", "to", "other", "languages", "for", "form", "understanding", ".", "Finally", ",", "Table", "4", "shows", "the", "evaluation", "results", "on", "the", "multitask", "learning", ".", "In", "this", "setting", ",", "the", "pre", "-", " ", "trained", "LayoutXLM", "model", "is", "fine", "-", "tuned", "with", "all", "8", "languages", "simultaneously", "and", "evaluated", "on", "each", "specific", "language", ",", "in", "order", "to", "investigate", "whether", "improvements", "can", "be", "obtained", "by", "multilingual", "finetuning", ".", "We", "observe", "that", "the", "multitask", "learning", "further", "improves", "the", "model", "performance", "compared", "to", "the", "language", "-", "specific", "fine", "-", "tuning", ",", "which", "also", "confirms", "that", "document", "understanding", "can", "benefit", "from", "the", "layout", "invariance", "among", "different", "languages", ".", "Multimodal", "pre", "-", "training", "has", "become", "popular", "in", "recent", "years", "due", "to", "its", "successful", "applications", "in", "vision", "-", "language", "representation", "learning", ".", " ", "Lu", "et", "al", ".", "(", "2019", ")", "proposed", "ViLBERT", "for", "learning", "taskagnostic", "joint", "representations", "of", "image", "content", "and", "natural", "language", "by", "extending", "the", "popular", "BERT", "architecture", "to", "a", "multimodal", "two", "-", "stream", "model", ".", " ", "Su", "et", "al", ".", "(", "2020", ")", "proposed", "VL", "-", "BERT", "that", "adopts", "the", "Transformer", "model", "as", "the", "backbone", ",", "and", "extends", "it", "to", "take", "both", "visual", "and", "linguistic", "embedded", "features", "as", "input", ".", " ", "Li", "et", "al", ".", "(", "2019", ")", "propose", "Visual", "-", "BERT", "consists", "of", "a", "stack", "of", "Transformer", "layers", "that", "implicitly", "align", "elements", "of", "an", "input", "text", "and", "regions", "in", "an", "associated", "input", "image", "with", "selfattention", ".", " ", "Chen", "et", "al", ".", "(", "2020", ")", "introduced", "UNITER", "that", "learns", "through", "large", "-", "scale", "pre", "-", "training", 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"set", "of", "labeled", "samples", ".", "Over", "these", "iterations", ",", "the", "label", "noise", "in", "the", "training", "set", "is", "expected", "to", "reduce", ".", "In", "the", "following", ",", "we", "give", "more", "details", "about", "the", "combination", "of", "this", "training", "and", "filtering", "procedure", "with", "existing", "techniques", "from", "semi", "-", "supervised", "learning", ".", "Let", "train", "and", "valid", "(", "D", "i", ",", "D", "val", ")", "denote", "a", "training", "procedure", "which", "will", "be", "explained", "in", "detail", "in", "Section", "2.", "3", ".", "Using", "these", "notations", ",", "the", "label", "filtering", "algorithm", "is", "given", "in", "Algorithm", "1.", "The", "label", "filtering", "is", "performed", "on", "the", "original", "label", "set", "from", "iteration", "0.", "In", "this", "way", ",", "clean", "labels", "erroneously", "removed", "in", "an", "earlier", "iteration", "(", "e.g.", ",", "labels", "of", "hard", "to", 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"[", "3", "]", "and", "[", "4", "]", ",", "the", "authors", "used", "domain", "and", "dynamics", "randomization", ",", "respectively", ".", "In", "[", "5", "]", ",", "the", "authors", "propose", "a", "new", "multi", "-", "stage", "RL", "agent", ",", "DARLA", "(", "DisentAngled", "Representation", "Learning", "Agent", ")", ",", "which", "learns", "to", "see", "before", "learning", "to", "act", ".", "More", "recently", ",", "domain", "adaptation", "has", "been", "studied", "for", "robotic", "manipulators", "[", "6", "]", "[", "7", "]", "[", "8", "]", "[", "9", "]", "[", "10", "]", "[", "11", "]", "in", "which", "the", "authors", "use", "raw", "(", "pixel", ")", "images", "as", "state", "for", "deep", "reinforcement", "learning", ".", "To", "achieve", "zero", "-", "shot", "RL", "requires", "addressing", "the", "uncertainty", ",", "un", "-", "modeled", "dynamics", ",", "and", "perception", "challenges", "across", "all", "three", "components", ",", "namely", ",", "agent", ",", "environment", ",", "and", "interpreter", ".", "There", "are", "currently", "two", "schools", "of", "thought", ",", "one", "focusing", "on", "improving", "dynamics", "and", "the", "other", "on", "perception", ".", "We", "argue", "that", "the", "key", "to", "achieving", "robust", "zero", "-", "shot", "reinforcement", "learning", "requires", "jointly", "addressing", "uncertainty", "in", "dynamics", "and", "variability", "in", "perception", ".", "We", "propose", "a", "new", "deep", "neural", "network", "architecture", "named", "Deep", "Attention", "Convolutional", "Neural", "Network", "(", "DACNN", ")", ".", "An", "overview", "of", "the", "steps", "of", "our", "proposed", "approach", "is", "shown", "in", "Figure", "1.", "Our", "key", "contribution", "is", "that", "our", "attention", "model", "uniquely", "captures", "underlying", "components", "in", "the", "modern", "control", "theoretic", "approach", ",", "i.e.", ",", "image", "-", "based", "servo", "-", "ing", ",", "without", "the", "need", "for", "separation", "of", "perception", "and", "control", ".", "The", "image", "-", "based", "servoing", "have", "been", "succesully", "applied", "to", "robotic", "control", "use", "cases", "including", "but", "not", "limited", "to", "drones", ".", "The", "recent", "image", "-", "based", "servo", "-", "ing", "methods", "use", "image", "feature", "vectors", "which", "are", "specific", "transformation", "of", "the", "raw", "pixels", ".", "We", "prove", "that", "our", "attention", "model", "uniquely", "captures", "the", "image", "feature", "vectors", ",", "i.e.", ",", "in", "image", "-", "based", "visual", "servo", "control", ",", "via", "annotation", "vectors", ".", "Annotation", "vectors", "are", "extracted", "from", "a", "CNN", "as", "described", "in", "[", "12", "]", ".", "By", "defining", "the", "image", "features", "as", "annotation", "vectors", ",", "the", "full", "image", "error", "is", "defined", "in", "term", "of", "the", "weights", "of", "the", "annotation", "vectors", ".", "We", "assume", "that", "the", "annotation", "vectors", "have", "fixed", "orientation", "in", "the", "inertial", "frame", ".", "This", "assumption", "allows", "the", "passivity", "-", "like", "features", "of", "the", "dynamic", "system", "to", "transfer", "to", "the", "full", "image", "error", "when", "a", "spherical", "camera", "geometry", "is", "used", ".", "Therefore", ",", "we", "jointly", "solve", "the", "perception", "and", "control", "problem", "via", "the", "attention", "model", "that", "results", "in", "robust", "domain", "adaptation", "with", "zero", "-", "shot", "RL", ".", "A", "complete", "characterization", "of", "the", "class", "of", "systems", "which", "can", "be", "rendered", "passive", "from", "is", "beyond", "the", "scope", "of", "this", "paper", ".", "However", ",", "this", "class", "is", "broad", ",", "and", "encompasses", "mechanical", "systems", "modeled", "by", "Euler", "-", "Lagrange", "equations", "[", "13", "]", ".", "In", "this", "section", ",", "we", "describe", "each", "constructing", "block", "of", "the", "overall", "architecture", "of", "our", "proposed", "approach", "in", "Figure", "1.", "First", ",", "we", "describe", "the", "core", "of", "our", "architecture", ",", "attention", "neural", "networks", ".", "Second", ",", "we", "describe", "the", "underlying", "assumptions", "that", "enable", "attention", "networks", "to", "perform", "better", "than", "the", "current", "state", "-", "of", "-", "the", "art", "approaches", ".", "Finally", ",", "we", "provide", "how", "autonomous", "driving", "physics", "satisfy", "the", "assumptions", "for", "deep", "reinforcement", "learning", "with", "attention", "networks", ".", "Our", "hypothesis", "is", "that", "under", "certain", "assumptions", "on", "the", "control", "system", "and", "sensor", "configuration", ",", "a", "specific", "type", "of", "neural", "network", ",", "i.e.", ",", "attention", "network", ",", "enables", "joint", "perception", "and", "stable", "control", "of", "the", "system", "even", "there", "are", "significant", "changes", "in", "the", "environment", "such", "as", "texture", "and", "lighting", "that", "transforms", "the", "observation", "space", ".", "There", "are", "several", "formulation", "of", "attention", "networks", "for", "image", "-", "captioning", "and", "natural", "language", "processing", ".", "To", "the", "best", "of", "our", "knowledge", ",", "the", "attention", "mechanism", "in", "these", "applications", "are", "used", "in", "conjunction", "with", "recurrent", "neural", "networks", ".", "There", "are", "several", "formulations", "of", "attention", "models", "in", "recurrent", "neural", "networks", "[", "14", ",", "12", ",", "15", ",", "16", "]", ".", "Attention", "enables", "neural", "networks", "to", "\"", "focus", "\"", "selectively", "on", "different", "parts", "of", "the", "input", "while", "generating", "the", "corresponding", "parts", "of", "the", "output", "sequence", ".", "This", "selective", "\"", "focus", "\"", "for", "a", "corresponding", "input", "is", "then", "learned", "through", "back", "-", "propogation", ".", "Our", "formulation", "is", "inspired", "from", "the", "attention", "model", "in", "[", "14", "]", "where", "the", "attention", "-", "based", "model", "can", "attend", "to", "salient", "part", "of", "an", "image", "while", "generating", "its", "caption", ".", "Intuitively", ",", "attention", "enables", "the", "model", "to", "see", "what", "parts", "of", "the", "image", "to", "focus", "on", "as", "it", "generates", "a", "caption", ".", "It", "is", "very", "much", "equivalent", "to", "how", "humans", "perceive", "when", "performing", "image", "caption", "generation", "or", "long", "length", "machine", "translation", ".", "In", "the", "context", "of", "autonomous", "driving", ",", "the", "vehicle", "needs", "to", "focus", "on", "the", "ques", "from", "the", "road", "such", "as", "white", "and", "yellow", "lines", "but", "not", "on", "the", "entire", "road", ",", "i.e.", ",", "grey", "asphalt", ",", "unless", "there", "is", "an", "obstacle", "or", "another", "vehicle", ".", "Our", "main", "goal", "is", "to", "learn", "the", "shortest", "path", "on", "an", "arbitrarily", "-", "drawn", "track", "using", "a", "ground", "robot", "or", "vehicle", "as", "the", "highest", "possible", "speed", "without", "going", "off", "-", "the", "-", "track", ",", "hitting", "obstacles", "or", "other", "vehicles", ".", "We", "assume", "that", "the", "ground", "vehicle", "control", "is", "based", "only", "on", "raw", "(", "pixel", ")", "image", "and", "there", "is", "no", "other", "sensor", "for", "position", "or", "velocity", ".", "In", "the", "following", ",", "first", ",", "we", "consider", "the", "image", "-", "based", "control", "formulation", "using", "construct", "from", "the", "image", "-", "based", "visual", "servo", "(", "IBVS", ")", "theory", "and", "the", "kinematic", "model", "of", "our", "vehicle", "as", "defined", "in", "[", "17", "]", ".", "We", "provide", "the", "necessary", "conditions", "required", "to", "preserve", "passivity", "-", "like", "properties", ".", "Second", ",", "we", "consider", "the", "full", "image", "error", "for", "the", "control", "problem", ".", "We", "propose", "that", "the", "image", "features", "and", "full", "image", "error", "is", "defined", "in", "terms", "of", "annotation", "vectors", "and", "their", "corresponding", "weights", ".", "We", "show", "that", "the", "proposed", "formulation", "guarantees", "a", "stabilizing", "controller", ".", "Finally", ",", "we", "describe", "the", "learning", "task", "based", "on", "attention", "model", ".", "The", "image", "-", "based", "only", "IBVS", "approach", "for", "our", "ground", "vehicle", "problem", "can", "be", "solved", "if", "and", "only", "if", "the", "image", "geometry", "is", "spherical", ".", "In", "the", "classical", "setting", ",", "the", "state", "of", "our", "vehicle", "is", "defined", "as", "s", "=", "[", "x", ",", "y", ",", "\u03c8", ",", "v", "]", "where", "(", "x", ",", "y", ")", "is", "the", "position", "of", "the", "vehicle", "on", "a", "2D", "plane", ",", "\u03c8", "is", "the", "steering", "angle", "of", "the", "center", "of", "the", "mass", ",", "and", "v", "is", "the", "velocity", "of", "the", "vehicle", "in", "2D", "plane", ".", "The", "state", "transition", "function", "is", "defined", "by", "the", "discrete", "-", "time", "formulation", "of", "the", "kinematic", "model", "in", "Equations", "1", "-", "4", "as", "formulated", "in", "[", "17", "]", ":", "l", "r", "is", "the", "distance", "of", "the", "center", "of", "mass", "to", "the", "rear", "axle", ",", "L", "is", "the", "length", "of", "the", "vehicle", ",", "a", "is", "the", "acceleration", ",", "and", "\u03b4", "f", "is", "the", "steering", "of", "the", "front", "vehicle", "1.", "The", "proposed", "kinematic", "performs", "at", "par", "with", "the", "dynamic", "model", "for", "model", "predictive", "control", "off", "-", "road", "test", "using", "actual", "-", "size", "passenger", "automobiles", ".", "This", "kinematic", "model", "satisfies", "the", "passivity", "property", "for", "the", "control", "system", ".", "In", "the", "classical", "IBVS", "formulation", ",", "the", "control", "state", "is", "inferred", "from", "the", "sensor", "-", "based", "observations", ".", "That", "is", ",", "the", "sensor", "state", "is", "the", "raw", "-", "pixel", "image", "and", "a", "transformation", "matrix", "is", "used", "to", "map", "observations", "into", "the", "control", "state", ".", "In", "our", "deep", "reinforcement", "learning", "formulation", ",", "we", "consider", "observations", "as", "the", "state", "and", "the", "control", "state", "transformation", "is", "implicitly", "embedded", "into", "the", "neural", "network", "and", "will", "not", "be", "inferred", "directly", ".", "The", "deep", "reinforcement", "learning", "algorithm", "will", "infer", "on", "the", "control", "state", "through", "a", "reward", "function", "by", "making", "trial", "-", "and", "-", "error", "based", "decision", "on", "the", "observation", "space", ",", "i.e.", ",", "raw", "pixel", "images", ".", "In", "our", "and", "IBVS", "formulation", ",", "the", "observation", "state", "is", "defined", "as", "S", "\u2208", "R", "L", "where", "S", "=", "[", "a", "1", ",", ".", ".", ".", "a", "L", "]", "\u2208", "S", "is", "a", "matrix", "and", "each", "column", "a", "i", "\u2208", "R", "D", "corresponds", "to", "a", "D", "-", "dimensional", "feature", "extracted", "from", "the", "observed", "image", ",", "L", "and", "D", "are", "finite", "integers", ".", "The", "geometry", "of", "the", "camera", "is", "modeled", "by", "its", "image", "surface", "S", "relative", "to", "its", "focal", "point", ".", "Therefore", ",", "the", "image", "feature", "a", "i", "can", "be", "written", "as", "a", "function", "of", "is", "projection", "P", "i", "onto", "the", "image", "surface", "S", "in", "the", "body", "fixed", "frame", ".", "The", "image", "feature", "in", "our", "formulation", "is", "the", "output", "of", "the", "convolutional", "neural", "network", "layers", ",", "and", "the", "input", "to", "the", "convolutional", "network", "layers", "is", "the", "raw", "-", "pixel", "image", ".", "Theorem", "2.", "1", ".", "The", "passivity", "-", "like", "properties", "of", "the", "body", "fixed", "frame", "dynamics", "of", "a", "rigid", "object", "in", "the", "image", "space", "are", "preserved", "if", "and", "only", "if", "the", "image", "geometry", "is", "of", "a", "spherical", "camera", ".", "The", "proof", "of", "Theorem", "2.", "1", "is", "in", "[", "18", "]", ".", "Our", "kinematic", "equations", ",", "Equations", "1", "-", "4", ",", "already", "exhibits", "a", "simple", "linear", "cascade", "system", ",", "i.e.", ",", "\u1e8b", "=", "vR", "and", "v", "=", "a", "where", "R", "is", "a", "rotation", "matrix", ".", "Since", "cascade", "systems", "exhibit", "passivity", "-", "like", "properties", ",", "to", "guarantee", "that", "the", "controlled", "system", "inherits", "passivity", "-", "like", "properties", ",", "we", "need", "to", "show", "that", "the", "gradient", "of", "the", "full", "image", "error", "contains", "a", "skew", "-", "symmetric", "matrix", "on", "angular", "velocities", ".", "In", "the", "next", "section", ",", "we", "define", "the", "full", "image", "error", "in", "terms", "of", "an", "attention", "network", ".", "The", "overall", "neural", "network", "architecture", "with", "the", "deep", "attention", "network", "for", "our", "approach", "is", "shown", "in", "Figure", "2.", "Intuitively", ",", "the", "objective", "of", "a", "visual", "servo", "algorithm", "in", "image", "space", "is", "to", "match", "the", "observed", "image", "to", "a", "known", "\"", "model", "\"", "image", "of", "the", "target", ".", "The", "target", "is", "an", "image", "of", "the", "environment", "with", "the", "desired", "outcome", ".", "In", "the", "context", "of", "autonomous", "vehicle", ",", "a", "target", "is", "an", "image", "of", "the", "road", "where", "the", "vehicle", "is", "within", "the", "white", "lines", "and", "away", "from", "obstacles", "and", "other", "vehicles", ".", "Our", "approach", "does", "not", "require", "a", "known", "model", "image", "of", "the", "target", "for", "controls", ".", "However", ",", "we", "need", "to", "engineer", "a", "reward", "function", "that", "will", "indirectly", "provide", "the", "means", "to", "discriminate", "between", "desired", "versus", "undesired", "behavior", ".", "Therefore", ",", "it", "is", "necessary", "to", "examine", "the", "error", "in", "the", "image", "space", ".", "Furthermore", ",", "we", "hypothesize", "that", "our", "attention", "network", "model", "reduces", "the", "image", "space", "error", "compared", "to", "naively", "feeding", "image", "features", "extracted", "from", "CNN", "layers", ".", "The", "full", "image", "error", "between", "the", "observed", "and", "known", "model", "image", "is", "defined", "using", "a", "combination", "matrix", "approach", "where", "a", "*", "i", "are", "the", "desired", "image", "features", "and", "C", "is", "the", "combination", "matrix", "that", "preserve", "the", "passivitylike", "properties", ".", "Assuming", "that", "C", "is", "full", "rank", ",", "we", "can", "rewrite", "the", "full", "image", "error", "as", "a", "weighted", "sum", "where", "\u03b1", "i", "\u2265", "0.", "The", "choice", "of", "\u03b1", "i", "becomes", "the", "design", "component", "for", "the", "control", "algorithm", ".", "We", "propose", "that", "in", "the", "above", "formulation", "a", "i", "can", "be", "chosen", "as", "the", "annotation", "vectors", "in", "a", "our", "modified", "attention", "model", "and", "\u03b1", "i", "are", "the", "corresponding", "weights", "of", "the", "annotation", "vectors", ".", "Suppose", "that", "a", "set", "of", "image", "features", ",", "annotation", "vectors", "are", "extracted", "from", "a", "CNN", "as", "in", "[", "14", "]", ".", "The", "output", "of", "the", "attention", "layer", "from", "the", "annotation", "vectors", "corresponds", "to", "the", "features", "extracted", "at", "different", "image", "locations", ".", "The", "extractor", "produces", "a", "finite", "number", "L", "of", "annotation", "vectors", "a", "=", "{", "a", "1", ",", "...", ",", "a", "L", "}", ",", "a", "i", "\u2208", "R", "D", "where", "D", "is", "a", "finite", "integer", ".", "These", "annotation", "vectors", "form", "the", "state", "space", "of", "our", "MDP", ".", "We", "define", "a", "context", "vector", "\u1e91", "where", "\u03c6", "is", "a", "weighted", "sum", ",", "For", "each", "location", "i", ",", "the", "mechanism", "generates", "a", "positive", "weight", "\u03b1", "i", "which", "can", "be", "interpreted", "either", "as", "the", "probability", "that", "location", "i", "is", "the", "right", "place", "to", "focus", "for", "producing", "the", "control", "action", "(", "the", "\"", "hard", "\"", "but", "stochastic", "attention", "mechanism", ")", ",", "or", "as", "the", "relative", "importance", "to", "give", "to", "location", "i", "in", "weighted", "sum", "of", "the", "the", "a", "i", "vectors", ".", "The", "weight", "\u03b1", "i", "of", "each", "annotation", "vector", "a", "i", "is", "computed", "by", "an", "attention", "model", "f", "att", ".", "The", "weight", "\u03b1", "i", "is", "calculated", "by", "the", "softmax", "function", "where", "h", "t\u22121", "are", "hidden", "state", "vectors", "from", "the", "previous", "LSTM", "cell", "and", "f", "att", "an", "attention", "model", ".", "In", "the", "literature", ",", "there", "are", "multiple", "formulations", "of", "the", "f", "att", "model", ",", "i.e.", ",", "additive", "and", "multiplicative", ".", "In", "the", "following", ",", "we", "describe", "our", "formulation", "of", "f", "att", "based", "on", "additive", "models", "The", "only", "input", "to", "the", "attention", "model", "f", "att", "is", "the", "annotation", "vectors", ".", "Additive", "attention", "(", "or", "multilayer", "perceptron", "(", 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"that", "we", "can", "stabilize", "the", "system", "if", "the", "velocity", "is", "available", "as", "a", "control", "input", ",", "i.e.", ",", "kinematic", "control", ".", "This", "condition", "is", "satisfied", "by", "our", "design", ".", "While", "the", "visual", "features", "used", "as", "state", "provide", "means", "for", "robustness", "to", "camera", "and", "target", "calibration", "errors", ",", "the", "rigid", "-", "body", "dynamics", "of", "the", "camera", "ego", "-", "motion", "are", "highly", "coupled", "when", "expressed", "as", "target", "motion", "in", "the", "image", "plane", ".", "Therefore", ",", "a", "direct", "adaptive", "control", "approach", "provide", "better", "results", ".", "We", "consider", "a", "general", "formulation", "of", "the", "ground", "robot", "navigation", "as", "Markov", "decision", "process", "(", "MDP", ")", "and", "use", "a", "vanilla", "clipped", "proximate", "policy", "optimization", "algorithm", "[", "19", "]", ".", "In", "standard", "policy", 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"and", "real", "track", "environment", "respectively", "but", "we", "keep", "the", "track", "shape", "the", "same", "in", "all", "experiments", ".", "Second", ",", "we", "modify", "the", "track", "shape", "as", "well", "as", "the", "color", "and", "texture", ".", "We", "consider", "two", "baselines", "in", "both", "sim2sim", "and", "sim2real", "transfer", "experiments", ".", "First", "baseline", "has", "vanilla", "CNN", "layers", "to", "extract", "features", "without", "our", "attention", "mechanism", ".", "Second", "baseline", "is", "based", "on", "the", "DARLA", "approach", "where", "we", "use", "DARLA", "'s", "\u03b2", "-", "VAE", "neural", "network", "to", "learn", "a", "latent", "state", "representation", "and", "then", "use", "the", "same", "output", "layers", "from", "our", "approach", "to", "learn", "the", "control", "task", ".", "Our", "implementation", "of", "DARLA", "is", "as", "described", "in", "[", "22", "]", ",", "and", "applied", "to", "the", "autonomous", "vehicle", 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0.316119521856308, "NIL"], [1894, 1895, 0.2131417691707611, "NIL"], [1906, 1908, 0.14883127808570862, "NIL"], [1905, 1908, 0.1201152354478836, "NIL"], [1922, 1924, 0.11895369738340378, "NIL"], [1894, 1894, 0.10400784760713577, "NIL"], [1906, 1907, 0.09308762848377228, "NIL"], [1923, 1924, 0.09259254485368729, "NIL"], [1907, 1907, 0.08751396834850311, "NIL"], [1903, 1908, 0.08367092907428741, "NIL"], [1907, 1908, 0.07819708436727524, "NIL"], [1897, 1900, 0.0747830793261528, "NIL"], [1914, 1914, 0.07086006551980972, "NIL"], [1897, 1897, 0.06960655003786087, "NIL"], [1893, 1893, 0.06951069086790085, "NIL"], [1900, 1900, 0.06924944370985031, "NIL"], [1895, 1895, 0.06648623943328857, "NIL"], [1898, 1900, 0.057399965822696686, "NIL"], [1893, 1897, 0.056376006454229355, "NIL"], [1897, 1908, 0.05632345378398895, "NIL"], [1893, 1894, 0.053092487156391144, "NIL"], [1900, 1908, 0.050738003104925156, "NIL"], [1920, 1920, 0.049825266003608704, "NIL"], [1918, 1918, 0.04933745786547661, "NIL"], [1908, 1908, 0.04911494255065918, "NIL"], [1905, 1907, 0.04792983829975128, "NIL"], [1898, 1908, 0.04781552031636238, "NIL"], [1912, 1912, 0.04770582914352417, "NIL"], [1894, 1897, 0.04508182033896446, "NIL"], [1904, 1907, 0.04507406800985336, "NIL"], [1894, 1900, 0.04346488416194916, "NIL"], [1902, 1908, 0.0424010194838047, "NIL"], [1923, 1923, 0.04047149792313576, "NIL"], [1912, 1914, 0.03320262208580971, "NIL"], [1893, 1902, 0.03243023529648781, "NIL"], [1899, 1908, 0.03218965232372284, "NIL"], [1916, 1916, 0.031982142478227615, "NIL"], [1893, 1900, 0.031030787155032158, "NIL"], [1899, 1900, 0.030949875712394714, "NIL"], [1916, 1918, 0.030441341921687126, "NIL"], [1897, 1898, 0.02977444976568222, "NIL"], [1903, 1907, 0.027329979464411736, "NIL"], [1900, 1907, 0.02646423876285553, "NIL"], [1895, 1897, 0.025468172505497932, "NIL"], [1897, 1907, 0.0249237809330225, "NIL"], [1894, 1902, 0.024877255782485008, "NIL"], [1903, 1903, 0.023854414001107216, "NIL"], [1898, 1898, 0.023691991344094276, "NIL"], [1898, 1907, 0.023470602929592133, "NIL"], [1923, 1925, 0.023242752999067307, "NIL"], [1894, 1903, 0.022255893796682358, "NIL"], [1914, 1918, 0.021912584081292152, "NIL"], [1893, 1903, 0.02183813415467739, "NIL"], [1894, 1898, 0.020541194826364517, "NIL"], [1894, 1905, 0.020040202885866165, "NIL"], [1894, 1904, 0.01970982551574707, "NIL"], [1906, 1906, 0.019472219049930573, "NIL"], [1924, 1924, 0.01934386044740677, "NIL"], [1904, 1904, 0.018742702901363373, "NIL"]], [[1927, 1928, 0.579923689365387, "Method"], [1938, 1940, 0.44359713792800903, "NIL"], [1955, 1958, 0.19985024631023407, "NIL"], [1927, 1927, 0.1884293258190155, "NIL"], [1930, 1933, 0.157710999250412, "NIL"], [1939, 1940, 0.14176203310489655, "NIL"], [1942, 1945, 0.13995687663555145, "NIL"], [1960, 1964, 0.10473167151212692, "NIL"], [1956, 1958, 0.10106594115495682, "NIL"], [1930, 1932, 0.09418696165084839, "NIL"], [1966, 1967, 0.09009037166833878, "NIL"], [1926, 1928, 0.08818212151527405, 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0.01150924526154995, "NIL"], [1975, 1986, 0.010524233803153038, "NIL"], [1979, 1981, 0.010381228290498257, "NIL"], [1980, 1981, 0.009930594824254513, "NIL"], [1978, 1981, 0.009836309589445591, "NIL"], [1977, 1982, 0.009818227030336857, "NIL"], [1976, 1986, 0.009811164811253548, "NIL"], [1981, 1986, 0.009478842839598656, "NIL"], [1969, 1969, 0.00898441020399332, "NIL"], [1970, 1971, 0.007971491664648056, "NIL"], [1976, 1982, 0.007852965034544468, "NIL"], [1978, 1986, 0.00746475113555789, "NIL"], [1979, 1986, 0.0074157011695206165, "NIL"], [1971, 1971, 0.0065737273544073105, "NIL"], [1975, 1982, 0.005170844960957766, "NIL"]], [[1994, 1996, 0.5896374583244324, "ModelArchitecture"], [1993, 1996, 0.5864194631576538, "NIL"], [1998, 1999, 0.37661078572273254, "NIL"], [2024, 2029, 0.3741867244243622, "NIL"], [1989, 1990, 0.3732089698314667, "NIL"], [2020, 2022, 0.32123416662216187, "NIL"], [2011, 2012, 0.2933890223503113, "NIL"], [2010, 2013, 0.2645287811756134, "Method"], [2015, 2016, 0.2316761016845703, "NIL"], [2020, 2029, 0.19334237277507782, "NIL"], [1987, 1991, 0.1903519183397293, "MLModelGeneric"], [2011, 2013, 0.18837983906269073, "NIL"], [1994, 1995, 0.18416890501976013, "NIL"], [1995, 1996, 0.1773284375667572, "NIL"], [1989, 1991, 0.17560391128063202, "NIL"], [1987, 1996, 0.16415217518806458, "NIL"], [2031, 2032, 0.1502957046031952, "NIL"], [2029, 2029, 0.13004492223262787, "NIL"], [1989, 1996, 0.12929554283618927, "NIL"], [1988, 1990, 0.12717999517917633, "NIL"], [2025, 2029, 0.10608985275030136, "NIL"], [2026, 2029, 0.10222963243722916, "NIL"], [2010, 2012, 0.09873165935277939, "NIL"], [1987, 1990, 0.09471625834703445, "NIL"], [1995, 1995, 0.09255214780569077, "NIL"], [2027, 2029, 0.08772749453783035, "NIL"], [1988, 1991, 0.08477967977523804, "NIL"], [2022, 2022, 0.08178088814020157, "NIL"], [2012, 2012, 0.07827043533325195, "NIL"], [2019, 2022, 0.07645951956510544, "NIL"], [2019, 2019, 0.07611661404371262, "NIL"], [1996, 1996, 0.07527206838130951, 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"problem", ",", "one", "has", "to", "apply", "a", "learning", "procedure", "of", "the", "sort", "proposed", "in", "Song", "and", "Ermon", "(", "2019", ")", ",", "in", "which", "samples", "with", "different", "noise", "levels", "are", "used", ".", "Depending", "on", "the", "dimension", "of", "the", "data", ",", "the", "different", "noise", "levels", "have", "to", "be", "spaced", "narrowly", "enough", "to", "avoid", "empty", "regions", "in", "the", "data", "space", ".", "In", "the", "following", ",", "we", "will", "use", "Gaussian", "noise", "and", "employ", "a", "Gaussian", "scale", "mixture", "to", "produce", "the", "noisy", "data", "samples", "for", "the", "training", "(", "for", "details", ",", "See", "Section", "3.", "1", "and", "Appendix", "A", ")", ".", "Another", "interesting", "property", "of", "denoising", "score", "matching", "was", "suggested", "in", "the", "denoising", "autoencoder", "literature", "(", "Vincent", "et", "al", ".", ",", "2010", ";", "Karklin", "and", "Simoncelli", ",", "2011", ")", ".", "With", "increasing", "noise", "level", ",", "the", "learned", "features", "tend", "to", "have", "larger", "spatial", "scale", ".", "In", "our", "experiment", "we", "observe", "similar", "phenomenon", "when", "training", "model", "with", "denoising", "score", "matching", "with", "single", "noise", "scale", ".", "If", "one", "compare", "samples", "in", "Figure", "B.1", ",", "Appendix", "B", ",", "it", "is", "evident", "that", "noise", "level", "of", "0.", "3", "produced", "a", "model", "that", "learned", "short", "range", "correlation", "that", "spans", "only", "a", "few", "pixels", ",", "noise", "level", "of", "0.", "6", "learns", "longer", "stroke", "structure", "without", "coherent", "overall", "structure", ",", "and", "noise", "level", "of", "1", "learns", "more", "coherent", "long", "range", "structure", "without", "details", "such", "as", "stroke", "width", "variations", ".", "This", "suggests", "that", "training", "with", "single", "noise", "level", "in", "denoising", "score", "matching", "is", "not", "sufficient", "for", "learning", "a", "model", "capable", "of", "high", "-", "quality", "sample", "synthesis", ",", "as", "such", "a", "model", "have", "to", "capture", "data", "structure", "of", "all", "scales", ".", "Motivated", "by", "the", "analysis", "in", "section", "2", ",", "we", "strive", "to", "develop", "an", "EBM", "based", "on", "denoising", "score", "matching", "that", "can", "be", "trained", "with", "noisy", "samples", "in", "which", "the", "noise", "level", "is", "not", "fixed", "but", "drawn", "from", "a", "distribution", ".", "The", "model", "should", "approximate", "the", "Parzen", "density", "estimator", "of", "the", "data", "p", "\u03c30", "(", "x", "x", "x", ")", "=", "q", "\u03c30", "(", "x", "x", "x|x", "x", "x", ")", "p", "(", "x", "x", "x", ")", "dx", ".", "Specifically", ",", "the", "learning", "should", "minimize", "the", "difference", "between", "the", "derivative", "of", "the", "energy", "and", "the", "score", "of", "p", "\u03c30", "under", "the", "expectation", "E", "p", "M", "(", "x", "x", "x", ")", "rather", "than", "E", "p\u03c3", "0", "(", "x", "x", "x", ")", ",", "the", "expectation", "taken", "in", "standard", "denoising", "score", "matching", ".", "Here", "p", "M", "(", "x", "x", "x", ")", "=", "q", "M", "(", "x", "x", "x|x", "x", "x", ")", "p", "(", "x", "x", "x", ")", "dx", "is", "chosen", "to", "cover", "the", "signal", "space", "more", "evenly", "to", "avoid", "the", "measure", "concentration", "issue", "described", "above", ".", "The", "resulting", "Multiscale", "Score", "Matching", "(", "MSM", ")", "objective", "is", ":", "Compared", "to", "the", "objective", "of", "denoising", "score", "matching", "(", "1", ")", ",", "the", "only", "change", "in", "the", "new", "objective", "(", "4", ")", "is", "the", "expectation", ".", "Both", "objectives", "are", "consistent", ",", "if", "p", "M", "(", "x", "x", "x", ")", "and", "p", "\u03c30", "(", "x", "x", "x", ")", "have", "the", "same", "support", ",", "as", "shown", "formally", "in", "Proposition", "1", "of", "Appendix", "A", ".", "In", "Proposition", "2", ",", "we", "prove", "that", "Equation", "4", "is", "equivalent", "to", "the", "following", "denoising", "score", "matching", "objective", ":", "The", "above", "results", "hold", "for", "any", "noise", "kernel", "q", "\u03c30", "(", "x", "x", "x|x", "x", "x", ")", ",", "but", "Equation", "5", "contains", "the", "reversed", "expectation", ",", "which", "is", "difficult", "to", "evaluate", "in", "general", ".", "To", "proceed", ",", "we", "choose", "q", "\u03c30", "(", "x", "x", "x|x", "x", "x", ")", "to", "be", "Gaussian", ",", "and", "also", "choose", "q", "M", "(", "x", "x", "x|x", "x", "x", ")", "to", "be", "a", "Gaussian", "scale", "mixture", ":", "After", "algebraic", "manipulation", "and", "one", "approximation", "(", "see", "the", "derivation", "following", "Proposition", "2", "in", "Appendix", "A", ")", ",", "we", "can", "transform", "Equation", "5", "into", "a", "more", "convenient", "form", ",", "which", "we", "call", "Multiscale", "Denoising", "Score", "Matching", "(", "MDSM", "):", "The", "square", "loss", "term", "evaluated", "at", "noisy", "points", "x", "x", "x", "at", "larger", "distances", "from", "the", "true", "data", "points", "x", "x", "x", "will", "have", "larger", "magnitude", ".", "Therefore", ",", "in", "practice", "it", "is", "convenient", "to", "add", "a", "monotonically", "decreasing", "term", "l", "(", "\u03c3", ")", "for", "balancing", "the", "different", "noise", "scales", ",", "e.g.", "l", "(", "\u03c3", ")", "=", "1", "\u03c3", "2", ".", "Ideally", ",", "we", "want", "our", "model", "to", "learn", "the", "correct", "gradient", "everywhere", ",", "so", "we", "would", "need", "to", "add", "noise", "of", "all", "levels", ".", "However", ",", "learning", "denoising", "score", "matching", "at", "very", "large", "or", "very", "small", "noise", "levels", "is", "useless", ".", "At", "very", "large", "noise", "levels", "the", "information", "of", "the", "original", "sample", "is", "completely", "lost", ".", "Conversely", ",", "in", "the", "limit", "of", "small", "noise", ",", "the", "noisy", "sample", "is", "virtually", "indistinguishable", "from", "real", "data", ".", "In", "neither", "case", "one", "can", "learn", "a", "gradient", "which", "is", "informative", "about", "the", "data", "structure", ".", "Thus", ",", "the", "noise", "range", "needs", "only", "to", "be", "broad", "enough", "to", "encourage", "learning", "of", "data", "features", "over", "all", "scales", ".", "Particularly", ",", "we", "do", "not", "sample", "\u03c3", "but", "instead", "choose", "a", "series", "of", "fixed", "\u03c3", "values", "\u03c3", "4", ",", "we", "arrive", "at", "the", "final", "objective", ":", "It", "may", "seem", "that", "\u03c3", "0", "is", "an", "important", "hyperparameter", "to", "our", "model", ",", "but", "after", "our", "approximation", "\u03c3", "0", "become", "just", "a", "scaling", "factor", "in", "front", "of", "the", "energy", "function", ",", "and", "can", "be", "simply", "set", "to", "one", "as", "long", "as", "the", "temperature", "range", "during", "sampling", "is", "scaled", "accordingly", "(", "See", "Section", "3.", "2", ")", ".", "Therefore", "the", "only", "hyper", "-", "parameter", "is", "the", "rang", "of", "noise", "levels", "used", "during", "training", ".", "On", "the", "surface", ",", "objective", "(", "7", ")", "looks", "similar", "to", "the", "one", "in", "Song", "and", "Ermon", "(", "2019", ")", ".", "The", "important", "difference", "is", "that", "Equation", "7", "approximates", "a", "single", "distribution", ",", "namely", "p", "\u03c30", "(", "x", "x", "x", ")", ",", "the", "data", "smoothed", "with", "one", "fixed", "kernel", "q", "\u03c30", "(", "x", "x", "x|x", "x", "x", ")", ".", "In", "contrast", ",", "Song", "and", "Ermon", "(", "2019", ")", "approximate", "the", "score", "of", "multiple", "distributions", ",", "the", "family", "of", "distributions", "{", "p", "\u03c3i", "(", "x", "x", "x", ")", ":", "i", "=", "1", ",", "...", ",", "n", "}", ",", "resulting", "from", "the", "data", "smoothed", "by", "kernels", "of", "different", "widths", "\u03c3", "i", ".", "Because", "our", "model", "learns", "only", "a", "single", "target", "distribution", ",", "it", "does", "not", "require", "noise", "magnitude", "as", "input", ".", "Langevin", "dynamics", "has", "been", "used", "to", "sample", "from", "neural", "network", "energy", "functions", "(", "Du", "and", "Mordatch", ",", "2019", ";", "Nijkamp", "et", "al", ".", ",", "2019", ")", ".", "However", ",", "the", "studies", "described", "difficulties", "with", "mode", "exploration", "unless", "very", "large", "number", "of", "sampling", "steps", "is", "used", ".", "To", "improve", "mode", "exploration", ",", "we", "propose", "incorporating", "simulated", "annealing", "in", "the", "Langevin", "dynamics", ".", "Simulated", "annealing", "(", "Kirkpatrick", "et", "al", ".", ",", "1983", ";", "Neal", ",", "2001", ")", "improves", "mode", "exploration", "by", "sampling", "first", "at", "high", "temperature", "and", "then", "cooling", "down", "gradually", ".", "This", "has", "been", "successfully", "applied", "to", "challenging", "computational", "problems", ",", "such", "as", "combinatorial", "optimization", ".", "To", "apply", "simulated", "annealing", "to", "Langevin", "dynamics", ".", "Note", "that", "in", "a", "model", "of", "Brownian", "motion", "of", "a", "physical", "particle", ",", "the", "temperature", "in", "the", "Langevin", "equation", "enters", "as", "a", "factor", "\u221a", "T", "in", "front", "of", "the", "noise", "term", ",", "some", "literature", "uses", "\u03b2", "\u22121", "where", "\u03b2", "=", "1", "/", "T", "(", "Jordan", "et", "al", ".", ",", "1998", ")", ".", "Adopting", "the", "\u221a", "T", "convention", ",", "the", "Langevin", "sampling", "process", "(", "Bellec", "et", "al", ".", ",", "2017", ")", "is", "given", "by", ":", "where", "T", "t", "follows", "some", "annealing", "schedule", ",", "and", "denotes", "step", "length", ",", "which", "is", "fixed", ".", "During", "sampling", ",", "samples", "behave", "very", "much", "like", "physical", "particles", "under", "Brownian", "motion", "in", "a", "potential", "field", ".", "Because", "the", "particles", "have", "average", "energies", "close", "to", "the", "their", "current", "thermic", "energy", ",", "they", "explore", "the", "state", "space", "at", "different", "distances", "from", "data", "manifold", "depending", "on", "temperature", ".", "Eventually", ",", "they", "settle", "somewhere", "on", "the", "data", "manifold", ".", "The", "behavior", "of", "the", "particle", "'s", "energy", "value", "during", "a", "typical", "annealing", "process", "is", "depicted", "in", "Appendix", "Figure", "F.1B", ".", "If", "the", "obtained", "sample", "is", "still", "slightly", "noisy", ",", "we", "can", "apply", "a", "single", "step", "gradient", "denoising", "jump", "(", "Saremi", "and", "Hyvarinen", ",", "2019", ")", "to", "improve", "sample", "quality", ":", "This", "denoising", "procedure", "can", "be", "applied", "to", "noisy", "sample", "with", "any", "level", "of", "Gaussian", "noise", "because", "in", "our", "model", "the", "gradient", "automatically", "has", "the", "right", "magnitude", "to", "denoise", "the", "sample", ".", "This", "process", "is", "justified", "by", "the", "Empirical", "Bayes", "interpretation", "of", "this", "denoising", "process", ",", "as", "studied", "in", "Saremi", "and", "Hyvarinen", "(", "2019", ")", ".", "Song", "and", "Ermon", "(", "2019", ")", "also", "call", "their", "sample", "generation", "process", "annealed", "Langevin", "dynamics", ".", "It", "should", "be", "noted", "that", "their", "sampling", "process", "does", "not", "coincide", "with", "Equation", "8.", "Their", "sampling", "procedure", "is", "best", "understood", "as", "sequentially", "sampling", "a", "series", "of", "distributions", "corresponding", "to", "data", "distribution", "corrupted", "by", "different", "levels", "of", "noise", ".", "Preprint", "No", "normalization", "layer", "was", "used", "in", "any", "of", "the", "networks", ".", "We", "designed", "the", "output", "layer", "of", "all", "networks", "to", "take", "a", "generalized", "quadratic", "form", "(", "Fan", "et", "al", ".", ",", "2018", ")", ".", "Because", "the", "energy", "function", "is", "anticipated", "to", "be", "approximately", "quadratic", "with", "respect", "to", "the", "noise", "level", ",", "this", "modification", "was", "able", "to", "boost", "the", "performance", "significantly", ".", "For", "more", "detail", "on", "training", "and", "model", "architecture", ",", "see", "Appendix", "D", ".", "One", "notable", "result", "is", "that", "since", "our", "training", "method", "does", "not", "involve", "sampling", ",", "we", "achieved", "a", "speed", "up", "of", "roughly", "an", "order", "of", "magnitude", "compared", "to", "the", "maximum", "-", "likelihood", "training", "using", "Langevin", "dynamics", "1.", "Our", "method", "thus", "enables", "the", "training", "of", "energy", "-", "based", "models", "even", "when", "limited", "computational", "resources", "prohibit", "maximum", "likelihood", "methods", ".", "We", "found", "that", "the", "choice", "of", "the", "maximum", "noise", "level", "has", "little", "effect", "on", "learning", "as", "long", "as", "it", "is", "large", "enough", "to", "encourage", "learning", "of", "the", "longest", "range", "features", "in", "the", "data", ".", "However", ",", "as", "expected", ",", "learning", "with", "too", "small", "or", "too", "large", "noise", "levels", "is", "not", "beneficial", "and", "can", "even", "destabilize", "the", "training", "process", ".", "Further", ",", "our", "method", "appeared", "to", "be", "relatively", "insensitive", "to", "how", "the", "noise", "levels", "are", "distributed", "over", "a", "chosen", "range", ".", "Geometrically", "spaced", "noise", "as", "in", "(", "Song", "and", "Ermon", ",", "2019", ")", "and", "linearly", "spaced", "noise", "both", "work", ",", "although", "in", "our", "case", "learning", "with", "linearly", "spaced", "noise", "was", "somewhat", "more", "robust", ".", "For", "sampling", "the", "learned", "energy", "function", "we", "used", "annealed", "Langevin", "dynamics", "with", "an", "empirically", "optimized", "annealing", "schedule", ",", "see", "Figure", "F.1B", "for", "the", "particular", "shape", "of", "annealing", "schedule", "we", "used", ".", "In", "contrast", ",", "annealing", "schedules", "with", "theoretical", "guaranteed", "convergence", "property", "takes", "extremely", "long", "(", "Geman", "and", "Geman", ",", "1984", ")", ".", "The", "range", "of", "temperatures", "to", "use", "in", "the", "sampling", "process", "depends", "on", "the", "choice", "of", "\u03c3", "0", ",", "as", "the", "equilibrium", "distribution", "is", "roughly", "images", "with", "Gaussian", "noise", "of", "magnitude", "\u221a", "T", "\u03c3", "0", "added", "on", "top", ".", "To", "ease", "traveling", "between", "modes", "far", "apart", "and", "ensure", "even", "sampling", ",", "the", "initial", "temperature", "needs", "to", "be", "high", "enough", "to", "inject", "noise", "of", "sufficient", "magnitude", ".", "A", "choice", "of", "T", "=", "100", ",", "which", "corresponds", "to", "added", "noise", "of", "magnitude", "\u221a", "100", "*", "0.", "1", "=", "1", ",", "seems", "to", "be", "sufficient", "starting", "point", ".", "For", "step", "length", "we", "generally", "used", "0.", "02", ",", "although", "any", "value", "within", "the", "range", "[", "0.", "015", ",", "0.", "05", "]", "seemed", "to", "work", "fine", ".", "After", "the", "annealing", "process", "we", "performed", "a", "single", "step", "denoising", "to", "further", "enhance", "sample", "quality", ".", "Unconditional", "Image", "Generation", ".", "We", "demonstrate", "the", "generative", "ability", "of", "our", "model", "by", "displaying", "samples", "obtained", "by", "annealed", "Langevin", "sampling", "and", "single", "step", "denoising", "jump", ".", "We", "evaluated", "Preprint", "50k", "sampled", "images", "after", "training", "on", "CIFAR-10", "with", "two", "performance", "scores", ",", "Inception", "(", "Salimans", "et", "al", ".", ",", "2016", ")", "and", "FID", "(", "Heusel", "et", "al", ".", ",", "2017", ")", ".", "We", "achieved", "Inception", "Score", "of", "8.", "31", "and", "FID", "of", "31.7", ",", "comparable", "to", "modern", "GAN", "approaches", ".", "Scores", "for", "CelebA", "dataset", "are", "not", "reported", "here", "as", "they", "are", "not", "commonly", "reported", "and", "may", "depend", "on", "the", "specific", "pre", "-", "processing", "used", ".", "More", "samples", "and", "training", "images", "are", "provided", "in", "Appendix", "for", "visual", "inspection", ".", "We", "believe", "that", "visual", "assessment", "is", "still", "essential", "because", "of", "the", "possible", "issues", "with", "the", "Inception", "score", "(", "Barratt", "and", "Sharma", ",", "2018", ")", ".", "Indeed", ",", "we", "also", "found", "that", "the", "visually", "impressive", "samples", "were", "not", "necessarily", "the", "one", "achieving", "the", "highest", "Inception", "Score", ".", "Although", "overfitting", "is", "not", "a", "common", "concern", "for", "generative", "models", ",", "we", "still", "tested", "our", "model", "for", "overfitting", ".", "We", "found", "no", "indication", "for", "overfitting", "by", "comparing", "model", "samples", "with", "their", "nearest", "neighbors", "in", "the", "data", "set", ",", "see", " ", "We", "repeated", "with", "our", "model", "the", "3", "channel", "MNIST", "mode", "coverage", "experiment", "similar", "to", "the", "one", "in", "Kumar", "et", "al", ".", "(", "2019", ")", ".", "An", "energy", "-", "based", "model", "was", "trained", "on", "3", "-", "channel", "data", "where", "each", "channel", "is", "a", "random", "MNIST", "digit", ".", "Then", "8000", "samples", "were", "taken", "from", "the", "model", "and", "each", "channel", "was", "classified", "using", "a", "small", "MNIST", "classifier", "network", ".", "We", "obtained", "results", "of", "the", "966", "modes", ",", "comparable", "to", "GAN", "approaches", ".", "Training", "was", "successful", "and", "our", "model", "assigned", "low", "energy", "to", "all", "the", "learned", "modes", ",", "but", "some", "modes", "were", "not", "accessed", "during", "sampling", ",", "likely", "due", "to", "the", "Langevin", "Dynamics", "failing", "to", "explore", "these", "modes", ".", "A", "better", "sampling", "technique", "such", "as", "HMC", "Neal", "et", "al", ".", "(", "2011", ")", "or", "a", "Maximum", "Entropy", "Generator", "(", "Kumar", "et", "al", ".", ",", "2019", ")", "could", "improve", "this", "result", ".", "Image", "Inpainting", ".", "Image", "impainting", "can", "be", "achieved", "with", "our", "model", "by", "clamping", "a", "part", "of", "the", "image", "to", "ground", "truth", "and", "performing", "the", "same", "annealed", "Langevin", "and", "Jump", "sampling", "procedure", "on", "the", "missing", "part", "of", "the", "image", ".", "Noise", "appropriate", "to", "the", "sampling", "temperature", "need", "to", "be", "added", "to", "the", "clamped", "inputs", ".", "The", "quality", "of", "inpainting", "results", "of", "our", "model", "trained", "on", "CelebA", "and", "CIFAR-10", "can", "be", "assessed", "in", "Figure", "3.", "For", "CIFAR-10", "inpainting", "results", "we", "used", "the", "test", "set", ".", "Log", "likelihood", "estimation", ".", "For", "energy", "-", "based", "models", ",", "the", "log", "density", "can", "be", "obtained", "after", "estimating", "the", "partition", "function", "with", "Annealed", "Importance", "Sampling", "(", "AIS", ")", "(", "Salakhutdinov", "and", "Murray", ",", "2008", ")", "or", "Reverse", "AIS", "(", "Burda", "et", "al", ".", ",", "2015", ")", ".", "In", "our", "experiment", "on", "CIFAR-10", 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0.006807080004364252, "NIL"]], [[1921, 1923, 0.3842126131057739, "NIL"], [1917, 1919, 0.15751662850379944, "NIL"], [1927, 1929, 0.07925225794315338, "NIL"], [1918, 1919, 0.0728970319032669, "NIL"], [1922, 1923, 0.0707138180732727, "NIL"], [1923, 1923, 0.06806335598230362, "NIL"], [1916, 1919, 0.06436119973659515, "NIL"], [1921, 1922, 0.05150093883275986, "NIL"], [1928, 1929, 0.0505242720246315, "NIL"], [1917, 1918, 0.04688414931297302, "NIL"], [1921, 1924, 0.043859753757715225, "NIL"], [1918, 1918, 0.043835222721099854, "NIL"], [1919, 1919, 0.02418265864253044, "NIL"], [1922, 1922, 0.02202487364411354, "NIL"], [1928, 1928, 0.01976810023188591, "NIL"], [1916, 1918, 0.01701878011226654, "NIL"], [1929, 1929, 0.014859006740152836, "NIL"], [1923, 1924, 0.014500642195343971, "NIL"], [1927, 1928, 0.013911115005612373, "NIL"], [1917, 1917, 0.013892466202378273, "NIL"], [1927, 1930, 0.013748882338404655, "NIL"], [1916, 1916, 0.012628532946109772, "NIL"], [1922, 1924, 0.011334702372550964, "NIL"], [1928, 1930, 0.011241411790251732, "NIL"], [1916, 1917, 0.009276051074266434, "NIL"], [1924, 1924, 0.009097735397517681, "NIL"], [1927, 1927, 0.008961143903434277, "NIL"], [1929, 1930, 0.006452032830566168, "NIL"]], [[1942, 1944, 0.6473262310028076, "Method"], [1940, 1940, 0.3791539669036865, "MLModelGeneric"], [1946, 1948, 0.29113802313804626, "NIL"], [1942, 1942, 0.15004059672355652, "NIL"], [1940, 1944, 0.14836205542087555, "NIL"], [1939, 1940, 0.12833672761917114, "NIL"], [1932, 1933, 0.10837090760469437, "NIL"], [1943, 1944, 0.10674240440130234, "NIL"], [1942, 1948, 0.09890629351139069, "NIL"], [1944, 1944, 0.09056031703948975, "NIL"], [1939, 1944, 0.08782561868429184, "NIL"], [1942, 1943, 0.07951223850250244, "NIL"], [1947, 1948, 0.07231152057647705, "NIL"], [1940, 1948, 0.06845062226057053, "NIL"], [1940, 1942, 0.06077192723751068, "NIL"], [1939, 1939, 0.05993998050689697, "NIL"], [1939, 1948, 0.05856633558869362, "NIL"], [1946, 1947, 0.05712719261646271, "NIL"], [1939, 1942, 0.04370836913585663, "NIL"], [1947, 1947, 0.04232267662882805, "NIL"], [1940, 1943, 0.04124356433749199, "NIL"], [1939, 1943, 0.04047757387161255, "NIL"], [1940, 1947, 0.037394411861896515, "NIL"], [1942, 1947, 0.03633788973093033, "NIL"], [1939, 1947, 0.03603891655802727, "NIL"], [1931, 1933, 0.03418809548020363, "NIL"], [1948, 1948, 0.0324404239654541, "NIL"], [1944, 1948, 0.03217882290482521, "NIL"], [1936, 1937, 0.02487896755337715, "NIL"], [1944, 1947, 0.02416393533349037, "NIL"], [1946, 1946, 0.02384457178413868, "NIL"], [1939, 1946, 0.02286372520029545, "NIL"], [1939, 1949, 0.02192130871117115, "NIL"], [1940, 1946, 0.02125130221247673, "NIL"], [1946, 1949, 0.020730776712298393, "NIL"], [1933, 1933, 0.020273027941584587, "NIL"], [1943, 1948, 0.020072758197784424, "NIL"], [1931, 1931, 0.01918962225317955, "NIL"], [1942, 1946, 0.018634244799613953, "NIL"], [1943, 1943, 0.01685144565999508, "NIL"], [1944, 1946, 0.016839252784848213, "NIL"], [1940, 1949, 0.016523201018571854, "NIL"], [1935, 1937, 0.0157368965446949, "NIL"], [1942, 1949, 0.014483085833489895, "NIL"], [1944, 1949, 0.011988121084868908, "NIL"], [1947, 1949, 0.011792480945587158, "NIL"], [1937, 1937, 0.01167429517954588, "NIL"], [1936, 1936, 0.011352772824466228, "NIL"], [1935, 1935, 0.011333458125591278, "NIL"], [1933, 1937, 0.010128160007297993, "NIL"], [1935, 1936, 0.009976762346923351, "NIL"], [1943, 1947, 0.009509545750916004, "NIL"], [1948, 1949, 0.007604415528476238, "NIL"], [1933, 1935, 0.0072676511481404305, "NIL"], [1933, 1936, 0.007018049713224173, "NIL"], [1932, 1937, 0.0069461301900446415, "NIL"], [1943, 1949, 0.005721847526729107, "NIL"], [1943, 1946, 0.005516201723366976, "NIL"], [1932, 1935, 0.005096507258713245, "NIL"], [1931, 1937, 0.004307951312512159, "NIL"]], [[1971, 1972, 0.7877628803253174, "MLModelGeneric"], [1953, 1953, 0.39927029609680176, "NIL"], [1975, 1977, 0.32232922315597534, "NIL"], [1991, 1993, 0.24298809468746185, "NIL"], [2005, 2009, 0.22232140600681305, "NIL"], [2014, 2016, 0.20114785432815552, "NIL"], [1995, 1997, 0.17188191413879395, "NIL"], [1965, 1969, 0.1379903256893158, "NIL"], [1965, 1966, 0.13370802998542786, "NIL"], [1985, 1989, 0.13351978361606598, "NIL"], [1974, 1977, 0.13083302974700928, "NIL"], [2007, 2009, 0.12890785932540894, "NIL"], [1985, 1986, 0.1256592720746994, "NIL"], [2000, 2001, 0.12549607455730438, "NIL"], [1988, 1989, 0.1140453964471817, "NIL"], [1968, 1969, 0.11390561610460281, "NIL"], [2000, 2003, 0.11254124343395233, "NIL"], [2003, 2003, 0.10483862459659576, "NIL"], [1971, 1977, 0.1024286150932312, "NIL"], [2004, 2009, 0.09577261656522751, "NIL"], [1991, 1997, 0.09041429311037064, "NIL"], [2006, 2009, 0.08545707166194916, "NIL"], [2000, 2009, 0.08217184245586395, "NIL"], [1981, 1983, 0.0763174369931221, "NIL"], [1965, 1965, 0.0753931850194931, "NIL"], [1990, 1993, 0.07457996159791946, "NIL"], [1969, 1969, 0.0710720494389534, "NIL"], [1996, 1997, 0.07079324126243591, "NIL"], [1958, 1959, 0.0672796443104744, "NIL"], [2011, 2011, 0.06708631664514542, "NIL"], [2000, 2000, 0.06453464180231094, "NIL"], [1972, 1972, 0.06394721567630768, "NIL"], [2003, 2009, 0.06371261924505234, "NIL"], [1989, 1989, 0.06240485981106758, "NIL"], [1985, 1985, 0.06137233227491379, "NIL"], [2005, 2016, 0.059347912669181824, "NIL"], [1992, 1993, 0.05911121517419815, "NIL"], [2003, 2004, 0.057893361896276474, "NIL"], [1985, 1993, 0.055019035935401917, "NIL"], [1979, 1983, 0.05371902883052826, "NIL"], [2005, 2011, 0.05265038460493088, "NIL"], [2000, 2011, 0.051955919712781906, "NIL"], [1976, 1977, 0.05179872363805771, "NIL"], [1980, 1983, 0.05167495459318161, "NIL"], [1973, 1977, 0.051214009523391724, "NIL"], [1972, 1977, 0.049188148230314255, "NIL"], [1964, 1966, 0.04825468361377716, "NIL"], [1975, 1983, 0.04397661238908768, "NIL"], [1982, 1983, 0.04307543858885765, "NIL"], [1997, 1997, 0.04203282669186592, "NIL"], [2014, 2015, 0.04118421673774719, "NIL"], [1958, 1958, 0.04098124802112579, "NIL"], [2011, 2016, 0.040908586233854294, "NIL"], [1974, 1983, 0.04048076272010803, "NIL"], [1951, 1951, 0.04047039896249771, "NIL"], [1971, 1971, 0.040136560797691345, "NIL"], [2004, 2011, 0.03993469849228859, "NIL"], [2008, 2009, 0.03986389935016632, "NIL"], [1995, 2001, 0.039151061326265335, "NIL"], [1990, 1997, 0.03888121619820595, "NIL"]], [[2027, 2029, 0.740272045135498, "Method"], [2035, 2036, 0.7326381802558899, "MLModelGeneric"], [2047, 2048, 0.6232277750968933, "MLModelGeneric"], [2046, 2048, 0.4651678502559662, "NIL"], [2039, 2043, 0.38502946496009827, "Method"], [2023, 2025, 0.29325926303863525, "Method"], [2028, 2029, 0.2623787820339203, "NIL"], [2052, 2053, 0.2143658697605133, "NIL"], [2021, 2021, 0.19499582052230835, "NIL"], [2055, 2056, 0.18479223549365997, "NIL"], [2042, 2043, 0.18256650865077972, "NIL"], [2027, 2027, 0.178318053483963, "NIL"], [2023, 2029, 0.16701140999794006, "NIL"], [2021, 2025, 0.15833984315395355, "NIL"], [2051, 2053, 0.12149154394865036, "NIL"], [2052, 2056, 0.12052834779024124, "NIL"], [2052, 2052, 0.11300800740718842, "NIL"], [2034, 2036, 0.11041683703660965, "NIL"], [2035, 2043, 0.09182432293891907, "NIL"], [2034, 2034, 0.09164418280124664, "NIL"], [2024, 2025, 0.09050220996141434, "NIL"], [2043, 2043, 0.08920660614967346, "NIL"], [2021, 2024, 0.08795583993196487, "NIL"], [2020, 2021, 0.08382660150527954, "NIL"], [2021, 2027, 0.08315785974264145, "NIL"], [2021, 2029, 0.08284197747707367, "NIL"], [2021, 2023, 0.07896893471479416, "NIL"], [2048, 2048, 0.07386370003223419, "NIL"], [2029, 2029, 0.07201613485813141, "NIL"], [2035, 2037, 0.06784623861312866, "NIL"], [2039, 2042, 0.06711199879646301, "NIL"], [2037, 2043, 0.06700503826141357, "NIL"], [2051, 2056, 0.06376086920499802, "NIL"], [2023, 2024, 0.06336704641580582, "NIL"], [2034, 2043, 0.059855204075574875, "NIL"], [2050, 2053, 0.05949575453996658, "NIL"], [2051, 2052, 0.056682150810956955, "NIL"], [2056, 2056, 0.05426590144634247, "NIL"], [2036, 2036, 0.05186782404780388, "NIL"], [2026, 2029, 0.050777506083250046, "NIL"], [2034, 2037, 0.04975241422653198, "NIL"], [2024, 2029, 0.049629390239715576, "NIL"], [2035, 2035, 0.0466969832777977, "NIL"], [2053, 2053, 0.04519934207201004, "NIL"], [2021, 2028, 0.04440482705831528, "NIL"], [2052, 2054, 0.04383794963359833, "NIL"], [2042, 2042, 0.04294778034090996, "NIL"], [2034, 2035, 0.04279053583741188, "NIL"], [2051, 2051, 0.04262683168053627, "NIL"], [2047, 2047, 0.042569879442453384, "NIL"], [2027, 2028, 0.04196203500032425, "NIL"], [2024, 2024, 0.03940850496292114, "NIL"], [2036, 2043, 0.03558899089694023, "NIL"], [2023, 2027, 0.03547918051481247, "NIL"], [2020, 2025, 0.034226905554533005, "NIL"], [2053, 2056, 0.03412453457713127, "NIL"], [2051, 2054, 0.03344251587986946, "NIL"], [2039, 2041, 0.03337264433503151, "NIL"], [2046, 2047, 0.032254960387945175, "NIL"], [2050, 2051, 0.03220883011817932, "NIL"]], [[2082, 2083, 0.7367509603500366, "DatasetGeneric"], [2074, 2076, 0.7304919958114624, "Method"], [2070, 2071, 0.633371889591217, "MLModelGeneric"], [2071, 2071, 0.536801278591156, "ModelArchitecture"], [2086, 2088, 0.1526924967765808, "NIL"], [2070, 2072, 0.13183321058750153, "NIL"], [2075, 2076, 0.12489072233438492, "NIL"], [2070, 2076, 0.12264683842658997, "NIL"], [2095, 2096, 0.1161944642663002, "NIL"], [2074, 2074, 0.10550778359174728, "NIL"], [2071, 2076, 0.08544328808784485, "NIL"], [2069, 2071, 0.08028009533882141, "NIL"], [2060, 2061, 0.08016084134578705, "NIL"], [2071, 2072, 0.07785084843635559, "NIL"], [2076, 2076, 0.07325286418199539, "NIL"], [2071, 2074, 0.06138254329562187, "NIL"], [2096, 2096, 0.05460893735289574, "NIL"], [2080, 2080, 0.05367813631892204, "NIL"], [2086, 2087, 0.053033117204904556, "NIL"], [2082, 2082, 0.046846065670251846, "NIL"], [2087, 2088, 0.04561909660696983, "NIL"], [2091, 2092, 0.04547382891178131, "NIL"], [2069, 2076, 0.043836381286382675, "NIL"], [2082, 2088, 0.04228094220161438, "NIL"], [2083, 2083, 0.04126090556383133, "NIL"], [2093, 2093, 0.03873145952820778, "NIL"], [2074, 2075, 0.038446858525276184, "NIL"], [2069, 2069, 0.03843187913298607, "NIL"], [2091, 2091, 0.03692759573459625, "NIL"], [2087, 2087, 0.032161083072423935, "NIL"], [2061, 2061, 0.03187403082847595, "NIL"], [2090, 2092, 0.031460221856832504, "NIL"], [2072, 2076, 0.03131639212369919, "NIL"], [2093, 2096, 0.031128525733947754, "NIL"], [2071, 2075, 0.029831305146217346, "NIL"], [2080, 2083, 0.02922593057155609, "NIL"], [2082, 2087, 0.027655763551592827, "NIL"], [2080, 2088, 0.027534471824765205, "NIL"], [2063, 2064, 0.025610197335481644, "NIL"], [2094, 2096, 0.02559058926999569, "NIL"], [2088, 2088, 0.02481169067323208, "NIL"], [2082, 2085, 0.024064145982265472, "NIL"], [2090, 2091, 0.023200243711471558, "NIL"], [2068, 2069, 0.021144995465874672, "NIL"], [2069, 2072, 0.01999974064528942, "NIL"], [2067, 2071, 0.01990063115954399, "NIL"], [2067, 2076, 0.01944142021238804, "NIL"], [2090, 2090, 0.019286062568426132, "NIL"], [2080, 2087, 0.01908397488296032, 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"NIL"], [2104, 2105, 0.08245672285556793, "NIL"], [2099, 2099, 0.07762846350669861, "NIL"], [2112, 2114, 0.0715705156326294, "NIL"], [2132, 2132, 0.07048386335372925, "NIL"], [2109, 2115, 0.06755125522613525, "NIL"], [2126, 2131, 0.060001190751791, "NIL"], [2102, 2104, 0.051955826580524445, "NIL"], [2109, 2109, 0.05054832622408867, "NIL"], [2107, 2109, 0.048963841050863266, "NIL"], [2128, 2130, 0.04789998382329941, "NIL"], [2117, 2125, 0.047466594725847244, "NIL"], [2109, 2110, 0.045218970626592636, "NIL"], [2103, 2108, 0.04507305845618248, "NIL"], [2107, 2115, 0.040636077523231506, "NIL"], [2117, 2117, 0.04051477089524269, "NIL"], [2126, 2126, 0.04002293199300766, "NIL"], [2117, 2118, 0.03933015838265419, "NIL"], [2101, 2101, 0.03841603919863701, "NIL"], [2112, 2115, 0.03835456073284149, "NIL"], [2102, 2103, 0.03832864388823509, "NIL"], [2104, 2104, 0.037724897265434265, "NIL"], [2110, 2110, 0.037392206490039825, "NIL"], [2101, 2104, 0.03729499876499176, "NIL"], [2105, 2106, 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"the", "change", "of", "variables", "formula", "where", "the", "second", "factor", "on", "the", "RHS", "is", "just", "due", "to", "the", "Jacobian", "of", "the", "transformation", ".", "Real", "Non", "-", "Volume", "Preserving", "(", "NVP", ")", "flows", "[", "20", "]", "are", "normalizing", "flows", "for", "which", "the", "mapping", "G", "is", "composed", "of", "multiple", "simpler", "invertible", "functions", "called", "affine", "layers", ",", "which", "we", "denote", "by", "g", "(", ")", ",", "and", "whose", "precise", "definition", "is", "given", "in", "Appendix", "A", ".", "Letting", "L", "denote", "the", "number", "of", "such", "layers", ",", "the", "flow", "may", "be", "defined", "recursively", "as", "G", "(", ")", ":", "=", "g", "(", ")", "\u2022", "G", "(", "\u22121", ")", ",", "for", "=", "1", ",", "...", ",", "L", ",", "with", "the", "understanding", "that", "G", "(", "0", ")", "is", "the", "identity", "and", "G", "(", "L", ")", "corresponds", "to", "the", "complete", 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"training", "data", ".", "Here", ",", "a", "priori", "we", "do", "not", "have", "any", "dataset", ",", "thus", "we", "need", "to", "generate", "our", "data", ";", "e.g.", ";", "through", "traditional", "Monte", "Carlo", "techniques", "such", "as", "parallel", "tempering", "[", "22", "]", ".", "Another", "major", "difference", "is", "that", "a", "tractable", "expression", "for", "the", "true", "probability", "distribution", "is", "known", ";", "i.e.", "the", "Boltzmann", "distribution", "over", "x", "\u2208", "R", "N", "with", "Hamiltonian", "density", "H", "\u03b2", "(", "x", ")", "is", "given", "by", "Eq", ".", "3.", "This", "allows", "for", "two", "viable", "approaches", "towards", "training", "the", "flow", "to", "approximate", "the", "true", "distribution", "-", "one", "based", "on", "minimizing", "the", "reverse", "KL", "divergence", "and", "one", "based", "on", "minimizing", "the", "forward", "KL", "divergence", ".", "In", "this", "approach", "the", "loss", "function", "is", 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"first", "assembled", "a", "dataset", "D", "of", "spin", "configurations", "using", "parallel", "-", "tempering", "(", "PT", ")", "(", "see", "for", "example", "[", "24", "]", ")", ".", "We", "simulated", "20", "parallel", "systems", "(", "called", "replicas", ")", ",", "each", "at", "a", "different", "temperature", ".", "We", "recorded", "the", "spin", "-", "configurations", "throughout", "the", "parallel", "tempering", "after", "each", "sweep", "of", "all", "N", "spins", ",", "until", "100", ",", "000", "samples", "had", "been", "obtained", "for", "each", "temperature", ".", "We", "then", "repeated", "this", "procedure", "for", "10", "realizations", "of", "the", "coupling", "matrix", "J", "ij", ".", "Lastly", ",", "to", "train", "the", "normalizing", "flow", "the", "discrete", "Ising", "spin", "configurations", "must", "be", "converted", "to", "continuous", "configurations", ".", "We", "used", "each", "spin", "configuration", "s", "to", "generate", "a", "single", "x", "configuration", "using", "the", "joint", "distribution", "x", "\u223c", "p", "(", "x|s", ")", "(", "given", "by", "Eq", ".", "6", ")", ".", "shows", "that", "the", "quality", "of", "the", "normalizing", "flow", "approximation", "to", "the", "true", "Boltzmann", "distribution", "nonetheless", "becomes", "quite", "poor", "at", "low", "-", "temperatures", ".", "This", "is", "an", "indication", "that", "reverse", "KL", "-", "trained", "flow", "is", "not", "capturing", "key", "properties", "of", "the", "spin", "-", "glass", "phase", "at", "low", "-", "temperatures", ".", "In", "Fig", ".", "2", "(", "a", ")", "we", "plot", "the", "reverse", "KL", "loss", "throughout", "the", "course", "of", "training", ".", "The", "loss", "is", "roughly", "constant", "for", "the", "first", "100", "iterations", ",", "after", "which", "it", "drops", "sharply", ".", "For", "T", "/J", "<", "T", "crit", "it", "then", "continues", "to", "decrease", "slowly", "with", "additional", "training", ".", "The", "magnitude", "of", "the", "drop", "increases", "for", "low", "temperatures", ".", "A", "measure", "of", "the", "quality", "of", "the", "trained", "flow", "may", "be", "obtained", "by", "examining", "the", "tightness", "of", "the", "free", "energy", "bound", "in", "Eq", ".", "18", ",", "or", "equivalently", ",", "the", "smallness", "of", "the", "reverse", "KL", "divergence", ".", "In", "order", "to", "estimate", "the", "KL", "divergence", ",", "we", "first", "evaluated", "the", "Helmholtz", "free", "energy", "F", "x", "using", "the", "relation", "between", "Z", "x", "and", "Z", "s", "in", "Eq", ".", "4.", "In", "the", "spin", "-", "glass", "phase", "(", "T", "<", "T", "crit", ")", "the", "discrete", "partition", "function", "Z", "s", "was", "estimated", "using", "the", "results", "of", "the", "parallel", "tempering", "described", "above", ",", "while", "in", "the", "paramagnetic", "phase", "(", "T", ">", "T", "crit", ")", "we", "used", "the", "replica", "-", "symmetric", "expression", "F", "s", "=", "\u2212N", "\u03b2J", "2", "/4", "\u2212", "N", "ln", "2", "/", "\u03b2", ",", "where", "F", "s", ":", "=", "\u2212\u03b2", "\u22121", "ln", "Z", "s", ".", "Importantly", ",", "the", "replica", "-", "symmetric", "expression", "is", "exact", "in", "the", "paramagnetic", "phase", "and", "in", "the", "large", "-", "N", "limit", ".", "Fig", ".", "2", "(", "b", ")", "shows", "that", "the", "reverse", "KL", "divergence", "is", "rather", "high", "at", "low", "temperatures", ",", "and", "decreases", "rapidly", "as", "the", "temperature", "is", "raised", ".", "The", "inset", "shows", "the", "estimated", "value", "of", "the", "two", "free", "energies", ",", "Gibbs", "and", "Helmholtz", ".", "Similarly", ",", "in", "Fig", ".", "3", "(", "a", ")", "we", "plot", "the", "forward", "KL", "loss", "throughout", "the", "course", "of", "training", ".", "In", "the", "spin", "-", "glass", "phase", ",", "learning", "proceeds", "slowly", "at", "first", "100", "iterations", "or", "so", ",", "and", "then", "decreases", "much", "more", "rapidly", "afterwards", ".", "In", "the", "paramagnetic", "phase", ",", "the", "loss", "decreases", "quickly", "with", "the", "first", "100", "iterations", ",", "and", "then", "decreases", "much", "more", "slowly", "afterwards", ".", "For", "the", "critical", "temperature", ",", "T", "=", "T", "crit", ",", "the", "loss", "curve", "is", "essentially", "flat", ",", "and", "there", "is", "not", "a", "period", "of", "steep", "decline", ".", "Another", "interesting", "observation", "is", "that", "the", "variation", "in", "the", "value", "of", "the", "loss", "increases", "as", "T", "decreases", ".", "The", "data", "for", "the", "lowest", "temperature", "considered", ",", "T", "/J", "=", "0.", "2", ",", "shows", "that", "after", "about", "1000", "training", "iterations", "there", "are", "occasionally", "large", "fluctuations", "in", "the", "value", "of", "the", "loss", ".", "As", "with", "the", "reverse", "KL", "loss", "function", ",", "the", "quality", "of", "the", "learned", "flow", "can", "be", "measured", "by", "estimating", "the", "KL", "divergence", "and", "the", "tightness", "of", "the", "bound", "Eq", ".", "21", ".", "This", "is", "depicted", "in", "Fig", ".", "3", "(", "b", ")", ",", "and", "the", "inset", "compares", "the", "asymptotic", "value", "of", "the", "forward", "KL", "loss", "with", "the", "Shannon", "entropy", "of", "the", "physical", "distribution", "p", "(", "x", ")", ",", "which", "we", "evaluated", "using", "the", "results", "of", "the", "parallel", "tempering", "simulations", ".", "Compared", "to", "the", "reverse", "KL", "divergence", ",", "the", "forward", "KL", "divergence", "first", "increases", "rapidly", "as", "the", "temperature", "is", "raised", ",", "reaches", "a", "peak", "at", "about", "T", "=", "0.", "5", ",", "then", "decreases", "rapidly", "across", "the", "spin", "-", "glass", "phase", "transition", ",", "and", "finally", "approaches", "an", "asymptotic", "value", "as", "the", "temperature", "is", "increased", "further", ".", "The", "forward", "KL", "divergence", "achieves", "much", "smaller", "values", "than", "the", "reverse", "KL", "divergence", "in", "the", "spin", "-", "glass", "phase", "-", "the", "maximum", "value", "of", "the", "forward", "KL", "divergence", "is", "an", "order", "of", "magnitude", "smaller", "than", "the", "maximum", "value", "of", "the", "reverse", "KL", "divergence", ".", "One", "important", "point", "is", "that", "the", "estimate", "of", "the", "forward", "KL", "divergence", "actually", "becomes", "negative", "for", "high", "temperatures", ".", "As", "the", "KL", "divergence", "is", "non", "-", "negative", ",", "this", "indicates", "that", "the", "error", "in", "the", "estimate", "is", "large", "enough", "to", "change", "the", "value", "from", "positive", "to", "negative", ".", "We", "initially", "observed", "a", "similar", "phenomenon", "in", "estimating", "the", "reverse", "KL", "loss", ",", "but", "we", "were", "able", "to", "improve", "our", "estimate", "in", "the", "paramagnetic", "phase", "by", "using", "the", "exact", "replica", "symmetric", "expression", "for", "the", "free", "energy", ".", "We", "are", "not", "aware", "of", "an", "analogous", "expression", "for", "the", "Shannon", "entropy", "H[p", "(", "x", ")", "]", ".", "Correspondingly", ",", "the", "estimated", "KL", "divergence", "is", "quite", "small", "for", "the", "entire", "range", "of", "temperatures", "studied", ",", "although", "it", "does", "experience", "a", "peak", "at", "T", "=", "0.", "5", ".", "Spin", "-", "glasses", "are", "characterized", "by", "the", "presence", "of", "a", "large", "number", "of", "metastable", "states", ".", "These", "are", "typically", "separated", "from", "one", "another", "by", "large", "energy", "barriers", ",", "and", "as", "a", "result", "ergodicity", "is", "broken", "at", "low", "temperatures", "and", "the", "system", "will", "become", "stuck", "in", "one", "of", "the", "many", "states", ".", "The", "closeness", "of", "two", "such", "states", "\u03b1", "and", "\u03b2", "may", "be", "measured", "by", "the", "overlap", "between", "them", ":", "Here", ",", "m", "(", "\u03b1", ")", "i", "is", "the", "average", "per", "-", "site", "magnetization", ",", "or", "marginal", "probabilities", ",", "within", "the", "state", "\u03b1", ",", "and", "similarly", "for", "m", "(", "\u03b2", ")", "i", ".", "As", "shown", "by", "Parisi", ",", "the", "distribution", "of", "overlap", "values", "P", "J", "(", "q", ")", "for", "a", "given", "spin", "-", "glass", "instance", "may", "be", "used", "as", "an", "order", "parameter", "for", "the", "spin", "-", "glass", "phase", "[", "25", "]", ".", "This", "represents", "a", "key", "distinction", "from", "more", "conventional", "phases", "of", "matter", "where", "the", "order", "parameter", "is", "simply", "a", "real", "number", "-", "here", ",", "it", "is", "an", "entire", "function", ".", "Equivalently", ",", "the", "order", "parameter", "for", "a", "spin", "-", "glass", "could", "be", "considered", "to", "be", "the", "infinite", "collection", "of", "real", "numbers", "defined", "by", "the", "moments", "of", "the", "overlap", "distribution", ".", "This", "unique", "nature", "of", "the", "spin", "-", "glass", "order", "parameter", "underscores", "the", "complexity", "of", "these", "systems", "compared", "to", "more", "conventional", "phases", "of", "matter", ".", "In", "order", "to", "evaluate", "the", "extent", "to", "which", "the", "trained", "normalizing", "flows", "have", "successfully", "approximated", "the", "spin", "-", "glass", "phase", "we", "examined", "the", "overlap", "distribution", ".", "P", "J", "(", "q", ")", "may", "be", "approximated", "by", "sampling", "the", "spin", "-", "glass", "and", "computing", "the", "configurational", "overlaps", "between", "two", "randomly", "chosen", "spin", "configurations", "s", "(", "a", ")", "and", "s", "(", "b", ")", ":", "i", ".", "As", "sample", "size", "grows", ",", "the", "distribution", "of", "configurational", "overlaps", "q", "ab", "will", "approach", "the", "overlap", "distribution", "P", "J", "(", "q", ")", ".", "In", "Fig", ".", "4", "we", "plot", "numerical", "estimates", "of", "the", "non", "-", "disorder", "-", "averaged", "overlap", "distribution", "P", "J", "(", "q", ")", "for", "the", "parallel", "tempering", "data", "and", "samples", "obtained", "from", "both", "the", "forward", "and", "reverse", "KL", "-", "trained", "flows", ".", "4", "Neither", "the", "reverse", "or", "forward", "-", "trained", "flow", "perfectly", "matches", "the", "PT", "result", ",", "although", "the", "forward", "and", "PT", "results", "qualitatively", "match", ".", "The", "fact", "that", "the", "forward", "-", "trained", "flow", "is", "able", "to", "produce", "a", "bi", "-", "modal", "overlap", "distribution", "demonstrates", "that", "it", "has", "captured", "an", "important", "characteristic", "of", "the", "spin", "-", "glass", "phase", ".", "In", "contrast", ",", "the", "overlap", "distribution", "for", "the", "reverse", "KL", "-", "trained", "flow", "has", "just", "a", "single", "peak", "near", "q", "=", "1", "for", "T", "<", "T", "crit", ",", "which", "indicates", "that", "most", "of", "the", "samples", "are", "very", "close", "to", "one", "another", ".", "This", "suggests", "that", "the", "flow", "has", "not", "successfully", "modeled", "the", "key", "property", "of", "the", "spin", "-", "glass", "phase", ",", "namely", "the", "existence", "of", "many", "metastable", "states", ".", "Further", "evidence", "for", "this", "conclusion", "comes", "from", "examining", "the", "magnetization", ",", "M", "=", "i", "s", "i", ".", "We", "find", "that", "M", "\u2248", "0", "for", "all", "sampling", "methods", ",", "but", "the", "reverse", "KL", "-", "trained", "flow", "is", "unique", "in", "that", "it", "produces", "non", "-", "zero", "per", "-", "site", "magnetizations", ",", "i.e.", "s", "i", "=", "0.", "This", "is", "consistent", "with", "the", "hypothesis", "that", "the", "flow", "distribution", "has", "collapsed", "onto", "just", "a", "single", "mode", "of", "the", "true", "distribution", ".", "Indeed", ",", "this", "is", "a", "known", "failure", "mode", "of", "models", "trained", "on", "the", "reverse", "KL", "divergence", ".", "5", "One", "of", "the", "most", "remarkable", "properties", "of", "spin", "-", "glasses", "is", "that", "their", "state", "space", "can", "be", "endowed", "with", "highly", "non", "-", "trivial", "topological", "structure", ",", "which", "emerges", "naturally", "from", "seemingly", "unstructured", "Hamiltonians", ".", "For", "instance", ",", "the", "simple", "SK", "model", "Hamiltonian", ",", "with", "a", "featureless", "fully", "connected", "underlying", "graph", "and", "iid", "random", "couplings", ",", "can", "be", "shown", "to", "generate", "a", "simple", "hierarchical", "structure", "in", "its", "solution", "space", ".", "Specifically", ",", "the", "low", "energy", "states", "of", "the", "SK", "model", "obey", "an", "interesting", "relation", "known", "as", "ultrametricity", "[", "27", "]", ".", "Given", "any", "triplet", "of", "states", ",", "a", ",", "b", ",", "and", "c", ",", "the", "3", "possible", "overlaps", "q", "ab", ",", "q", "ac", "and", "q", "bc", "may", "be", "converted", "into", "a", "set", "of", "Hamming", "distances", "d", "ab", ":", "=", "(", "1", "\u2212", "q", "ab", ")", "/2", "which", "form", "the", "3", "sides", "of", "the", "triangle", "connecting", "the", "states", ".", "The", "standard", "triangle", "inequality", "is", "d", "ac", "\u2264", "d", "ab", "+", "d", "bc", ",", "and", "in", "the", "SK", "model", ",", "these", "distances", "are", "known", "to", "obey", "the", "stronger", "inequality", "d", "ac", "\u2264", "max", "(", "d", "ab", ",", "d", "bc", ")", "which", "defines", "ultrametric", "spaces", ".", "This", "condition", "implies", "some", "geometric", "properties", ",", "for", "example", "that", "all", "triangles", "are", "either", "equilateral", "or", "acute", "isosceles", ".", "The", "distribution", "of", "triangles", "may", "be", "computed", "analytically", "in", "the", "SK", "model", "using", "the", "the", "replica", "approach", "with", "Parisi", "'s", "replica", "symmetry", "breaking", "ansatz", ".", "One", "finds", "that", "in", "the", "spin", "-", "glass", "phase", "1", "/", "4", "of", "the", "triangles", "are", "the", "equilateral", ",", "and", "3", "/", "4", "are", "acute", "isosceles", ".", "6", "herefore", ",", "as", "a", "final", "test", "of", "the", "quality", "of", "our", "learned", "continuous", "spin", "-", "glasses", "trained", "with", "normalizing", "flows", ",", "it", "would", "be", "essential", "to", "examine", "if", "such", "models", "can", "actually", "generate", "the", "emergent", "hierarchical", "/", "ultrametric", "structure", "of", "the", "SK", "Hamiltonian", ".", "We", "plot", "the", "distribution", "of", "triangle", "side", "lengths", "in", "Fig", ".", "5.", "Letting", "d", "min", ",", "d", "mid", ",", "d", "max", "denote", "the", "ordered", "distances", ",", "the", "cluster", "near", "the", "origin", "of", "Fig", ".", "5", "corresponds", "to", "equilateral", "triangles", "and", "the", "other", "cluster", "on", "the", "x", "-", "axis", "corresponds", "to", "acute", "isosceles", "triangles", ".", "This", "same", "plot", "was", "used", "in", "[", "28", "]", "in", "the", "context", "of", "the", "bipartite", "SK", "model", ".", "We", "have", "demonstrated", "that", "normalizing", "flows", "may", "be", "successfully", "trained", "to", "learn", "the", "spin", "-", "glass", "phase", "of", "the", "SK", "model", ".", "Recall", "that", "the", "flow", "induces", "a", "sequence", "of", "Hamiltonian", "densities", "H", "G", "(", ")", "(", "z", "(", ")", ")", "which", "interpolate", "from", "a", "Gaussian", "energy", "landscape", "at", "=", "0", "to", "the", "complex", ",", "multi", "-", "modal", "landscape", "that", "corresponds", "to", "the", "spin", "-", "glass", "phase", "for", "=", "L", ".", "This", "suggests", "that", "there", "is", "a", "phase", "transition", "within", "the", "flow", ",", "e.g.", ",", "in", "passing", "from", "layer", "to", "layer", "+", "1.", "In", "order", "to", "confirm", "this", "conjecture", ",", "would", "ideally", "be", "a", "continuous", "parameter", "which", "would", "allow", "for", "a", "critical", "layer", "c", "to", "be", "found", ",", "and", "then", "critical", "exponents", "could", "be", "calculated", "with", "respect", "to", "(", "\u2212", "c", ")", "/L", ".", "One", "way", "to", "achieve", "this", "scenario", "would", "be", "to", "take", "L", "\u2192", "\u221e", ",", "so", "that", "the", "normalizing", "flow", "is", "composed", "of", "an", "infinite", "number", "of", "layers", ",", "each", "of", "which", "implements", "an", "infinitesimal", "diffeormorphism", ".", "This", "would", "allow", "for", "additional", "theoretical", "analysis", "but", "would", "diminish", "the", "practical", "relevance", "since", "it", "is", "unclear", "how", "the", "abstracted", "normalizing", "flow", "with", "infinite", "layers", "relates", "to", "the", "finite", "-", "L", "trained", "models", "considered", "above", ".", "An", "interesting", "alternative", "would", "be", "to", "use", "a", "form", "of", "flow", "based", "on", "a", "1", "-", "parameter", "diffeomorphism", "such", "as", "Neural", "Ordinary", "Differential", "Equations", "(", "Neural", "ODEs", ")", "[", "29", "]", ".", "In", "lieu", "of", "taking", "the", "L", "\u2192", "\u221e", "limit", "or", "considering", "a", "different", "class", "of", "generative", "models", ",", "we", "will", "simply", "investigate", "the", "statistics", "of", "the", "internal", "layers", "of", "our", "trained", "flows", "and", "establish", "that", ",", "as", "increases", ",", "there", "appears", "to", "be", "a", "transition", "from", "the", "paramagnetic", "phase", "to", "the", "spin", "-", "glass", "phase", ".", "Following", "this", "approach", ",", "in", "Fig", ".", "6", "we", "plot", "the", "sequence", "of", "overlap", "distributions", "P", "J", "(", "q", ")", "for", "each", "internal", "layer", "of", "the", "flow", "for", "3", "distinct", "temperatures", ".", "Fig", ".", "6", "(", "a", ")", "shows", "that", "deep", "in", "the", "spin", "-", "glass", "phase", "the", "overlap", "distribution", "is", "transformed", "from", "the", "uni", "-", "modal", "distribution", "of", "the", "Gaussian", "prior", "to", "a", "bi", "-", "modal", "distribution", "in", "going", "from", "=", "1", "to", "=", "2.", "Each", "additional", "layer", "then", "increases", "the", "separation", "of", "the", "two", "modes", "as", "the", "flow", "distribution", "becomes", "a", "closer", "approximation", "to", "the", "physical", "distribution", ".", "Fig", ".", "6", "(", "b", ")", "shows", "that", "increasing", "the", "temperature", "(", "but", "keeping", "within", "the", "spin", "-", "glass", "phase", ")", "causes", "the", "uni", "-", "modal", "to", "bi", "-", "modal", "transition", "to", "occur", "deeper", "in", "the", "flow", ".", "Lastly", ",", "Fig", ".", "6", "(", "c", ")", "demonstrates", "that", "in", "the", "paramagnetic", "phase", "the", "overlap", "distribution", "of", "all", "layers", "is", "uni", "-", "modal", ",", "and", "there", "is", "no", "sign", "of", "a", "phase", "transition", "within", "the", "flow", ".", "To", "gain", "more", "insight", "into", "the", "nature", "of", "the", "transition", "that", "occurs", "as", "is", "increased", "within", "the", "flow", ",", "in", "Fig", ".", "7", "we", "plot", "the", "triangle", "distance", "distribution", "for", "each", "internal", "layer", "for", "T", "/J", "=", "0.", "2", ".", "As", "in", "Fig", ".", "6", ",", "in", "going", "from", "=", "1", "to", "=", "2", "the", "distribution", "appears", "to", "qualitatively", "change", ",", "and", "the", "triangle", "distribution", "becomes", "bi", "-", "modal", ".", "In", "this", "case", "the", "two", "modes", "correspond", "to", "equilateral", "and", "acute", "isosceles", "triangles", ".", "In", "the", "paramagnetic", "phase", "(", "and", "in", "the", "strict", "large", "-", "N", "limit", ")", ",", "there", "are", "only", "equilateral", "triangles", ",", "whereas", "the", "spin", "-", "glass", "phase", "is", "characterized", "by", "both", "equilateral", "and", "acute", "isosceles", ".", "Taken", "together", ",", "the", "results", "of", "Fig", ".", "6", "and", "Fig", ".", "7", "show", "that", "the", "flow", "transforms", "a", "quadratic", "energy", "landscape", "into", "a", "spin", "-", "glass", "landscape", "via", "an", "incremental", "process", ",", "with", "each", "affine", "layer", "bringing", "the", "normalizing", "flow", "distribution", "closer", "to", "the", "true", "spin", "-", "glass", "distribution", ".", "We", "have", "demonstrated", "that", "real", "NVP", "flows", "can", "be", "successfully", "trained", "to", "model", "complex", "spin", "-", "glass", "distributions", ".", "We", "evaluated", "two", "methods", "for", "training", 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"quadratic", "one", ",", "we", "can", "think", "of", "G", "\u22121", "as", "a", "coarse", "-", "graining", ".", "Importantly", ",", "the", "coarse", "-", "graining", "is", "with", "respect", "to", "the", "ruggedness", "of", "the", "energy", "landscape", "-", "no", "degrees", "of", "freedom", "have", "been", "integrated", "out", ",", "and", "no", "information", "has", "been", "lost", "because", "the", "flow", "is", "invertible", ".", "This", "resembles", "simulated", "annealing", "[", "32", "]", "and", "adiabatic", "quantum", "computation", "[", "33", "]", "for", "discrete", "optimization", "in", "which", "one", "starts", "with", "significant", "thermal", "or", "quantum", "fluctuations", ",", "smoothing", "the", "energy", "landscape", "to", "be", "originally", "convex", ",", "and", "then", "gradually", "(", "adiabatically", ")", "transform", "it", "to", "a", "non", "-", "trivial", "noncovex", "distribution", "via", "very", "slow", "(", "exponential", "in", "the", "worse", "-", "case", 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"NIL"], [1903, 1909, 0.02284005843102932, "NIL"], [1906, 1909, 0.021921619772911072, "NIL"], [1896, 1899, 0.02029024064540863, "NIL"], [1909, 1909, 0.019316796213388443, "NIL"], [1905, 1908, 0.01853501982986927, "NIL"], [1896, 1902, 0.018349172547459602, "NIL"], [1902, 1903, 0.014489437453448772, "NIL"], [1907, 1909, 0.014402072876691818, "NIL"], [1901, 1908, 0.013871284201741219, "NIL"], [1897, 1902, 0.013171088881790638, "NIL"], [1899, 1909, 0.012700792402029037, "NIL"], [1899, 1902, 0.012348033487796783, "NIL"], [1907, 1907, 0.012140541337430477, "NIL"], [1903, 1908, 0.012089577503502369, "NIL"], [1901, 1910, 0.011864451691508293, "NIL"], [1905, 1907, 0.011731397360563278, "NIL"], [1902, 1909, 0.010685311630368233, "NIL"], [1909, 1910, 0.010418293997645378, "NIL"], [1907, 1908, 0.009768176823854446, "NIL"], [1903, 1910, 0.009657305665314198, "NIL"], [1906, 1908, 0.009624925442039967, "NIL"], [1897, 1908, 0.00951953511685133, "NIL"], [1897, 1903, 0.009387768805027008, "NIL"], [1896, 1903, 0.008958691731095314, "NIL"], [1896, 1901, 0.00884408038109541, "NIL"], [1906, 1906, 0.008616292849183083, "NIL"], [1905, 1910, 0.008558913134038448, "NIL"], [1907, 1910, 0.008323836140334606, "NIL"], [1903, 1907, 0.008069674484431744, "NIL"], [1897, 1901, 0.008005295880138874, "NIL"], [1902, 1908, 0.007765703834593296, "NIL"], [1899, 1903, 0.007658880669623613, "NIL"], [1899, 1901, 0.007325968239456415, "NIL"], [1899, 1908, 0.007141835056245327, "NIL"], [1901, 1907, 0.00695768790319562, "NIL"], [1899, 1910, 0.00674134586006403, "NIL"], [1905, 1906, 0.006372015457600355, "NIL"], [1902, 1910, 0.006290143821388483, "NIL"], [1899, 1907, 0.006042777560651302, "NIL"], [1906, 1910, 0.0060027590952813625, "NIL"], [1897, 1907, 0.005705688148736954, "NIL"], [1896, 1907, 0.005438400432467461, "NIL"], [1903, 1906, 0.004418489057570696, "NIL"], [1901, 1906, 0.0040517644956707954, "NIL"], [1897, 1906, 0.0033744594547897577, "NIL"], [1899, 1906, 0.0033189398236572742, "NIL"], [1896, 1906, 0.0032046150881797075, "NIL"]], [[1911, 1914, 0.16691641509532928, "NIL"], [1913, 1914, 0.049158018082380295, "NIL"], [1912, 1914, 0.04810220003128052, "NIL"], [1911, 1911, 0.04495913162827492, "NIL"], [1911, 1912, 0.03916695713996887, "NIL"], [1911, 1913, 0.03617675229907036, "NIL"], [1914, 1914, 0.024055596441030502, "NIL"], [1913, 1913, 0.017385104671120644, "NIL"], [1912, 1912, 0.01639760099351406, "NIL"], [1912, 1913, 0.014358177781105042, "NIL"], [1911, 1916, 0.014276014640927315, "NIL"], [1916, 1916, 0.01271277479827404, "NIL"], [1913, 1916, 0.004534323234111071, "NIL"], [1912, 1916, 0.00422901613637805, "NIL"], [1914, 1916, 0.004066914785653353, "NIL"]], [[1920, 1922, 0.22859272360801697, "NIL"], [1921, 1922, 0.08530236035585403, "NIL"], [1927, 1927, 0.05300616845488548, "NIL"], [1920, 1920, 0.03478653356432915, "NIL"], [1922, 1922, 0.0328388437628746, "NIL"], [1926, 1927, 0.031000198796391487, "NIL"], [1918, 1922, 0.02634536288678646, "NIL"], [1920, 1921, 0.022790255025029182, "NIL"], [1921, 1921, 0.02171594463288784, "NIL"], [1925, 1927, 0.019011637195944786, "NIL"], [1918, 1918, 0.018243346363306046, "NIL"], [1927, 1929, 0.01634802483022213, "NIL"], [1924, 1927, 0.015418954193592072, "NIL"], [1924, 1925, 0.012588534504175186, "NIL"], [1924, 1924, 0.010371342301368713, "NIL"], [1926, 1929, 0.010283092968165874, "NIL"], [1925, 1925, 0.009849931113421917, "NIL"], [1928, 1929, 0.006785244680941105, "NIL"], [1925, 1929, 0.005392016377300024, "NIL"], [1918, 1920, 0.005286782514303923, "NIL"], [1918, 1921, 0.0043556541204452515, "NIL"], [1924, 1929, 0.004008566029369831, "NIL"]], [[1933, 1934, 0.246429443359375, "NIL"], [1936, 1938, 0.16879989206790924, "NIL"], [1939, 1939, 0.14162175357341766, "NIL"], [1933, 1938, 0.1307547688484192, "NIL"], [1936, 1939, 0.09484395384788513, "NIL"], [1941, 1944, 0.09066645056009293, "NIL"], [1937, 1938, 0.08750330656766891, "NIL"], [1945, 1945, 0.08339641988277435, "NIL"], [1933, 1944, 0.07827389240264893, "NIL"], [1938, 1938, 0.06783138960599899, "NIL"], [1937, 1939, 0.06719012558460236, "NIL"], [1933, 1939, 0.06377464532852173, "NIL"], [1938, 1939, 0.06036714091897011, "NIL"], [1943, 1944, 0.058798979967832565, "NIL"], [1942, 1944, 0.05000206083059311, "NIL"], [1936, 1944, 0.049958717077970505, "NIL"], [1933, 1935, 0.04779757931828499, "NIL"], [1934, 1934, 0.04712258651852608, "NIL"], [1944, 1944, 0.04685990884900093, "NIL"], [1944, 1945, 0.04589911922812462, "NIL"], [1934, 1938, 0.04571693763136864, "NIL"], [1932, 1934, 0.0439448244869709, "NIL"], [1939, 1944, 0.04230538383126259, "NIL"], [1941, 1945, 0.04196911305189133, "NIL"], [1943, 1945, 0.041705772280693054, "NIL"], [1942, 1945, 0.03689683973789215, "NIL"], [1934, 1939, 0.03518917039036751, "NIL"], [1932, 1938, 0.03367241472005844, "NIL"], [1936, 1937, 0.033010710030794144, "NIL"], [1939, 1945, 0.032290343195199966, "NIL"], [1937, 1944, 0.031236639246344566, "NIL"], [1933, 1937, 0.030163638293743134, "NIL"], [1937, 1937, 0.027225516736507416, 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1938, 0.014432759024202824, "NIL"], [1934, 1943, 0.013863608241081238, "NIL"], [1941, 1941, 0.013601367361843586, "NIL"], [1934, 1942, 0.013543585315346718, "NIL"]], [[1964, 1965, 0.3277586102485657, "NIL"], [1961, 1965, 0.31937146186828613, "NIL"], [1967, 1968, 0.1369728296995163, "NIL"], [1961, 1962, 0.12702450156211853, "NIL"], [1970, 1972, 0.09140899032354355, "NIL"], [1968, 1968, 0.08376921713352203, "NIL"], [1962, 1965, 0.07704377919435501, "NIL"], [1961, 1968, 0.05931277200579643, "NIL"], [1964, 1964, 0.05808534845709801, "NIL"], [1967, 1972, 0.05713929608464241, "NIL"], [1964, 1968, 0.051659129559993744, "NIL"], [1967, 1969, 0.049075882881879807, "NIL"], [1972, 1972, 0.04262630641460419, "NIL"], [1965, 1965, 0.041514866054058075, "NIL"], [1968, 1972, 0.039438843727111816, "NIL"], [1962, 1968, 0.036254867911338806, "NIL"], [1962, 1962, 0.03541720658540726, "NIL"], [1968, 1969, 0.034618813544511795, "NIL"], [1970, 1970, 0.03428073227405548, "NIL"], [1965, 1968, 0.03353022411465645, "NIL"], [1967, 1970, 0.030603934079408646, "NIL"], [1961, 1969, 0.029161512851715088, "NIL"], [1974, 1975, 0.028662636876106262, "NIL"], [1968, 1970, 0.02700340934097767, "NIL"], [1964, 1975, 0.02626962587237358, "NIL"], [1961, 1963, 0.02601783722639084, "NIL"], [1961, 1972, 0.02495751902461052, "NIL"], [1961, 1970, 0.02445218339562416, "NIL"], [1958, 1959, 0.02406834438443184, "NIL"], [1964, 1972, 0.023670703172683716, "NIL"], [1975, 1975, 0.02339700236916542, "NIL"], [1956, 1959, 0.023078585043549538, "NIL"], [1964, 1969, 0.022640187293291092, "NIL"], [1956, 1956, 0.022169504314661026, "NIL"], [1961, 1964, 0.021858301013708115, "NIL"], [1962, 1964, 0.020261792466044426, "NIL"], [1967, 1975, 0.020226970314979553, "NIL"], [1967, 1974, 0.019626706838607788, "NIL"], [1962, 1967, 0.019600097090005875, "NIL"], [1962, 1969, 0.0195019394159317, "NIL"], [1964, 1967, 0.01943802461028099, "NIL"], [1962, 1963, 0.01893473044037819, "NIL"], [1964, 1970, 0.018812835216522217, "NIL"], [1962, 1970, 0.018057452514767647, "NIL"], [1965, 1975, 0.01786833442747593, "NIL"], [1962, 1971, 0.017491905018687248, "NIL"], [1961, 1967, 0.017319025471806526, "NIL"], [1974, 1974, 0.017279459163546562, "NIL"], [1968, 1975, 0.016944149509072304, "NIL"], [1965, 1967, 0.016563769429922104, "NIL"], [1965, 1976, 0.016378693282604218, "NIL"], [1964, 1974, 0.015917053446173668, "NIL"], [1964, 1971, 0.015801357105374336, "NIL"], [1965, 1969, 0.01505614910274744, "NIL"], [1965, 1971, 0.014947962015867233, "NIL"], [1962, 1972, 0.014625336043536663, "NIL"], [1974, 1976, 0.014513451606035233, "NIL"], [1968, 1971, 0.013349374756217003, "NIL"], [1968, 1976, 0.012857313267886639, "NIL"], [1965, 1970, 0.012681936845183372, "NIL"]], [[2017, 2017, 0.9739658236503601, "ReferenceLink"], [2014, 2014, 0.5944786071777344, "NIL"], [1990, 1991, 0.5700474977493286, "ModelArchitecture"], [2013, 2015, 0.5562888383865356, "Method"], [2014, 2015, 0.29636049270629883, "NIL"], [1995, 1999, 0.25859764218330383, "Method"], [2007, 2011, 0.2166072130203247, "Method"], [1991, 1991, 0.18062929809093475, "NIL"], [1996, 1999, 0.1721699833869934, "NIL"], [1990, 1990, 0.16644442081451416, "NIL"], [2009, 2011, 0.1602957546710968, "NIL"], [2013, 2014, 0.15043959021568298, "NIL"], [1994, 1999, 0.1006607711315155, "NIL"], [1996, 1998, 0.09038573503494263, "NIL"], [2004, 2005, 0.08445550501346588, "NIL"], [2016, 2017, 0.0634969174861908, "NIL"], [1995, 1998, 0.06116515398025513, "NIL"], [2008, 2011, 0.052870046347379684, "NIL"], [2007, 2007, 0.052269332110881805, "NIL"], [2013, 2018, 0.05222489684820175, "NIL"], [1994, 1994, 0.05056443810462952, "NIL"], [2003, 2003, 0.04684052988886833, "NIL"], [1985, 1987, 0.04528002440929413, "NIL"], [2007, 2008, 0.04203590750694275, "NIL"], [1993, 1994, 0.03930479288101196, "NIL"], [1984, 1987, 0.03904500976204872, "NIL"], [1980, 1982, 0.03828265890479088, "NIL"], [2003, 2005, 0.037977516651153564, "NIL"], [2017, 2018, 0.036485373973846436, "NIL"], [2014, 2017, 0.03433097526431084, "NIL"], [2002, 2003, 0.03362848237156868, "NIL"], [2014, 2018, 0.03316418081521988, "NIL"], [1999, 1999, 0.033072952181100845, "NIL"], [1993, 1999, 0.03079482913017273, "NIL"], [2015, 2015, 0.029664140194654465, "NIL"], [2009, 2009, 0.026221558451652527, "NIL"], [1994, 1998, 0.026106800884008408, "NIL"], [1980, 1987, 0.02457984909415245, "NIL"], [2006, 2007, 0.02394450455904007, "NIL"], [1994, 1995, 0.02376367338001728, "NIL"], [1981, 1982, 0.023702135309576988, "NIL"], [2007, 2009, 0.02264954149723053, "NIL"], [1984, 1984, 0.022511597722768784, "NIL"], [1984, 1985, 0.022304745391011238, "NIL"], [2016, 2018, 0.022229572758078575, "NIL"], [2006, 2011, 0.021702971309423447, "NIL"], [2002, 2002, 0.020683590322732925, "NIL"], [2011, 2011, 0.019589219242334366, "NIL"], [1993, 1993, 0.01954222284257412, "NIL"], [2004, 2011, 0.019467754289507866, "NIL"], [1995, 1995, 0.019129879772663116, "NIL"], [1996, 1996, 0.019114186987280846, "NIL"], [2005, 2005, 0.018128108233213425, "NIL"], [1981, 1987, 0.018109243363142014, "NIL"], [1980, 1983, 0.018078073859214783, "NIL"], [1984, 1988, 0.01705281436443329, "NIL"], [1998, 1999, 0.016699237748980522, "NIL"], [1980, 1984, 0.016586363315582275, "NIL"], [1986, 1987, 0.016412368044257164, "NIL"], [1980, 1981, 0.016120122745633125, "NIL"]], [[2020, 2022, 0.6912801265716553, "Method"], [2021, 2021, 0.44484031200408936, "NIL"], [2035, 2038, 0.2531825304031372, "NIL"], [2021, 2022, 0.20530138909816742, "NIL"], [2028, 2029, 0.19505329430103302, "NIL"], [2028, 2031, 0.13172149658203125, "NIL"], [2036, 2038, 0.12837012112140656, "NIL"], [2029, 2029, 0.09644799679517746, "NIL"], [2030, 2031, 0.09534148871898651, "NIL"], [2020, 2021, 0.08615007996559143, "NIL"], [2029, 2031, 0.07737070322036743, "NIL"], [2026, 2026, 0.06845298409461975, "NIL"], [2037, 2038, 0.054630011320114136, "NIL"], [2036, 2037, 0.053924642503261566, "NIL"], [2033, 2038, 0.051567889750003815, "NIL"], [2022, 2022, 0.04937022179365158, "NIL"], [2028, 2030, 0.04480116069316864, "NIL"], [2020, 2020, 0.04477657750248909, "NIL"], [2034, 2038, 0.044619280844926834, "NIL"], [2031, 2031, 0.039011843502521515, "NIL"], [2024, 2024, 0.037309832870960236, "NIL"], [2035, 2037, 0.03557385504245758, "NIL"], [2033, 2033, 0.03481866419315338, "NIL"], [2036, 2036, 0.033824555575847626, "NIL"], [2030, 2030, 0.032225560396909714, "NIL"], [2038, 2038, 0.030271518975496292, "NIL"], [2029, 2030, 0.0257418230175972, "NIL"], [2037, 2037, 0.023936118930578232, "NIL"], [2024, 2026, 0.022232666611671448, "NIL"], [2035, 2036, 0.015729622915387154, "NIL"], [2033, 2037, 0.01117733959108591, "NIL"], [2033, 2036, 0.007245768792927265, "NIL"], [2034, 2037, 0.0071503715589642525, "NIL"], [2034, 2036, 0.004822671879082918, "NIL"]], [[2058, 2062, 0.14805735647678375, "NIL"], [2041, 2045, 0.13368546962738037, "NIL"], [2065, 2067, 0.07030487805604935, "NIL"], [2050, 2050, 0.06580539792776108, "NIL"], [2059, 2062, 0.058840177953243256, "NIL"], [2050, 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"sets", "and", "use", "10", "-", "fold", "cross", "-", "validation", "whenever", "computationally", "feasible", ".", "Note", "that", "while", "we", "perform", "an", "extensive", "grid", "search", "for", "the", "baselines", ",", "we", "only", "search", "over", "a", "small", "set", "of", "configurations", "for", "NPTs", ".", "We", "refer", "the", "reader", "to", "Appendix", "E", "for", "further", "details", "on", "the", "setup", "for", "datasets", "and", "baselines", ",", "and", "Appendix", "C.1", "for", "NPT", "hyperparameters", ".", "Tabular", "Data", "Results", ".", "We", "report", "the", "average", "rank", "order", "for", "NPT", "and", "various", "tree", "-", "based", "and", "deep", "learning", "baselines", "in", "Table", "1.", "NPT", "achieves", "the", "highest", "average", "ranking", "on", "binary", "and", "multi", "-", "class", "classification", "tasks", ",", "outperforming", "CatBoost", "and", "XGBoost", ",", "two", "popular", "state", "-", "of", "-", "the", "-", "art", 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"classification", ",", "and", "(", "R", ")", "MSE", "for", "regression", ",", "we", "refer", "the", "reader", "to", "Appendix", "B.7", ".", "In", "the", "appendix", ",", "we", "present", "ablations", "which", "suggest", "that", "the", "performance", "of", "NPT", "is", "robust", "across", "a", "wide", "range", "of", "hyperparameter", "choices", "(", "Appendix", "B.4", ")", "and", "that", "both", "the", "introduction", "of", "the", "ABA", "layer", "and", "the", "stochastic", "feature", "masking", "contribute", "positively", "to", "the", "performance", "of", "NPTs", "(", "Appendix", "B.5", ")", ".", "Image", "Data", "Results", ".", "On", "CIFAR-10", ",", "we", "replace", "our", "linear", "encoder", "with", "a", "CNN", "followed", "by", "ABD", "layers", "on", "the", "CNN", "encodings", ",", "achieving", "a", "test", "accuracy", "of", "93.7", "%", ".", "We", "achieve", "98.3", "%", "accuracy", "on", "MNIST", "using", "linear", "patching", "[", "25", "]", ".", "Crucially", ",", "we", "show", "in", "\u00a7", "4.", "3", "that", "NPTs", "learn", "to", "make", "use", "of", "interactions", "between", "images", "on", "both", "the", "CIFAR-10", "and", "MNIST", "datasets", ",", "supporting", "the", "claim", "that", "attention", "between", "datapoints", "is", "useful", "beyond", "tabular", "data", ".", "We", "also", "explore", "linear", "patching", "on", "CIFAR-10", ".", "See", "Appendix", "B.8", "for", "these", "results", "along", "with", "setup", "details", "and", "further", "discussion", ".", "To", "determine", "if", "NPTs", "can", "successfully", "learn", "to", "exploit", "interactions", "between", "datapoints", "(", "Q2", ")", ",", "we", "introduce", "a", "task", "with", "strong", "input", "correlations", "for", "which", "we", "know", "ground", "-", "truth", "interactions", ".", "Concretely", ",", "we", "use", "the", "UCI", "Protein", "regression", "dataset", "(", "cf", ".", "\u00a7", "4.", "1", ")", "to", "construct", "the", "following", "semi", "-", "synthetic", "task", ":", 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"fashion", "on", "one", "of", "our", "benchmark", "datasets", "depend", "on", "relationships", "between", "datapoints", "at", "test", "time", ".", "Concretely", ",", "for", "each", "target", "value", "in", "the", "input", "we", "randomize", "the", "data", "for", "all", "other", "datapoints", "by", "independently", "shuffling", "each", "of", "their", "attributes", "across", "the", "rows", ".", "We", "then", "evaluate", "the", "loss", "on", "the", "prediction", "at", "the", "target", "entry", "and", "repeat", "this", "procedure", "for", "all", "test", "datapoints", ".", "This", "completely", "corrupts", "the", "information", "from", "all", "datapoints", "except", "the", "one", "for", "which", "we", "evaluate", ".", "Hence", ",", "a", "model", "that", "relies", "meaningfully", "on", "attention", "between", "datapoints", "will", "show", "deteriorating", "performance", ".", "We", "give", "an", "algorithm", "for", "the", "corruption", "procedure", "as", "well", "as", "further", "discussion", 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"baselines", "considered", "in", "\u00a7", "4.", "1", ".", "We", "note", "that", "minor", "differences", "in", "performance", "are", "often", "still", "significant", ",", "as", "differences", "between", "competing", "models", "in", "\u00a7", "4.", "1", "are", "often", "likewise", "small", ".", "Interestingly", ",", "on", "certain", "datasets", "such", "as", "Forest", "Cover", ",", "Kick", ",", "and", "Breast", "Cancer", ",", "corrupted", "inputs", "do", "not", "significantly", "affect", "performance", ".", "It", "appears", "that", "when", "NPTs", "do", "not", "find", "it", "advantageous", "to", "rely", "on", "attention", "between", "datapoints", "during", "training", ",", "they", "can", "learn", "to", "completely", "ignore", "other", "inputs", ",", "essentially", "collapsing", "into", "a", "standard", "parametric", "model", ".", "This", "supports", "our", "earlier", "claims", "that", "NPTs", "can", "learn", "end", "-", "to", "-", "end", "from", "data", "the", "extent", "to", "which", 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"learn", "to", "average", "out", ".", "Altogether", ",", "we", "conclude", "that", "NPTs", "can", "and", "do", "learn", "representations", "which", "rely", "on", "interactions", "between", "datapoints", "for", "prediction", ".", "Limitations", ".", "NPTs", "share", "scaling", "limitations", "with", "all", "na\u00efvely", "non", "-", "parametric", "approaches", "[", "74", "]", "and", "GNNs", "[", "52", "]", ".", "We", "demonstrate", "this", "in", "a", "preliminary", "analysis", "of", "the", "computational", "cost", "of", "NPTs", "and", "the", "baseline", "methods", "-", "including", "training", "time", "and", "CPU", "/", "GPU", "memory", "requirements", "-", "in", "Appendix", "B.6", ".", "While", "we", "have", "seen", "success", "with", "random", "minibatching", "(", "\u00a7", "2.", "6", ")", ",", "future", "work", "might", "consider", "applying", "principled", "attention", "approximations", ",", "such", "as", "learning", "representative", "input", "points", "[", "59", "]", ",", "kernelization", "[", "19", ",", "47", "]", ",", "or", "other", "sparsity", "-", "inducing", "methods", "[", "5", ",", "18", ",", "84", "]", ",", "to", "improve", "the", "scalability", "of", "NPTs", ".", "Future", "Work", ".", "We", "believe", "that", "the", "unique", "predictive", "mechanism", "of", "NPTs", "makes", "them", "an", "interesting", "object", "of", "study", "for", "other", "tasks", "including", "continual", "learning", ",", "multi", "-", "task", "learning", ",", "few", "-", "shot", "generalization", ",", "and", "domain", "adaptation", ".", "For", "example", ",", "when", "predicting", "under", "distribution", "shift", ",", "general", "relations", "between", "datapoints", "and", "attributes", "may", "remain", "valid", "and", "allow", "NPTs", "to", "accommodate", "such", "scenarios", "better", ".", "Additionally", ",", "future", "work", "could", "explore", "the", "connections", "to", "stochastic", "processes", ",", "e.g.", ",", "by", "extending", "NPTs", "to", "be", "approximately", "consistent", ",", "similar", "to", "Neural", "Processes", "[", "36", ",", "37", ",", "49", "]", ".", "Conclusions", ".", "We", "have", "introduced", "Non", "-", "Parametric", "Transformers", "(", "NPTs", ")", ",", "a", "novel", "deep", "learning", "architecture", "that", "takes", "the", "entire", "dataset", "as", "input", "and", "uses", "self", "-", "attention", "to", "model", "complex", "relationships", "between", "datapoints", ".", "NPTs", "challenge", "and", "naturally", "extend", "parametric", "modeling", "as", "the", "dominant", "paradigm", "of", "deep", "learning", ".", "They", "have", "the", "additional", "flexibility", "to", "learn", "to", "predict", "by", "directly", "attending", "to", "other", "datapoints", ".", "Notably", ",", "NPTs", "learn", "this", "end", "-", "to", "-", "end", "from", "the", "data", "at", "hand", ".", "Empirically", ",", "NPTs", "achieve", "highly", "competitive", "performance", "on", "a", "variety", "of", "benchmarks", ",", "and", "additional", "experiments", "demonstrate", "their", "ability", "to", "solve", "complex", "reasoning", "tasks", "over", "datapoints", ".", "Further", ",", "we", "show", "that", "on", "real", "data", ",", "NPTs", "learn", "to", "rely", "on", "attention", "between", "datapoints", "for", "prediction", ".", "We", "believe", "that", "the", "characteristics", "of", "NPTs", "will", "make", "them", "an", "exciting", "object", "of", "further", "study", ".", "We", "here", "provide", "proof", "that", "NPT", "is", "equivariant", "to", "a", "permutation", "of", "the", "datapoints", ".", "This", "requires", ",", "among", "other", "things", ",", "showing", "that", "multi", "-", "head", "self", "-", "attention", "is", "equivariant", ".", "We", "were", "unable", "to", "find", "this", "proof", "in", "the", "existing", "literature", ",", "e.g.", ",", "Set", "Transformer", "[", "59", "]", "relies", "heavily", "on", "equivariance", "of", "self", "-", "attention", "but", "does", "not", "provide", "proof", ".", "In", "the", "following", ",", "we", "will", "refer", "to", "datapoints", "as", "the", "rows", "of", "our", "input", ",", "see", "e.g.", ",", "Fig", ".", "1.", "Lemma", "1.", "Any", "function", "of", "the", "form", "f", "(", "X", "1", ",", ".", ".", ".", ",", "X", "n", ")", "=", "(", "g", "(", "X", "1", ")", ",", ".", ".", ".", ",", "g", "(", "X", "n", ")", ")", "for", "some", "g", "is", "rowequivariant", ".", "These", "functions", "are", "denoted", "as", "'", "row", "-", "wise", "operations", "'", ",", "as", "they", "consist", "of", "the", "same", "function", "applied", "to", "each", "of", "the", "rows", "of", "the", "input", ".", "Proof", ".", "Follows", "immediately", "from", "the", "structure", "of", "f", ".", "Lemma", "2.", "The", "composition", "of", "row", "-", "equivariant", "functions", "is", "row", "-", "equivariant", ".", "Proof", ".", "This", "result", "is", "widely", "known", ",", "but", "a", "proof", "here", "is", "included", "for", "completeness", ".", "Let", "f", "and", "g", "be", "row", "-", "equivariant", ".", "Proof", ".", "Let", "\u03c3X", "be", "a", "permutation", "of", "the", "rows", "of", "X", ".", "Then", "we", "have", "Proof", ".", "Let", "the", "row", "-", "wise", "softmax", "function", "be", "denoted", "\u03c9", "(", "\u2022", ")", ".", "Then", "we", "have", "where", "Note", "that", "the", "above", "result", "states", "that", "the", "function", "XW", "Q", "(", "XW", "K", ")", "is", "not", "row", "-", "equivariant", "because", "of", "the", "additional", "permutation", "of", "the", "columns", ".", "Let", "\u03c3", "denote", "a", "permutation", "operator", "on", "matrices", ".", "Then", "straightforwardly", "we", "have", "the", "following", ":", "Finally", ",", "it", "remains", "to", "show", "that", "the", "final", "matrix", "multiplication", "step", "restores", "the", "row", "-", "equivariance", "property", "we", "seek", ".", "Which", "shows", "that", "self", "-", "attention", "is", "row", "-", "equivariant", ".", "Lemma", "5.", "The", "following", "hold", ":", "1.", "Multihead", "self", "-", "attention", "is", "equivariant", ".", "2.", "If", "f", "and", "g", "are", "row", "-", "equivariant", ",", "then", "the", "function", "Proof", ".", "We", "show", "each", "item", ".", "1.", "We", "know", "that", "X", "\u2192", "O", "i", "is", "equivariant", "from", "the", "previous", "lemma", ",", "and", "this", "trivially", "implies", "that", "X", "\u2192", "concat", "(", "O", "1", ",", ".", ".", ".", ",", "O", "k", ")", "will", "also", "be", "row", "-", "equivariant", ".", "Finally", ",", "because", "\u03c3AB", "=", "\u03c3", "(", "AB", ")", ",", "get", "that", "MHSelfAtt", "(", "H", ")", "is", "row", "-", "equivariant", ".", "2.", "Straightforward", ".", "Res", "(", "H", ")", "is", "a", "sum", "of", "two", "row", "-", "equivariant", "functions", "and", "so", "by", "a", "previous", "result", "will", "also", "be", "row", "-", "equivariant", ".", "4.", "Because", "rFF", "is", "again", "a", "row", "-", "wise", "operation", "and", "so", "trivially", "row", "-", "equivariant", ",", "the", "previous", "results", "on", "sums", "and", "compositions", "of", "row", "-", "equivariant", "functions", "directly", "yield", "row", "-", "equivariance", "of", "MHSA", ".", "5.", "ABD", "is", "by", "definition", "an", "application", "of", "MHSA", "(", "H", ")", ",", "and", "therefore", "is", "row", "-", "equivariant", "by", "the", "above", "result", ".", "6.", "ABA", "is", "a", "row", "-", "wise", "operation", "and", "is", "therefore", "trivially", "row", "-", "equivariant", ".", "Property", "A.0.1", ".", "NPT", "is", "row", "-", "equivariant", ".", "Proof", ".", "Each", "layer", "of", "NPT", "has", "been", "shown", "to", "be", "row", "-", "equivariant", ".", "Because", "NPT", "is", "a", "composition", "of", "such", "row", "-", "equivariant", "functions", ",", "it", "is", "therefore", "row", "-", "equivariant", ".", "We", "here", "display", "additional", "results", "for", "the", "semi", "-", "synthetic", "experiments", "of", "Section", "4.", "2", ".", "In", "Fig", ".", "B.1", ",", "we", "display", "attention", "weights", "for", "Attention", "Between", "Datapoints", "(", "ABD", ")", "for", "all", "depths", "and", "a", "subset", "of", "heads", "of", "the", "architecture", ".", "We", "see", "that", "some", ",", "but", "not", "all", ",", "attention", "heads", "display", "the", "desired", "diagonal", "lookup", "pattern", ".", "Note", "that", ",", "in", "this", "case", ",", "one", "head", "would", "suffice", "to", "implement", "lookup", "and", "perfectly", "solve", "the", "task", ".", "A", "brief", "comment", "on", "the", "attention", "maps", "with", "the", "\"", "double", "diagonal", "\"", "structure", "(", "e.g.", ",", "depth", "4", ",", "head", "0", "):", "we", "see", "that", "(", "a", ")", "original", "datapoints", "attend", "to", "the", "duplicate", "points", "and", "(", "b", ")", "duplicates", "also", "attend", "to", "duplicate", "datapoints", ".", "Behavior", "(", "a", ")", "makes", "sense", ":", "NPT", "needs", "to", "attend", "to", "the", "duplicates", "from", "the", "originals", "to", "look", "up", "the", "target", "values", ".", "This", "behavior", "in", "turn", "minimizes", "loss", ".", "Behavior", "(", "b", ")", "is", "irrelevant", "to", "loss", ",", "because", "NPT", "does", "not", "need", "to", "predict", "anything", "for", "the", "duplicates", ",", "and", "no", "loss", "is", "computed", ".", "However", ",", "(", "b", ")", "suggests", "that", "the", "query", "embeddings", "learned", "by", "the", "self", "-", "attention", "ignore", "the", "masked", "Setup", ".", "In", "Section", "4.", "2", ",", "we", "mention", "that", "with", "some", "concessions", "the", "original", "lookup", "task", "can", "also", "be", "solved", "by", "standard", "non", "-", "parametric", "models", ".", "However", ",", "we", "also", "mention", "that", "simple", "modifications", "to", "the", "task", "make", "it", ",", "again", ",", "unsolvable", "for", "any", "model", "of", "which", "we", "are", "aware", "other", "than", "NPT", ".", "We", "here", "demonstrate", "these", "hypotheses", "for", "two", "non", "-", "parametric", "models", ":", "k", "-", "Nearest", "Neighbors", "(", "k", "-", "NN", ")", "and", "Deep", "Kernel", "Learning", "(", "DKL", ")", ".", "First", ",", "we", "apply", "k", "-", "NN", "and", "DKL", "to", "the", "original", "duplication", "tasks", ".", "As", "mentioned", "in", "the", "main", "text", ",", "this", "already", "requires", "us", "to", "make", "some", "concessions", ":", "we", "now", "need", "to", "explicitly", "split", "the", "input", "data", "into", "a", "global", "training", "set", "(", "all", "duplicated", "datapoints", ")", "as", "well", "as", "a", "test", "set", "(", "all", "original", "datapoints", ")", ".", "That", "is", ",", "if", "all", "duplicate", "datapoints", "make", "up", "the", "training", "set", ",", "then", "non", "-", "parametric", "models", "are", "able", "to", "predict", "perfectly", "on", "the", "original", "datapoints", ",", "because", "most", "non", "-", "parametric", "models", "rely", "on", "distances", "in", "some", "manner", ",", "and", "here", ",", "distances", "in", "input", "feature", "space", "are", "sufficient", "to", "successfully", "match", "entries", ".", "This", "is", "trivially", "true", "for", "k", "-", "NN", "but", "also", "for", "DKL", ",", "where", "the", "RBF", "kernel", "of", "the", "GP", "will", "lead", "to", "the", "desired", "\"", "matching", "behavior", "\"", "as", "long", "as", "the", "learned", "neural", "network", "embedding", "does", "not", "collapse", "distances", ".", "In", "other", "words", ",", "NPTs", "would", "ideally", "learn", "a", "k", "-", "NN", "-", "style", "prediction", "for", "the", "semi", "-", "synthetic", "dataset", ".", "Crucially", ",", "while", "non", "-", "parametric", "models", "predict", "based", "on", "distances", "because", "of", "fixed", "design", "choices", ",", "NPTs", "learn", "this", "behavior", "and", "can", "just", "as", "well", "learn", "other", "more", "complicated", "relations", "between", "datapoints", ".", "We", "now", "present", "two", "modifications", "to", "the", "semi", "-", "synthetic", "dataset", ";", "NPT", "can", "accommodate", "them", "because", "the", "model", "learns", "the", "nature", "of", "interactions", ",", "but", "they", "significantly", "affect", "the", "performance", "of", "the", "fixed", "kernel", "methods", ".", "\u2022", "Random", "Features", ":", "A", "subset", "of", "the", "features", "are", "randomized", "across", "both", "original", "and", "duplicate", "datapoints", "independently", ".", "Specifically", ",", "we", "overwrite", "the", "entries", "of", "the", "last", "three", "features", "with", "noise", "drawn", "independently", "from", "a", "Gaussian", "distribution", "N", "(", "1", ",", "1", ")", ".", "To", "solve", "the", "task", ",", "matches", "between", "datapoints", "must", "now", "be", "computed", "using", "the", "subset", "of", "non", "-", "randomized", "features", "only", ".", "\u2022", "Add", "One", ":", "We", "add", "1", "to", "all", "target", "regression", "values", "only", "for", "the", "duplicate", "datapoints", ".", "Matches", "can", "still", "be", "made", "based", "on", "all", "features", ",", "but", "now", "a", "1", "must", "be", "subtracted", "from", "the", "lookup", "value", "to", "solve", "the", "task", ".", "As", "in", "the", "original", "setting", ",", "we", "train", "the", "models", "on", "the", "modified", "semi", "-", "synthetic", "datasets", "and", "check", "with", "novel", "test", "data", "whether", "they", "have", "learnt", "the", "correct", "relational", "mechanism", "underlying", "the", "experiment", ".", "Note", "that", "the", "Random", "Features", "and", "Add", "One", "settings", "also", "distinguish", "our", "setup", "from", "prompting", "in", "natural", "language", "processing", "literature", "[", "12", ",", "72", "]", "because", "the", "original", "datapoints", "are", "no", "longer", "\"", "correct", "\"", "input", "-", "output", "pairs", ";", "the", "model", "must", "use", "an", "underlying", "relational", "structure", "instead", "of", "memorization", "to", "solve", "the", "task", ".", "Results", ".", "Table", "3", "presents", "RMSE", "values", "obtained", "by", "the", "models", "when", "trained", "on", "the", "original", "duplication", "task", ",", "the", "two", "modifications", "separately", ",", "as", "well", "as", "both", "modifications", "applied", ".", "Evidently", ",", "for", "NPTs", ",", "the", "different", "scenarios", "do", "not", "lead", "to", "a", "large", "difference", "in", "performance", ";", "in", "all", "instances", ",", "they", "achieve", "near", "-", "perfect", "loss", "because", "their", "predictions", "leverage", "attention", "between", "datapoints", ".", "Careful", "optimization", "of", "NPT", "training", "convergence", "would", "likely", "lead", "to", "a", "further", "reduction", "in", "loss", ".", "Nevertheless", ",", "the", "achieved", "losses", "by", "NPT", "are", "more", "than", "a", "magnitude", "lower", "than", "those", "on", "the", "original", "data", "and", "correspond", "to", "a", "near", "-", "perfect", "Pearson", "-", "correlation", "with", "the", "target", "values", "of", "r", ">", "99.9", "%", ".", "We", "conclude", "that", "NPTs", "successfully", "learn", "to", "attend", "to", "the", "correct", "subset", "of", "features", ",", "to", "subtract", "1", "from", "the", "lookup", "target", "values", ",", "or", "to", "do", "both", "at", "the", "same", "time", ".", "Next", ",", "we", "consider", "the", "non", "-", "parametric", "models", ".", "First", ",", "we", "confirm", "in", "Original", "Synthetic", "that", "the", "non", "-", "parametric", "models", "can", "indeed", "solve", "the", "original", "lookup", "task", ".", "However", ",", "we", "find", "that", "neither", "DKL", "nor", "k", "-", "NN", "can", "accommodate", "any", "of", "the", "modifications", ",", "reverting", "to", "an", "RMSE", "that", "is", "worse", "than", "the", "performance", "of", "all", "baselines", "on", "the", "original", "Protein", "dataset", ",", "see", "Table", "11", ".", "5", "or", "k", "-", "Nearest", "Neighbor", ",", "k", "=", "1", "is", "clearly", "optimal", "in", "the", "original", "semi", "-", "synthetic", "setup", ".", "However", ",", "k", "-", "NN", "can", "not", "learn", "to", "ignore", "certain", "attributes", "(", "Random", "Features", ")", "and", "or", "to", "modify", "looked", "-", "up", "values", ".", "Setting", "k", ">", "1", "actually", "improves", "prediction", "because", "it", "considers", "other", "matching", "points", "in", "addition", "to", "the", "(", "now", "misleading", ")", "duplicates", "for", "prediction", ".", "However", ",", "even", "with", "k", ">", "1", ",", "k", "-", "NN", "does", "not", "achieve", "much", "better", "than", "guessing", "performance", "on", "the", "modified", "tasks", ".", "DKL", "also", "fails", "to", "accommodate", "any", "of", "the", "presented", "task", "modifications", ".", "We", "suspect", "that", "DKL", ",", "in", "theory", ",", "should", "be", "able", "to", "solve", "the", "Random", "Features", "task", ".", "That", "is", ",", "DKL", "should", "be", "able", "to", "use", "the", "neural", "network", "to", "learn", "a", "representation", "that", "discards", "any", "information", "from", "the", "randomized", "columns", ".", "We", "were", "unable", "to", "achieve", "this", ",", "but", "it", "may", "be", "possible", "with", "additional", "adaptations", "to", "the", "model", ".", "Ideally", ",", "we", "would", "condition", "the", "GP", "on", "new", "\"", "test", "data", "\"", "(", "the", "duplicates", ")", "in", "each", "minibatch", "during", "training", ".", "This", "was", "not", "easily", "possible", "with", "the", "GPyTorch", "codebase", ".", "6", "At", "test", "time", "however", ",", "we", "did", "directly", "reconstruct", "an", "exact", "GP", "using", "embedded", "inputs", "and", "RBF", "scale", "parameters", "learned", "during", "training", ".", "In", "any", "case", ",", "DKL", "can", "never", "solve", "the", "Add", "One", "scenario", "because", ",", "after", "independently", "transforming", "features", "with", "a", "neural", "network", ",", "DKL", "simply", "applies", "a", "GP", "in", "embedding", "space", ".", "This", "means", "that", "it", "will", "always", "naively", "interpolate", "target", "values", "between", "training", "data", "(", "duplicates", ")", "and", "test", "data", "(", "features", ")", "in", "embedding", "space", ",", "and", "can", "not", "learn", "interactions", "between", "points", ",", "such", "as", "subtracting", "1", "from", "all", "duplicate", "targets", ".", "Even", "further", ",", "there", "is", "another", "easy", "option", "of", "how", "to", "construct", "this", "experiment", "such", "that", "only", "NPT", "will", "be", "able", "to", "solve", "it", ":", "we", "could", "randomly", "sample", "the", "attribute", "for", "which", "we", "mask", "out", "the", "entry", ",", "i.e.", ",", "all", "columns", "can", "now", "be", "target", "columns", ".", "All", "non", "-", "parametric", "models", "presented", "here", "rely", "on", "a", "fixed", "set", "of", "features", "as", "input", "to", "predict", "for", "a", "fixed", "target", "column", ".", "They", "are", "not", "compatible", "with", "this", "style", "of", "\"", "imputation", "\"", "problem", ",", "i.e.", ",", "there", "is", "no", "way", "to", "even", "take", "as", "input", "data", "like", "this", "in", "such", "models", ".", "NPTs", ",", "however", ",", "take", "both", "features", "and", "targets", "as", "input", ",", "only", "using", "the", "masking", "mechanism", "to", "distinguish", "between", "features", "and", "targets", "as", "well", "as", "train", "and", "test", "data", ".", "Hence", ",", "they", "can", "easily", "adapt", "to", "this", "scenario", ".", "The", "bad", "results", "for", "the", "non", "-", "parametric", "models", "also", "highlight", "that", "these", "models", "must", "predict", "nonparametrically", ",", "unlike", "NPT", ",", "which", "could", "always", "fall", "back", "to", "parametric", "prediction", "if", "it", "can", "not", "learn", "the", "interactions", "required", "for", "a", "task", ".", "(", "k", ")", "-NN", "Hyperparameter", "details", ".", "We", "use", "the", "scikit", "-", "learn", "[", "69", "]", "Alternatively", ",", "we", "could", "also", "input", "datapoints", "individually", ",", "i.e.", ",", "decrease", "the", "minibatch", "size", "to", "1", ",", "to", "test", "if", "NPT", "depends", "on", "attention", "between", "datapoints", ".", "Indeed", ",", "we", "find", "that", "performance", "also", "deteriorates", "in", "this", "scenario", ".", "However", ",", "we", "believe", "that", "the", "Data", "Corruption", "experiment", "provides", "stronger", "evidence", "because", "it", "preserves", "batch", "statistics", "across", "attributes", ".", "This", "makes", "sure", "that", "performance", "deterioration", "is", "not", "caused", "by", "spurious", "factors", ",", "such", "as", "a", "decreased", "batch", "size", "that", "was", "not", "encountered", "in", "training", ".", "While", "NPT", "is", "generally", "compatible", "with", "varying", "batch", "sizes", ",", "we", "leave", "a", "thorough", "investigation", "of", "this", "for", "future", "work", ".", "We", "here", "give", "full", "details", "on", "the", "Data", "Deletion", "experiment", "presented", "in", "Section", "4.", "4", ".", "To", "recap", ",", "we", "consider", "the", "prediction", "of", "NPT", "for", "a", "single", "test", "sample", "i", "*", ".", "We", "then", "iteratively", "delete", "other", "datapoints", "from", "the", "input", "if", "they", "do", "not", "significantly", "change", "the", "prediction", "of", "NPT", "on", "i", "*", ".", "Algorithm", "2", "describes", "this", "in", "detail", ".", "We", "are", "then", "interested", "in", "differences", "between", "the", "deleted", "and", "the", "kept", "datapoints", ".", "Specifically", ",", "we", "compare", "the", "average", "feature", "space", "distance", "in", "input", "space", "between", "the", "active", "datapoint", "i", "*", "and", "either", "the", "kept", "datapoints", "R", "or", "deleted", "datapoints", "{", "1", ",", ".", ".", ".", ",", "n", "}", "\\", "(", "{", "i", "*", "}", "\u222a", "R", ")", ",", "obtaining", "average", "distances", "D", "i", "*", ",", "kept", ",", "D", "i", "*", ",", "deleted", ".", "We", "break", "out", "of", "the", "deletion", "algorithm", "if", "less", "than", "%", "of", "the", "original", "points", "remain", ",", "to", "reduce", "variance", "in", "our", "estimates", "of", "the", "kept", "statistic", ".", "We", "repeat", "Algorithm", "2", "for", "all", "5567", "test", "points", "i", "*", "\u2208", "D", "test", "in", "the", "Protein", "regression", "dataset", ".", "We", "perform", "a", "Wilcoxon", "signed", "-", "rank", "test", "on", "the", "pairs", "{", "D", "i", "*", ",", "kept", ",", "D", "i", "*", ",", "deleted", "}", "i", "*", "\u2208Dtest", "to", "determine", "if", "the", "median", "of", "the", "kept", "datapoints", "is", "less", "than", "the", "median", "of", "the", "deleted", "ones", ".", "The", "test", "is", "highly", "significant", "at", "p", "\u2248", "0", ",", "i.e.", ",", "smaller", "than", "the", "floating", "point", "precision", "of", "SciPy", "Stats", "allows", ".", "The", "raw", "Wilcoxon", "statistic", "is", "3125889.5", ".", "To", "make", "sure", "the", "difference", "is", "not", "an", "effect", "of", "sample", "size", ",", "we", "also", "construct", "a", "set", "of", "average", "differences", "to", "a", "set", "of", "randomly", "drawn", "datapoints", ".", "7", "That", "is", ",", "instead", "of", "using", "Algorithm", "2", "for", "targeted", "deletion", ",", "we", "randomly", "construct", "R", ",", "essentially", "only", "applying", "lines", "10", "and", "15", "of", "Algorithm", "2.", "For", "Displayed", "are", "average", "feature", "space", "differences", "and", "their", "standard", "errors", "between", "the", "active", "datapoint", "and", "the", "sets", "of", "kept", ",", "random", ",", "and", "deleted", "datapoints", "for", "a", "single", "batch", ".", "each", "active", "test", "row", "i", "*", ",", "we", "randomly", "delete", "as", "many", "datapoints", "as", "were", "deleted", "in", "targeted", "fashion", ".", "A", "Wilcoxon", "signed", "-", "rank", "test", "between", "the", "distances", "for", "the", "random", "and", "kept", "subset", "is", "likewise", "significant", "at", "p", "\u2248", "8.", "77", "\u2022", "10", "\u2212130", ".", "This", "is", "the", "value", "we", "report", "in", "the", "main", "body", ".", "We", "also", "run", "a", "computationally", "more", "demanding", "version", "of", "the", "algorithm", "with", "\u2206", "it", "\u2190", "0.", "005", ",", "\u2190", "0.", "01", "to", "see", "how", "many", "points", "we", "can", "successfully", "delete", ".", "This", "version", "of", "algorithm", "requires", "more", "computation", "which", "is", "why", "we", "limit", "execution", "to", "the", "test", "datapoints", "of", "a", "single", "batch", ".", "The", "results", "are", "statistically", "significant", "at", "5.", "26", "\u2022", "10", "\u221249", "for", "kept", "<", "deleted", "and", "8.", "38", "\u2022", "10", "\u221239", "for", "kept", "<", "random", "for", "a", "Wilcoxon", "signed", "-", "rank", "test", ".", "We", "illustrate", "the", "differences", "between", "the", "distances", "in", "Fig", ".", "B.3", ".", "We", "further", "note", "that", "using", "Algorithm", "2", ",", "we", "are", "able", "to", "reduce", "the", "set", "of", "datapoints", "present", "in", "the", "input", "to", "1", "%", "of", "the", "original", "n", "for", "79.5", "%", "of", "active", "test", "datapoints", "and", "to", "10", "%", "in", "99.5", "%", "of", "cases", ".", "Percentages", "refer", "to", "n", "=", "2048", "datapoints", "in", "total", ",", "of", "which", "398", "were", "test", "datapoints", ".", "All", "in", "all", ",", "these", "experiments", "strongly", "suggest", "that", "NPT", "relies", "on", "interactions", "between", "similar", "datapoints", "for", "prediction", ".", "We", "conduct", "an", "ablation", "study", "on", "the", "Protein", "and", "Boston", "Housing", "datasets", "(", "Table", "4", ")", ".", "For", "Protein", ",", "the", "same", "0.", "7", "/", "0.1", "/", "0.2", "train", "/", "validation", "/", "test", "split", "is", "used", "for", "all", "model", "configurations", ".", "Boston", "Housing", "uses", "a", "0.", "7", "/", "0.2", "/", "0.1", "train", "/", "validation", "/", "test", "split", "with", "10", "-", "fold", "cross", "-", "validation", ".", "Despite", "the", "significant", "difference", "in", "dataset", "sizes", "between", "Boston", "Housing", "(", "n", "=", "506", ")", "and", "Protein", "(", "n", "=", "45730", ")", ",", "and", "the", "fact", "that", "Boston", "Housing", "includes", "both", "categorical", "and", "continuous", "variables", ",", "the", "base", "models", "used", "for", "each", "dataset", "are", "nearly", "identical", ".", "On", "both", "datasets", ",", "we", "use", "an", "NPT", "model", "with", "8", "layers", ",", "8", "heads", ",", "per", "-", "attribute", "hidden", "dimension", "e", "=", "128", ",", "feature", "and", "target", "masking", "with", "p", "=", "0.", "15", "for", "each", ",", "a", "cosine", "annealing", "schedule", "for", "the", "loss", "tradeoff", "\u03bb", ",", "the", "LAMB", "[", "98", "]", "optimizer", "with", "Lookahead", "[", "99", "]", ",", "a", "flat", "-", "then", "-", "anneal", "learning", "rate", "schedule", "with", "cosine", "decay", "and", "base", "learning", "rate", "0.", "001", ",", "dropout", "with", "rate", "0.", "1", "on", "the", "attention", "weights", "and", "after", "linear", "layers", ",", "and", "gradient", "clipping", "at", "1.", "This", "configuration", "is", "essentially", "the", "same", "as", "the", "NPT", "-", "Base", "configuration", "described", "in", "Appendix", "C.1", ",", "which", "we", "use", "with", "minimal", "per", "-", "dataset", "modifications", "for", "all", "other", "results", "in", "this", "work", ".", "Different", "in", "our", "base", "models", "between", "the", "two", "datasets", "are", "the", "following", "settings", ".", "The", "Boston", "Housing", "model", "takes", "as", "input", "the", "full", "dataset", "(", "i.e.", ",", "batch", "size", "=", "507", ")", "and", "Protein", "uses", "minibatching", "with", "batch", "size", "=", "2048", ".", "Boston", "Housing", "trains", "for", "20", "000", "steps", ",", "and", "Protein", "for", "400", "000", ".", "As", "Table", "4", "shows", ",", "the", "performance", "of", "NPT", "is", "robust", "to", "a", "variety", "of", "significant", "hyperparameter", "choices", ".", "This", "illustrates", "that", "practitioners", "will", "likely", "not", "need", "to", "spend", "much", "time", "tuning", "hyperparameters", "Protein", "Dataset", ".", "See", "Table", "4", "for", "results", "and", "performed", "ablations", ".", "It", "is", "computationally", "too", "expensive", "for", "us", "to", "perform", "full", "cross", "-", "validation", "over", "all", "ablations", "for", "the", "Protein", "regression", "dataset", ".", "Instead", ",", "we", "report", "the", "results", "of", "a", "single", "5", "-", "fold", "cross", "-", "validation", "for", "the", "Base", "NPT", "configuration", "on", "Protein", "(", "also", "varying", "the", "model", "random", "state", ")", ".", "This", "results", "in", "an", "RMSE", "of", "3.", "40", "\u00b1", "0.", "05", "(", "\u03c3", ")", ".", "The", "standard", "deviation", "of", "the", "5", "-", "fold", "cross", "-", "validation", "allows", "us", "to", "roughly", "gauge", "which", "ablations", "have", "significant", "effect", ".", "Given", "the", "results", "in", "Table", "4", ",", "we", "find", "that", "the", "majority", "of", "ablations", "do", "not", "lead", "to", "meaningful", "changes", "in", "performance", ".", "Only", "the", "somewhat", "dramatic", "changes", "to", "the", "optimization", "of", "NPT", "result", "in", "its", "performance", "falling", "from", "the", "top", "rank", "on", "the", "Protein", "Dataset", "(", "second", "rank", "CatBoost", "has", "RMSE", "=", "3.", "51", "):", "removing", "stochastic", "feature", "masking", "(", "p", "feature", "=", "0", ")", ",", "removing", "both", "stochastic", "feature", "masking", "(", "p", "feature", "=", "0", ")", "and", "stochastic", "target", "masking", "(", "p", "target", "=", "1", ",", "training", "targets", "are", "always", "masked", "out", "at", "training", "time", "and", "NPT", "therefore", "can", "not", "learn", "to", "attend", "to", "training", "targets", "at", "test", "time", ")", ",", "or", "changing", "p", "feature", "to", "0.", "5", "(", "meaning", "that", "50", "%", "of", "all", "input", "features", "are", "masked", "out", ")", ".", "NPT", "appears", "to", "be", "particularly", "robust", "to", "changes", "in", "model", "complexity", ",", "e.g.", ",", "depth", "and", "number", "of", "heads", ",", "although", "the", "results", "suggest", "that", "we", "could", "have", "further", "increased", "the", "size", "of", "Base", "NPT", "to", "achieve", "slightly", "higher", "performance", ".", "Boston", "Dataset", ".", "See", "Table", "4", "for", "results", "and", "performed", "ablations", ".", "For", "the", "Boston", "dataset", ",", "we", "repeat", "ablations", "over", "all", "10", "CV", "splits", ".", "Similarly", ",", "ablations", "on", "the", "Boston", "dataset", "are", "largely", "inconsequential", ";", "none", "of", "them", "result", "in", "a", "statistically", "significant", "change", "in", "performance", "from", "the", "base", "model", ".", "The", "second", "rank", "performer", "on", "Boston", "is", "MLP", ",", "at", "RMSE", "=", "3.", "32", ".", "Only", "ablation", "of", "semi", "-", "supervision", "or", "changing", "p", "feature", "to", "0.", "5", "result", "in", "a", "change", "in", "the", "top", "ranking", "of", "NPT", "among", "the", "baselines", ".", "Altogether", ",", "the", "ablation", "study", "supports", "the", "claim", "that", "NPT", "can", "be", "applied", "successfully", "with", "very", "little", "tuning", "to", "datasets", "of", "vastly", "different", "sizes", "and", "feature", "types", ".", "Changes", "in", "model", "depth", "and", "number", "of", "heads", "do", "not", "appear", "significant", ",", "but", "using", "a", "reasonably", "low", "feature", "masking", "probability", "(", "e.g.", ",", "15", "%", ",", "as", "has", "been", "commonly", "used", "in", "the", "literature", "[", "24", "]", ")", "may", "be", "important", "to", "stable", "training", ".", "Supported", "by", "these", "ablations", ",", "we", "sweep", "over", "only", "a", "small", "selection", "of", "configurations", "for", "our", "main", "benchmark", "comparison", "in", "Section", "4.", "1", ".", "And", "indeed", ",", "it", "seems", "that", "NPT", "is", "robust", "to", "hyperparameter", "changes", ",", "given", "that", "these", "configurations", "perform", "well", "across", "vastly", "different", "settings", "(", "binary", "and", "multi", "-", "class", "classification", ",", "datasets", "with", "millions", "of", "datapoints", ",", "etc", ".", ")", "than", "those", "explored", "in", "the", "ablations", ".", "See", "Appendix", "E", "for", "details", ".", "We", "speculate", "that", "NPT", "'s", "robustness", "stems", "from", "(", "a", ")", "being", "a", "relatively", "overparametrized", "architecture", "that", "is", "powerful", "enough", "to", "model", "a", "wide", "variety", "of", "datasets", "and", "(", "b", ")", "from", "the", "effective", "regularization", "introduced", "by", "the", "feature", "masking", "mechanism", ".", "Finally", ",", "we", "emphasize", "that", "the", "aim", "of", "this", "work", "is", "to", "introduce", "the", "NPT", "architecture", "and", "examine", "its", "properties", ",", "not", "to", "spend", "significant", "effort", "and", "compute", "resources", "on", "achieving", "top", "performance", "across", "all", "benchmarks", ".", "We", "next", "present", "an", "additional", "ablation", "study", "targeting", "two", "core", "components", "of", "NPTs", "across", "all", "datasets", ":", "the", "Attention", "Between", "Attributes", "(", "ABA", ")", "layer", "and", "the", "stochastic", "feature", "masking", ".", "ABA", "Layer", ".", "First", ",", "we", "perform", "an", "ablation", "to", "test", "if", "ABA", "layers", "are", "beneficial", "in", "practice", ".", "For", "this", ",", "we", "simply", "leave", "out", "the", "ABA", "layers", ",", "such", "that", "the", "MLP", "at", "the", "end", "of", "the", "ABD", "layers", "(", "see", "\"", "rFF", "\"", "in", "Eq", ".", "(", "5", ")", ")", "is", "now", "the", "only", "way", "for", "the", "model", "to", "independently", "transform", "the", "features", "of", "input", "datapoints", ".", "Our", "results", ",", "given", "in", "Table", "5", ",", "show", "that", ",", "generally", ",", "ABA", "is", "a", "useful", "component", "of", "the", "NPT", "architecture", ".", "Leaving", "out", "ABA", "increases", "performance", "only", "for", "3", "/", "10", "datasets", ".", "Interestingly", ",", "all", "three", "of", "these", "datasets", "are", "regression", "tasks", ",", "which", "may", "warrant", "further", "investigation", ".", "We", "observe", "the", "largest", "difference", "for", "the", "Poker", "Hands", "dataset", ",", "which", "requires", "complex", "reasoning", "between", "input", "features", ":", "in", "the", "same", "number", "of", "training", "steps", ",", "the", "ablation", "only", "achieves", "57.4", "%", "accuracy", "compared", "to", "99.3", "%", "for", "full", "NPT", ".", "These", "results", "support", "our", "hypothesis", "that", "ABA", "is", "useful", "when", "the", "dataset", "requires", "complex", "transformations", "of", "the", "features", ".", "Our", "most", "general", "recommendation", "would", "be", "to", "default", "to", "using", "NPTs", "with", "ABA", "layers", ",", "as", "they", "boost", "performance", "on", "the", "majority", "of", "datasets", "we", "examine", ".", "However", ",", "if", "practitioners", "can", "spend", "the", "extra", "compute", ",", "exploring", "NPTs", "without", "ABA", "can", "be", "worthwhile", ".", "Stochastic", "Feature", "Masking", ".", "We", "perform", "an", "ablation", "to", "test", "if", "the", "stochastic", "feature", "masking", "objective", "(", "cf", ".", "\u00a7", "2.", "6", ")", "is", "beneficial", "in", "practice", ".", "For", "this", ",", "we", "simply", "disable", "all", "stochastic", "masking", "of", "input", "features", "by", "setting", "p", "features", "=", "0.", "Our", "results", ",", "also", "in", "Table", "5", ",", "show", "that", "for", "9", "/", "10", "datasets", ",", "enabling", "feature", "masking", "yields", "at", "least", "a", "small", "improvement", "in", "performance", ".", "Disabling", "feature", "masking", "is", "detrimental", "to", "the", "performance", "on", "the", "Poker", "Hands", "dataset", ",", "leading", "to", "a", "30", "%", "drop", "in", "accuracy", ".", "Again", ",", "our", "general", "recommendation", "would", "be", "to", "use", "NPTs", "with", "feature", "masking", "by", "default", ",", "as", "it", "rarely", "seems", "to", "decrease", "performance", "and", "sometimes", "helps", "significantly", ",", "but", "to", "explore", "NPTs", "without", "feature", "masking", "if", "feasible", ".", "We", "next", "compare", "the", "computational", "requirements", "of", "NPT", "against", "the", "various", "baselines", ".", "More", "specifically", ",", "we", "compare", "experiment", "runtimes", "and", "maximum", "memory", "usage", "on", "the", "Protein", "and", "Higgs", "datasets", ".", "We", "choose", "these", "datasets", "because", "they", "are", "representative", "of", "medium", "and", "large", "datasets", "in", "terms", "of", "computational", "requirements", ",", "with", "45", "730", "and", "11", "000", "000", "datapoints", "respectively", ".", "Note", "that", ",", "while", "we", "re", "-", "use", "hyperparameter", "configurations", "across", "datasets", "for", "NPTs", ",", "the", "baselines", "require", "a", "novel", "hyperparameter", "search", "to", "be", "performed", "for", "each", "dataset", "(", "cf", ".", "Appendices", "C", "and", "E", ")", ".", "Below", ",", "we", "include", "the", "cost", "of", "hyperparameter", "optimization", "for", "the", "baselines", ".", "Note", "that", "these", "numbers", "only", "provide", "a", "rough", "ordering", "of", "the", "compute", "and", "memory", "costs", "of", "the", "various", "methods", ".", "We", "did", "not", "optimize", "the", "baselines", "or", "NPT", "for", "memory", "usage", ",", "training", "time", ",", "or", "prediction", "speed", ".", "Additionally", ",", "while", "NPTs", "rely", "on", "GPU", "-", "accelerated", "PyTorch", "code", ",", "many", "of", "the", "baselines", "are", "CPU", "-", "only", ":", "therefore", ",", "the", "results", "depend", "on", "our", "particular", "CPU", "and", "GPU", "choices", ".", "We", "also", "give", "the", "number", "of", "CPUs", "used", "in", "each", "experiment", "for", "each", "baseline", ".", "Here", ",", "we", "maximize", "the", "number", "of", "CPUs", "used", "in", "parallel", "execution", "in", "order", "to", "speed", "up", "training", ".", "This", "is", "mainly", "limited", "by", "the", "memory", "used", "per", "process", ":", "e.g.", ",", "if", "we", "list", "#", "CPUs", "as", "1", ",", "this", "does", "not", "mean", "that", "we", "used", "a", "machine", "with", "only", "1", "CPU", ",", "but", "rather", "that", "each", "process", "used", "a", "significant", "amount", "of", "the", "total", "available", "memory", "and", "hence", "we", "could", "not", "increase", "the", "number", "of", "CPUs", "used", "in", "parallel", ".", "Note", "that", ",", "additionally", ",", "for", "the", "CPU", "baselines", ",", "we", "made", "use", "of", "high", "-", "memory", "instances", "when", "this", "was", "necessary", "to", "avoid", "out", "-", "of", "-", "memory", "issues", ".", "In", "summary", ",", "the", "numbers", "we", "give", "are", "a", "rough", "indication", "of", "the", "computational", "cost", "that", "a", "practitioner", "should", "expect", "to", "require", "in", "order", "to", "reproduce", "our", "results", ".", "It", "is", "likely", "that", "by", "tuning", "aspects", "of", "our", "setup", ",", "both", "for", "NPTs", "and", "the", "baselines", ",", "memory", "usage", "and/or", "runtimes", "could", "be", "improved", ".", "We", "display", "the", "observed", "computational", "costs", "in", "Tables", "6", "and", "7", "for", "the", "Protein", "and", "Higgs", "datasets", ".", "As", "of", "now", ",", "NPTs", "do", "generally", "require", "longer", "training", "times", "than", "the", "non", "-", "neural", "baselines", ".", "For", "example", ",", "for", "the", "Protein", "dataset", ",", "the", "selected", "hyperparameter", "configuration", "of", "NPT", "trains", "in", "11", "hours", ",", "while", "all", "boosting", "methods", "finish", "their", "runs", "in", "less", "than", "1", "hour", ",", "including", "the", "hyperparameter", "tuning", ".", "The", "exception", "to", "this", "rule", "is", "given", "by", "some", "of", "the", "baselines", ",", "e.g.", ",", "Random", "Forests", ",", "which", "do", "not", "scale", "well", "to", "large", "datasets", "such", "as", "Higgs", ".", "On", "Higgs", ",", "the", "NPT", "run", "takes", "5d", "22h", "compared", "to", "13d", "13h", "for", "Random", "Forests", ".", "With", "NPTs", ",", "we", "want", "to", "store", "as", "much", "data", "as", "possible", "in", "addition", "to", "the", "network", "weights", ";", "recall", "that", "this", "is", "done", "to", "improve", "the", "quality", "of", "the", "minibatch", "approximation", "of", "the", "full", "dataset", ".", "Therefore", ",", "as", "expected", ",", "NPT", "is", "much", "more", "GPU", "-", "memory", "intensive", "during", "training", "than", "TabNet", ",", "the", "only", "other", "baseline", "with", "a", "GPU", "-", "based", "implementation", ",", "for", "which", "maximizing", "minibatch", "size", "is", "not", "desirable", ".", "In", "particular", ",", "the", "peak", "GPU", "memory", "usage", "on", "Higgs", "for", "NPTs", "is", "19.18", "GB", "and", 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0.23041172325611115, "NIL"], [1987, 1988, 0.14667899906635284, "NIL"], [1974, 1976, 0.09594141691923141, "NIL"], [1986, 1987, 0.08028893917798996, "NIL"], [1976, 1979, 0.057480376213788986, "NIL"], [1973, 1979, 0.055778659880161285, "NIL"], [1974, 1980, 0.05062854662537575, "NIL"], [1974, 1977, 0.046471476554870605, "NIL"], [1985, 1988, 0.043705545365810394, "NIL"], [1979, 1979, 0.04307270795106888, "NIL"], [1975, 1979, 0.03836347162723541, "NIL"], [1988, 1988, 0.032862186431884766, "NIL"], [1987, 1989, 0.032704126089811325, "NIL"], [1978, 1979, 0.031094150617718697, "NIL"], [1979, 1980, 0.03101826086640358, "NIL"], [1977, 1977, 0.03023943118751049, "NIL"], [1972, 1979, 0.028648462146520615, "NIL"], [1977, 1980, 0.024177825078368187, "NIL"], [1971, 1979, 0.02240033447742462, "NIL"], [1976, 1976, 0.01814577728509903, "NIL"], [1974, 1981, 0.01703488640487194, "NIL"], [1981, 1981, 0.016907699406147003, "NIL"], [1972, 1973, 0.015912707895040512, "NIL"], [1973, 1973, 0.015542333945631981, 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