[{"data":1,"prerenderedAt":4636},["ShallowReactive",2],{"lang-switch-post-\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent":3,"post-pt-machine-learning-specialization-lab04-gradient-descent":4},"\u002Fen\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent",{"id":5,"title":6,"body":7,"cover":4621,"date":4622,"description":4623,"extension":4624,"meta":4625,"navigation":2887,"order":2878,"path":4626,"playlist":4627,"seo":4628,"status":4629,"stem":4630,"tags":4631,"__hash__":4635},"posts\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent.md","Lab Opcional: Gradiente Descendente",{"type":8,"value":9,"toc":4607},"minimark",[10,18,354,363,739,744,751,905,909,921,1286,1318,1322,1325,1933,2461,2684,2727,2849,2853,3033,3036,3176,3180,3183,3289,3296,3300,3360,3397,3429,3491,3494,3498,3504,3509,3512,3777,3833,3840,3843,3846,3852,3906,3910,4074,4077,4143,4175,4178,4182,4428,4431,4453,4468,4472,4487,4526,4537,4540,4543,4603],[11,12,13],"p",{},[14,15],"img",{"alt":16,"src":17},"Meme de pódio olímpico: nos primeiros cinco quadrinhos, o atleta comemora a medalha de ouro com um gráfico de uma tigela bem comportada, de um único fundo, ao lado. No último quadrinho, o pódio de verdade aparece com um gráfico de uma curva cheia de vales, e quem ganha o ouro, a prata ou o bronze depende de em qual vale cada um caiu","\u002Fimages\u002Fposts\u002Fmachine-learning-specialization\u002Flab04-gradient-descent\u002Fmeme-gradient-descent.jpg",[11,19,20,21,26,27,233,234,238,239,300,301,353],{},"Resumindo os dois posts anteriores: você ",[22,23,25],"a",{"href":24},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab02-model-representation","montou o modelo"," ",[28,29,32,93],"span",{"className":30},[31],"katex",[28,33,36],{"className":34},[35],"katex-mathml",[37,38,40],"math",{"xmlns":39},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[41,42,43,88],"semantics",{},[44,45,46,66,70,73,76,79,81,83,86],"mrow",{},[47,48,49,53],"msub",{},[50,51,52],"mi",{},"f",[44,54,55,58,63],{},[50,56,57],{},"w",[59,60,62],"mo",{"separator":61},"true",",",[50,64,65],{},"b",[59,67,69],{"stretchy":68},"false","(",[50,71,72],{},"x",[59,74,75],{"stretchy":68},")",[59,77,78],{},"=",[50,80,57],{},[50,82,72],{},[59,84,85],{},"+",[50,87,65],{},[89,90,92],"annotation",{"encoding":91},"application\u002Fx-tex","f_{w,b}(x) = wx + b",[28,94,97,199,223],{"className":95,"ariaHidden":61},[96],"katex-html",[28,98,101,106,176,180,183,187,192,196],{"className":99},[100],"base",[28,102],{"className":103,"style":105},[104],"strut","height:1.0361em;vertical-align:-0.2861em;",[28,107,110,115],{"className":108},[109],"mord",[28,111,52],{"className":112,"style":114},[109,113],"mathnormal","margin-right:0.1076em;",[28,116,119],{"className":117},[118],"msupsub",[28,120,124,167],{"className":121},[122,123],"vlist-t","vlist-t2",[28,125,128,162],{"className":126},[127],"vlist-r",[28,129,133],{"className":130,"style":132},[131],"vlist","height:0.3361em;",[28,134,136,141],{"style":135},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[28,137],{"className":138,"style":140},[139],"pstrut","height:2.7em;",[28,142,148],{"className":143},[144,145,146,147],"sizing","reset-size6","size3","mtight",[28,149,151,155,159],{"className":150},[109,147],[28,152,57],{"className":153,"style":154},[109,113,147],"margin-right:0.0269em;",[28,156,62],{"className":157},[158,147],"mpunct",[28,160,65],{"className":161},[109,113,147],[28,163,166],{"className":164},[165],"vlist-s","​",[28,168,170],{"className":169},[127],[28,171,174],{"className":172,"style":173},[131],"height:0.2861em;",[28,175],{},[28,177,69],{"className":178},[179],"mopen",[28,181,72],{"className":182},[109,113],[28,184,75],{"className":185},[186],"mclose",[28,188],{"className":189,"style":191},[190],"mspace","margin-right:0.2778em;",[28,193,78],{"className":194},[195],"mrel",[28,197],{"className":198,"style":191},[190],[28,200,202,206,209,212,216,220],{"className":201},[100],[28,203],{"className":204,"style":205},[104],"height:0.6667em;vertical-align:-0.0833em;",[28,207,57],{"className":208,"style":154},[109,113],[28,210,72],{"className":211},[109,113],[28,213],{"className":214,"style":215},[190],"margin-right:0.2222em;",[28,217,85],{"className":218},[219],"mbin",[28,221],{"className":222,"style":215},[190],[28,224,226,230],{"className":225},[100],[28,227],{"className":228,"style":229},[104],"height:0.6944em;",[28,231,65],{"className":232},[109,113],", depois ",[22,235,237],{"href":236},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab03-cost-function","montou um jeito de medir o quanto ele erra",", ",[28,240,242,267],{"className":241},[31],[28,243,245],{"className":244},[35],[37,246,247],{"xmlns":39},[41,248,249,264],{},[44,250,251,254,256,258,260,262],{},[50,252,253],{},"J",[59,255,69],{"stretchy":68},[50,257,57],{},[59,259,62],{"separator":61},[50,261,65],{},[59,263,75],{"stretchy":68},[89,265,266],{"encoding":91},"J(w,b)",[28,268,270],{"className":269,"ariaHidden":61},[96],[28,271,273,277,281,284,287,290,294,297],{"className":272},[100],[28,274],{"className":275,"style":276},[104],"height:1em;vertical-align:-0.25em;",[28,278,253],{"className":279,"style":280},[109,113],"margin-right:0.0962em;",[28,282,69],{"className":283},[179],[28,285,57],{"className":286,"style":154},[109,113],[28,288,62],{"className":289},[158],[28,291],{"className":292,"style":293},[190],"margin-right:0.1667em;",[28,295,65],{"className":296},[109,113],[28,298,75],{"className":299},[186],". Só que pra achar o melhor ",[28,302,304,326],{"className":303},[31],[28,305,307],{"className":306},[35],[37,308,309],{"xmlns":39},[41,310,311,323],{},[44,312,313,315,317,319,321],{},[59,314,69],{"stretchy":68},[50,316,57],{},[59,318,62],{"separator":61},[50,320,65],{},[59,322,75],{"stretchy":68},[89,324,325],{"encoding":91},"(w,b)",[28,327,329],{"className":328,"ariaHidden":61},[96],[28,330,332,335,338,341,344,347,350],{"className":331},[100],[28,333],{"className":334,"style":276},[104],[28,336,69],{"className":337},[179],[28,339,57],{"className":340,"style":154},[109,113],[28,342,62],{"className":343},[158],[28,345],{"className":346,"style":293},[190],[28,348,65],{"className":349},[109,113],[28,351,75],{"className":352},[186]," você ainda tava fazendo a coisa mais primitiva possível: arrastando slider e olhando o número cair. Funciona pra 2 pontos. Pra um dataset de verdade, com milhares de exemplos e dezenas de parâmetros, é impossível.",[11,355,356,357,362],{},"Esse post fecha o ciclo com o algoritmo que faz essa busca sozinho: o ",[358,359,361],"glossary-term",{"definition":360},"um algoritmo que ajusta os parâmetros do modelo passo a passo, sempre na direção que mais reduz o custo, até parar perto do mínimo","gradiente descendente",".",[11,364,365],{},[28,366,368,456],{"className":367},[31],[28,369,371],{"className":370},[35],[37,372,373],{"xmlns":39},[41,374,375,453],{},[44,376,377,379,381,383,386,389,416,419,421,423,425,427,429],{},[50,378,57],{},[59,380,78],{},[50,382,57],{},[59,384,385],{},"−",[50,387,388],{},"α",[390,391,392,410],"mfrac",{},[44,393,394,398,400,402,404,406,408],{},[50,395,397],{"mathvariant":396},"normal","∂",[50,399,253],{},[59,401,69],{"stretchy":68},[50,403,57],{},[59,405,62],{"separator":61},[50,407,65],{},[59,409,75],{"stretchy":68},[44,411,412,414],{},[50,413,397],{"mathvariant":396},[50,415,57],{},[190,417],{"width":418},"2em",[50,420,65],{},[59,422,78],{},[50,424,65],{},[59,426,385],{},[50,428,388],{},[390,430,431,447],{},[44,432,433,435,437,439,441,443,445],{},[50,434,397],{"mathvariant":396},[50,436,253],{},[59,438,69],{"stretchy":68},[50,440,57],{},[59,442,62],{"separator":61},[50,444,65],{},[59,446,75],{"stretchy":68},[44,448,449,451],{},[50,450,397],{"mathvariant":396},[50,452,65],{},[89,454,455],{"encoding":91},"w = w - \\alpha \\frac{\\partial J(w,b)}{\\partial w} \\qquad b = b - \\alpha \\frac{\\partial J(w,b)}{\\partial b}",[28,457,459,478,496,622,641],{"className":458,"ariaHidden":61},[96],[28,460,462,466,469,472,475],{"className":461},[100],[28,463],{"className":464,"style":465},[104],"height:0.4306em;",[28,467,57],{"className":468,"style":154},[109,113],[28,470],{"className":471,"style":191},[190],[28,473,78],{"className":474},[195],[28,476],{"className":477,"style":191},[190],[28,479,481,484,487,490,493],{"className":480},[100],[28,482],{"className":483,"style":205},[104],[28,485,57],{"className":486,"style":154},[109,113],[28,488],{"className":489,"style":215},[190],[28,491,385],{"className":492},[219],[28,494],{"className":495,"style":215},[190],[28,497,499,503,507,606,610,613,616,619],{"className":498},[100],[28,500],{"className":501,"style":502},[104],"height:1.355em;vertical-align:-0.345em;",[28,504,388],{"className":505,"style":506},[109,113],"margin-right:0.0037em;",[28,508,510,514,603],{"className":509},[109],[28,511],{"className":512},[179,513],"nulldelimiter",[28,515,517],{"className":516},[390],[28,518,520,594],{"className":519},[122,123],[28,521,523,591],{"className":522},[127],[28,524,527,547,558],{"className":525,"style":526},[131],"height:1.01em;",[28,528,530,534],{"style":529},"top:-2.655em;",[28,531],{"className":532,"style":533},[139],"height:3em;",[28,535,537],{"className":536},[144,145,146,147],[28,538,540,544],{"className":539},[109,147],[28,541,397],{"className":542,"style":543},[109,147],"margin-right:0.0556em;",[28,545,57],{"className":546,"style":154},[109,113,147],[28,548,550,553],{"style":549},"top:-3.23em;",[28,551],{"className":552,"style":533},[139],[28,554],{"className":555,"style":557},[556],"frac-line","border-bottom-width:0.04em;",[28,559,561,564],{"style":560},"top:-3.485em;",[28,562],{"className":563,"style":533},[139],[28,565,567],{"className":566},[144,145,146,147],[28,568,570,573,576,579,582,585,588],{"className":569},[109,147],[28,571,397],{"className":572,"style":543},[109,147],[28,574,253],{"className":575,"style":280},[109,113,147],[28,577,69],{"className":578},[179,147],[28,580,57],{"className":581,"style":154},[109,113,147],[28,583,62],{"className":584},[158,147],[28,586,65],{"className":587},[109,113,147],[28,589,75],{"className":590},[186,147],[28,592,166],{"className":593},[165],[28,595,597],{"className":596},[127],[28,598,601],{"className":599,"style":600},[131],"height:0.345em;",[28,602],{},[28,604],{"className":605},[186,513],[28,607],{"className":608,"style":609},[190],"margin-right:2em;",[28,611,65],{"className":612},[109,113],[28,614],{"className":615,"style":191},[190],[28,617,78],{"className":618},[195],[28,620],{"className":621,"style":191},[190],[28,623,625,629,632,635,638],{"className":624},[100],[28,626],{"className":627,"style":628},[104],"height:0.7778em;vertical-align:-0.0833em;",[28,630,65],{"className":631},[109,113],[28,633],{"className":634,"style":215},[190],[28,636,385],{"className":637},[219],[28,639],{"className":640,"style":215},[190],[28,642,644,647,650],{"className":643},[100],[28,645],{"className":646,"style":502},[104],[28,648,388],{"className":649,"style":506},[109,113],[28,651,653,656,736],{"className":652},[109],[28,654],{"className":655},[179,513],[28,657,659],{"className":658},[390],[28,660,662,728],{"className":661},[122,123],[28,663,665,725],{"className":664},[127],[28,666,668,685,693],{"className":667,"style":526},[131],[28,669,670,673],{"style":529},[28,671],{"className":672,"style":533},[139],[28,674,676],{"className":675},[144,145,146,147],[28,677,679,682],{"className":678},[109,147],[28,680,397],{"className":681,"style":543},[109,147],[28,683,65],{"className":684},[109,113,147],[28,686,687,690],{"style":549},[28,688],{"className":689,"style":533},[139],[28,691],{"className":692,"style":557},[556],[28,694,695,698],{"style":560},[28,696],{"className":697,"style":533},[139],[28,699,701],{"className":700},[144,145,146,147],[28,702,704,707,710,713,716,719,722],{"className":703},[109,147],[28,705,397],{"className":706,"style":543},[109,147],[28,708,253],{"className":709,"style":280},[109,113,147],[28,711,69],{"className":712},[179,147],[28,714,57],{"className":715,"style":154},[109,113,147],[28,717,62],{"className":718},[158,147],[28,720,65],{"className":721},[109,113,147],[28,723,75],{"className":724},[186,147],[28,726,166],{"className":727},[165],[28,729,731],{"className":730},[127],[28,732,734],{"className":733,"style":600},[131],[28,735],{},[28,737],{"className":738},[186,513],[740,741,743],"h2",{"id":742},"a-ideia-em-uma-frase","A ideia em uma frase",[11,745,746,747,750],{},"Lembra da tigela de sopa do ",[22,748,749],{"href":236},"post passado","? O gradiente descendente é literalmente isso: você começa em algum ponto qualquer da tigela e dá passos ladeira abaixo, sempre na direção que desce mais rápido, até chegar perto do fundo.",[11,752,753,754,869,870,899,900,904],{},"O \"sentir qual direção desce mais rápido\" é o trabalho da derivada, aquele ",[28,755,757,783],{"className":756},[31],[28,758,760],{"className":759},[35],[37,761,762],{"xmlns":39},[41,763,764,780],{},[44,765,766],{},[390,767,768,774],{},[44,769,770,772],{},[50,771,397],{"mathvariant":396},[50,773,253],{},[44,775,776,778],{},[50,777,397],{"mathvariant":396},[50,779,57],{},[89,781,782],{"encoding":91},"\\frac{\\partial J}{\\partial w}",[28,784,786],{"className":785,"ariaHidden":61},[96],[28,787,789,793],{"className":788},[100],[28,790],{"className":791,"style":792},[104],"height:1.2251em;vertical-align:-0.345em;",[28,794,796,799,866],{"className":795},[109],[28,797],{"className":798},[179,513],[28,800,802],{"className":801},[390],[28,803,805,858],{"className":804},[122,123],[28,806,808,855],{"className":807},[127],[28,809,812,829,837],{"className":810,"style":811},[131],"height:0.8801em;",[28,813,814,817],{"style":529},[28,815],{"className":816,"style":533},[139],[28,818,820],{"className":819},[144,145,146,147],[28,821,823,826],{"className":822},[109,147],[28,824,397],{"className":825,"style":543},[109,147],[28,827,57],{"className":828,"style":154},[109,113,147],[28,830,831,834],{"style":549},[28,832],{"className":833,"style":533},[139],[28,835],{"className":836,"style":557},[556],[28,838,840,843],{"style":839},"top:-3.394em;",[28,841],{"className":842,"style":533},[139],[28,844,846],{"className":845},[144,145,146,147],[28,847,849,852],{"className":848},[109,147],[28,850,397],{"className":851,"style":543},[109,147],[28,853,253],{"className":854,"style":280},[109,113,147],[28,856,166],{"className":857},[165],[28,859,861],{"className":860},[127],[28,862,864],{"className":863,"style":600},[131],[28,865],{},[28,867],{"className":868},[186,513]," na fórmula. Ela é a inclinação da superfície de custo naquele ponto específico. E ",[28,871,873,887],{"className":872},[31],[28,874,876],{"className":875},[35],[37,877,878],{"xmlns":39},[41,879,880,884],{},[44,881,882],{},[50,883,388],{},[89,885,886],{"encoding":91},"\\alpha",[28,888,890],{"className":889,"ariaHidden":61},[96],[28,891,893,896],{"className":892},[100],[28,894],{"className":895,"style":465},[104],[28,897,388],{"className":898,"style":506},[109,113]," (",[358,901,903],{"definition":902},"a letra grega usada pra taxa de aprendizado, o tamanho do passo que o algoritmo dá a cada iteração","alfa",") é o tamanho do passo que você dá cada vez.",[740,906,908],{"id":907},"por-que-subtrair-a-derivada","Por que subtrair a derivada",[11,910,911,912,916,917,920],{},"A derivada aponta pra onde o custo ",[913,914,915],"strong",{},"cresce",". Como você quer o custo menor, você anda pro lado ",[913,918,919],{},"oposto"," ao que ela aponta. Daí o sinal de menos na fórmula.",[922,923,924,1081],"table",{},[925,926,927],"thead",{},[928,929,930,935,939],"tr",{},[931,932,934],"th",{"align":933},"left","Situação",[931,936,938],{"align":937},"center","Sinal da derivada",[931,940,941,942],{"align":933},"O que acontece com ",[28,943,945,977],{"className":944},[31],[28,946,948],{"className":947},[35],[37,949,950],{"xmlns":39},[41,951,952,974],{},[44,953,954,956,958,960],{},[50,955,57],{},[59,957,385],{},[50,959,388],{},[390,961,962,968],{},[44,963,964,966],{},[50,965,397],{"mathvariant":396},[50,967,253],{},[44,969,970,972],{},[50,971,397],{"mathvariant":396},[50,973,57],{},[89,975,976],{"encoding":91},"w - \\alpha \\frac{\\partial J}{\\partial w}",[28,978,980,998],{"className":979,"ariaHidden":61},[96],[28,981,983,986,989,992,995],{"className":982},[100],[28,984],{"className":985,"style":205},[104],[28,987,57],{"className":988,"style":154},[109,113],[28,990],{"className":991,"style":215},[190],[28,993,385],{"className":994},[219],[28,996],{"className":997,"style":215},[190],[28,999,1001,1004,1007],{"className":1000},[100],[28,1002],{"className":1003,"style":792},[104],[28,1005,388],{"className":1006,"style":506},[109,113],[28,1008,1010,1013,1078],{"className":1009},[109],[28,1011],{"className":1012},[179,513],[28,1014,1016],{"className":1015},[390],[28,1017,1019,1070],{"className":1018},[122,123],[28,1020,1022,1067],{"className":1021},[127],[28,1023,1025,1042,1050],{"className":1024,"style":811},[131],[28,1026,1027,1030],{"style":529},[28,1028],{"className":1029,"style":533},[139],[28,1031,1033],{"className":1032},[144,145,146,147],[28,1034,1036,1039],{"className":1035},[109,147],[28,1037,397],{"className":1038,"style":543},[109,147],[28,1040,57],{"className":1041,"style":154},[109,113,147],[28,1043,1044,1047],{"style":549},[28,1045],{"className":1046,"style":533},[139],[28,1048],{"className":1049,"style":557},[556],[28,1051,1052,1055],{"style":839},[28,1053],{"className":1054,"style":533},[139],[28,1056,1058],{"className":1057},[144,145,146,147],[28,1059,1061,1064],{"className":1060},[109,147],[28,1062,397],{"className":1063,"style":543},[109,147],[28,1065,253],{"className":1066,"style":280},[109,113,147],[28,1068,166],{"className":1069},[165],[28,1071,1073],{"className":1072},[127],[28,1074,1076],{"className":1075,"style":600},[131],[28,1077],{},[28,1079],{"className":1080},[186,513],[1082,1083,1084,1152,1219],"tbody",{},[928,1085,1086,1118,1121],{},[1087,1088,1089,1117],"td",{"align":933},[28,1090,1092,1105],{"className":1091},[31],[28,1093,1095],{"className":1094},[35],[37,1096,1097],{"xmlns":39},[41,1098,1099,1103],{},[44,1100,1101],{},[50,1102,57],{},[89,1104,57],{"encoding":91},[28,1106,1108],{"className":1107,"ariaHidden":61},[96],[28,1109,1111,1114],{"className":1110},[100],[28,1112],{"className":1113,"style":465},[104],[28,1115,57],{"className":1116,"style":154},[109,113]," está à direita do mínimo",[1087,1119,1120],{"align":937},"positivo",[1087,1122,1123,1151],{"align":933},[28,1124,1126,1139],{"className":1125},[31],[28,1127,1129],{"className":1128},[35],[37,1130,1131],{"xmlns":39},[41,1132,1133,1137],{},[44,1134,1135],{},[50,1136,57],{},[89,1138,57],{"encoding":91},[28,1140,1142],{"className":1141,"ariaHidden":61},[96],[28,1143,1145,1148],{"className":1144},[100],[28,1146],{"className":1147,"style":465},[104],[28,1149,57],{"className":1150,"style":154},[109,113]," diminui, anda pra esquerda",[928,1153,1154,1185,1188],{},[1087,1155,1156,1184],{"align":933},[28,1157,1159,1172],{"className":1158},[31],[28,1160,1162],{"className":1161},[35],[37,1163,1164],{"xmlns":39},[41,1165,1166,1170],{},[44,1167,1168],{},[50,1169,57],{},[89,1171,57],{"encoding":91},[28,1173,1175],{"className":1174,"ariaHidden":61},[96],[28,1176,1178,1181],{"className":1177},[100],[28,1179],{"className":1180,"style":465},[104],[28,1182,57],{"className":1183,"style":154},[109,113]," está à esquerda do mínimo",[1087,1186,1187],{"align":937},"negativo",[1087,1189,1190,1218],{"align":933},[28,1191,1193,1206],{"className":1192},[31],[28,1194,1196],{"className":1195},[35],[37,1197,1198],{"xmlns":39},[41,1199,1200,1204],{},[44,1201,1202],{},[50,1203,57],{},[89,1205,57],{"encoding":91},[28,1207,1209],{"className":1208,"ariaHidden":61},[96],[28,1210,1212,1215],{"className":1211},[100],[28,1213],{"className":1214,"style":465},[104],[28,1216,57],{"className":1217,"style":154},[109,113]," aumenta, anda pra direita",[928,1220,1221,1252,1255],{},[1087,1222,1223,1251],{"align":933},[28,1224,1226,1239],{"className":1225},[31],[28,1227,1229],{"className":1228},[35],[37,1230,1231],{"xmlns":39},[41,1232,1233,1237],{},[44,1234,1235],{},[50,1236,57],{},[89,1238,57],{"encoding":91},[28,1240,1242],{"className":1241,"ariaHidden":61},[96],[28,1243,1245,1248],{"className":1244},[100],[28,1246],{"className":1247,"style":465},[104],[28,1249,57],{"className":1250,"style":154},[109,113]," está exatamente no mínimo",[1087,1253,1254],{"align":937},"zero",[1087,1256,1257,1285],{"align":933},[28,1258,1260,1273],{"className":1259},[31],[28,1261,1263],{"className":1262},[35],[37,1264,1265],{"xmlns":39},[41,1266,1267,1271],{},[44,1268,1269],{},[50,1270,57],{},[89,1272,57],{"encoding":91},[28,1274,1276],{"className":1275,"ariaHidden":61},[96],[28,1277,1279,1282],{"className":1278},[100],[28,1280],{"className":1281,"style":465},[104],[28,1283,57],{"className":1284,"style":154},[109,113]," não muda mais, o algoritmo parou sozinho",[11,1287,1288,1289,1317],{},"Repara na última linha: o algoritmo não precisa de um \"se chegou no mínimo, para\". Ele simplesmente para de se mexer sozinho, porque a derivada zera. E como a derivada vai encolhendo conforme você se aproxima do fundo, os passos também vão ficando menores por conta própria, mesmo com ",[28,1290,1292,1305],{"className":1291},[31],[28,1293,1295],{"className":1294},[35],[37,1296,1297],{"xmlns":39},[41,1298,1299,1303],{},[44,1300,1301],{},[50,1302,388],{},[89,1304,886],{"encoding":91},[28,1306,1308],{"className":1307,"ariaHidden":61},[96],[28,1309,1311,1314],{"className":1310},[100],[28,1312],{"className":1313,"style":465},[104],[28,1315,388],{"className":1316,"style":506},[109,113]," fixo. Isso é de graça, não é algo que você programa à parte.",[740,1319,1321],{"id":1320},"as-duas-derivadas-parciais","As duas derivadas parciais",[11,1323,1324],{},"Pra regressão linear com uma variável, a matemática dá nessas duas fórmulas (eu não precisei decorar a dedução, só entender o padrão):",[11,1326,1327],{},[28,1328,1330,1463],{"className":1329},[31],[28,1331,1333],{"className":1332},[35],[37,1334,1335],{"xmlns":39},[41,1336,1337,1460],{},[44,1338,1339,1363,1365,1374,1398,1448],{},[390,1340,1341,1357],{},[44,1342,1343,1345,1347,1349,1351,1353,1355],{},[50,1344,397],{"mathvariant":396},[50,1346,253],{},[59,1348,69],{"stretchy":68},[50,1350,57],{},[59,1352,62],{"separator":61},[50,1354,65],{},[59,1356,75],{"stretchy":68},[44,1358,1359,1361],{},[50,1360,397],{"mathvariant":396},[50,1362,57],{},[59,1364,78],{},[390,1366,1367,1371],{},[1368,1369,1370],"mn",{},"1",[50,1372,1373],{},"m",[1375,1376,1377,1380,1390],"msubsup",{},[59,1378,1379],{},"∑",[44,1381,1382,1385,1387],{},[50,1383,1384],{},"i",[59,1386,78],{},[1368,1388,1389],{},"0",[44,1391,1392,1394,1396],{},[50,1393,1373],{},[59,1395,385],{},[1368,1397,1370],{},[44,1399,1400,1402,1414,1416,1429,1431,1433,1446],{},[59,1401,69],{"fence":61},[47,1403,1404,1406],{},[50,1405,52],{},[44,1407,1408,1410,1412],{},[50,1409,57],{},[59,1411,62],{"separator":61},[50,1413,65],{},[59,1415,69],{"stretchy":68},[1417,1418,1419,1421],"msup",{},[50,1420,72],{},[44,1422,1423,1425,1427],{},[59,1424,69],{"stretchy":68},[50,1426,1384],{},[59,1428,75],{"stretchy":68},[59,1430,75],{"stretchy":68},[59,1432,385],{},[1417,1434,1435,1438],{},[50,1436,1437],{},"y",[44,1439,1440,1442,1444],{},[59,1441,69],{"stretchy":68},[50,1443,1384],{},[59,1445,75],{"stretchy":68},[59,1447,75],{"fence":61},[1417,1449,1450,1452],{},[50,1451,72],{},[44,1453,1454,1456,1458],{},[59,1455,69],{"stretchy":68},[50,1457,1384],{},[59,1459,75],{"stretchy":68},[89,1461,1462],{"encoding":91},"\\frac{\\partial J(w,b)}{\\partial w} = \\frac{1}{m} \\sum_{i=0}^{m-1} \\left(f_{w,b}(x^{(i)}) - y^{(i)}\\right) x^{(i)}",[28,1464,1466,1570],{"className":1465,"ariaHidden":61},[96],[28,1467,1469,1472,1561,1564,1567],{"className":1468},[100],[28,1470],{"className":1471,"style":502},[104],[28,1473,1475,1478,1558],{"className":1474},[109],[28,1476],{"className":1477},[179,513],[28,1479,1481],{"className":1480},[390],[28,1482,1484,1550],{"className":1483},[122,123],[28,1485,1487,1547],{"className":1486},[127],[28,1488,1490,1507,1515],{"className":1489,"style":526},[131],[28,1491,1492,1495],{"style":529},[28,1493],{"className":1494,"style":533},[139],[28,1496,1498],{"className":1497},[144,145,146,147],[28,1499,1501,1504],{"className":1500},[109,147],[28,1502,397],{"className":1503,"style":543},[109,147],[28,1505,57],{"className":1506,"style":154},[109,113,147],[28,1508,1509,1512],{"style":549},[28,1510],{"className":1511,"style":533},[139],[28,1513],{"className":1514,"style":557},[556],[28,1516,1517,1520],{"style":560},[28,1518],{"className":1519,"style":533},[139],[28,1521,1523],{"className":1522},[144,145,146,147],[28,1524,1526,1529,1532,1535,1538,1541,1544],{"className":1525},[109,147],[28,1527,397],{"className":1528,"style":543},[109,147],[28,1530,253],{"className":1531,"style":280},[109,113,147],[28,1533,69],{"className":1534},[179,147],[28,1536,57],{"className":1537,"style":154},[109,113,147],[28,1539,62],{"className":1540},[158,147],[28,1542,65],{"className":1543},[109,113,147],[28,1545,75],{"className":1546},[186,147],[28,1548,166],{"className":1549},[165],[28,1551,1553],{"className":1552},[127],[28,1554,1556],{"className":1555,"style":600},[131],[28,1557],{},[28,1559],{"className":1560},[186,513],[28,1562],{"className":1563,"style":191},[190],[28,1565,78],{"className":1566},[195],[28,1568],{"className":1569,"style":191},[190],[28,1571,1573,1577,1646,1649,1726,1729,1892,1895],{"className":1572},[100],[28,1574],{"className":1575,"style":1576},[104],"height:1.304em;vertical-align:-0.35em;",[28,1578,1580,1583,1643],{"className":1579},[109],[28,1581],{"className":1582},[179,513],[28,1584,1586],{"className":1585},[390],[28,1587,1589,1635],{"className":1588},[122,123],[28,1590,1592,1632],{"className":1591},[127],[28,1593,1596,1610,1618],{"className":1594,"style":1595},[131],"height:0.8451em;",[28,1597,1598,1601],{"style":529},[28,1599],{"className":1600,"style":533},[139],[28,1602,1604],{"className":1603},[144,145,146,147],[28,1605,1607],{"className":1606},[109,147],[28,1608,1373],{"className":1609},[109,113,147],[28,1611,1612,1615],{"style":549},[28,1613],{"className":1614,"style":533},[139],[28,1616],{"className":1617,"style":557},[556],[28,1619,1620,1623],{"style":839},[28,1621],{"className":1622,"style":533},[139],[28,1624,1626],{"className":1625},[144,145,146,147],[28,1627,1629],{"className":1628},[109,147],[28,1630,1370],{"className":1631},[109,147],[28,1633,166],{"className":1634},[165],[28,1636,1638],{"className":1637},[127],[28,1639,1641],{"className":1640,"style":600},[131],[28,1642],{},[28,1644],{"className":1645},[186,513],[28,1647],{"className":1648,"style":293},[190],[28,1650,1653,1659],{"className":1651},[1652],"mop",[28,1654,1379],{"className":1655,"style":1658},[1652,1656,1657],"op-symbol","small-op","position:relative;top:0em;",[28,1660,1662],{"className":1661},[118],[28,1663,1665,1717],{"className":1664},[122,123],[28,1666,1668,1714],{"className":1667},[127],[28,1669,1672,1693],{"className":1670,"style":1671},[131],"height:0.954em;",[28,1673,1675,1678],{"style":1674},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[28,1676],{"className":1677,"style":140},[139],[28,1679,1681],{"className":1680},[144,145,146,147],[28,1682,1684,1687,1690],{"className":1683},[109,147],[28,1685,1384],{"className":1686},[109,113,147],[28,1688,78],{"className":1689},[195,147],[28,1691,1389],{"className":1692},[109,147],[28,1694,1696,1699],{"style":1695},"top:-3.2029em;margin-right:0.05em;",[28,1697],{"className":1698,"style":140},[139],[28,1700,1702],{"className":1701},[144,145,146,147],[28,1703,1705,1708,1711],{"className":1704},[109,147],[28,1706,1373],{"className":1707},[109,113,147],[28,1709,385],{"className":1710},[219,147],[28,1712,1370],{"className":1713},[109,147],[28,1715,166],{"className":1716},[165],[28,1718,1720],{"className":1719},[127],[28,1721,1724],{"className":1722,"style":1723},[131],"height:0.2997em;",[28,1725],{},[28,1727],{"className":1728,"style":293},[190],[28,1730,1733,1743,1792,1795,1835,1838,1841,1844,1847,1886],{"className":1731},[1732],"minner",[28,1734,1738],{"className":1735,"style":1737},[179,1736],"delimcenter","top:0em;",[28,1739,69],{"className":1740},[1741,1742],"delimsizing","size1",[28,1744,1746,1749],{"className":1745},[109],[28,1747,52],{"className":1748,"style":114},[109,113],[28,1750,1752],{"className":1751},[118],[28,1753,1755,1784],{"className":1754},[122,123],[28,1756,1758,1781],{"className":1757},[127],[28,1759,1761],{"className":1760,"style":132},[131],[28,1762,1763,1766],{"style":135},[28,1764],{"className":1765,"style":140},[139],[28,1767,1769],{"className":1768},[144,145,146,147],[28,1770,1772,1775,1778],{"className":1771},[109,147],[28,1773,57],{"className":1774,"style":154},[109,113,147],[28,1776,62],{"className":1777},[158,147],[28,1779,65],{"className":1780},[109,113,147],[28,1782,166],{"className":1783},[165],[28,1785,1787],{"className":1786},[127],[28,1788,1790],{"className":1789,"style":173},[131],[28,1791],{},[28,1793,69],{"className":1794},[179],[28,1796,1798,1801],{"className":1797},[109],[28,1799,72],{"className":1800},[109,113],[28,1802,1804],{"className":1803},[118],[28,1805,1807],{"className":1806},[122],[28,1808,1810],{"className":1809},[127],[28,1811,1814],{"className":1812,"style":1813},[131],"height:0.888em;",[28,1815,1817,1820],{"style":1816},"top:-3.063em;margin-right:0.05em;",[28,1818],{"className":1819,"style":140},[139],[28,1821,1823],{"className":1822},[144,145,146,147],[28,1824,1826,1829,1832],{"className":1825},[109,147],[28,1827,69],{"className":1828},[179,147],[28,1830,1384],{"className":1831},[109,113,147],[28,1833,75],{"className":1834},[186,147],[28,1836,75],{"className":1837},[186],[28,1839],{"className":1840,"style":215},[190],[28,1842,385],{"className":1843},[219],[28,1845],{"className":1846,"style":215},[190],[28,1848,1850,1854],{"className":1849},[109],[28,1851,1437],{"className":1852,"style":1853},[109,113],"margin-right:0.0359em;",[28,1855,1857],{"className":1856},[118],[28,1858,1860],{"className":1859},[122],[28,1861,1863],{"className":1862},[127],[28,1864,1866],{"className":1865,"style":1813},[131],[28,1867,1868,1871],{"style":1816},[28,1869],{"className":1870,"style":140},[139],[28,1872,1874],{"className":1873},[144,145,146,147],[28,1875,1877,1880,1883],{"className":1876},[109,147],[28,1878,69],{"className":1879},[179,147],[28,1881,1384],{"className":1882},[109,113,147],[28,1884,75],{"className":1885},[186,147],[28,1887,1889],{"className":1888,"style":1737},[186,1736],[28,1890,75],{"className":1891},[1741,1742],[28,1893],{"className":1894,"style":293},[190],[28,1896,1898,1901],{"className":1897},[109],[28,1899,72],{"className":1900},[109,113],[28,1902,1904],{"className":1903},[118],[28,1905,1907],{"className":1906},[122],[28,1908,1910],{"className":1909},[127],[28,1911,1913],{"className":1912,"style":1813},[131],[28,1914,1915,1918],{"style":1816},[28,1916],{"className":1917,"style":140},[139],[28,1919,1921],{"className":1920},[144,145,146,147],[28,1922,1924,1927,1930],{"className":1923},[109,147],[28,1925,69],{"className":1926},[179,147],[28,1928,1384],{"className":1929},[109,113,147],[28,1931,75],{"className":1932},[186,147],[11,1934,1935],{},[28,1936,1938,2050],{"className":1937},[31],[28,1939,1941],{"className":1940},[35],[37,1942,1943],{"xmlns":39},[41,1944,1945,2047],{},[44,1946,1947,1971,1973,1979,1999],{},[390,1948,1949,1965],{},[44,1950,1951,1953,1955,1957,1959,1961,1963],{},[50,1952,397],{"mathvariant":396},[50,1954,253],{},[59,1956,69],{"stretchy":68},[50,1958,57],{},[59,1960,62],{"separator":61},[50,1962,65],{},[59,1964,75],{"stretchy":68},[44,1966,1967,1969],{},[50,1968,397],{"mathvariant":396},[50,1970,65],{},[59,1972,78],{},[390,1974,1975,1977],{},[1368,1976,1370],{},[50,1978,1373],{},[1375,1980,1981,1983,1991],{},[59,1982,1379],{},[44,1984,1985,1987,1989],{},[50,1986,1384],{},[59,1988,78],{},[1368,1990,1389],{},[44,1992,1993,1995,1997],{},[50,1994,1373],{},[59,1996,385],{},[1368,1998,1370],{},[44,2000,2001,2003,2015,2017,2029,2031,2033,2045],{},[59,2002,69],{"fence":61},[47,2004,2005,2007],{},[50,2006,52],{},[44,2008,2009,2011,2013],{},[50,2010,57],{},[59,2012,62],{"separator":61},[50,2014,65],{},[59,2016,69],{"stretchy":68},[1417,2018,2019,2021],{},[50,2020,72],{},[44,2022,2023,2025,2027],{},[59,2024,69],{"stretchy":68},[50,2026,1384],{},[59,2028,75],{"stretchy":68},[59,2030,75],{"stretchy":68},[59,2032,385],{},[1417,2034,2035,2037],{},[50,2036,1437],{},[44,2038,2039,2041,2043],{},[59,2040,69],{"stretchy":68},[50,2042,1384],{},[59,2044,75],{"stretchy":68},[59,2046,75],{"fence":61},[89,2048,2049],{"encoding":91},"\\frac{\\partial J(w,b)}{\\partial b} = \\frac{1}{m} \\sum_{i=0}^{m-1} \\left(f_{w,b}(x^{(i)}) - y^{(i)}\\right)",[28,2051,2053,2157],{"className":2052,"ariaHidden":61},[96],[28,2054,2056,2059,2148,2151,2154],{"className":2055},[100],[28,2057],{"className":2058,"style":502},[104],[28,2060,2062,2065,2145],{"className":2061},[109],[28,2063],{"className":2064},[179,513],[28,2066,2068],{"className":2067},[390],[28,2069,2071,2137],{"className":2070},[122,123],[28,2072,2074,2134],{"className":2073},[127],[28,2075,2077,2094,2102],{"className":2076,"style":526},[131],[28,2078,2079,2082],{"style":529},[28,2080],{"className":2081,"style":533},[139],[28,2083,2085],{"className":2084},[144,145,146,147],[28,2086,2088,2091],{"className":2087},[109,147],[28,2089,397],{"className":2090,"style":543},[109,147],[28,2092,65],{"className":2093},[109,113,147],[28,2095,2096,2099],{"style":549},[28,2097],{"className":2098,"style":533},[139],[28,2100],{"className":2101,"style":557},[556],[28,2103,2104,2107],{"style":560},[28,2105],{"className":2106,"style":533},[139],[28,2108,2110],{"className":2109},[144,145,146,147],[28,2111,2113,2116,2119,2122,2125,2128,2131],{"className":2112},[109,147],[28,2114,397],{"className":2115,"style":543},[109,147],[28,2117,253],{"className":2118,"style":280},[109,113,147],[28,2120,69],{"className":2121},[179,147],[28,2123,57],{"className":2124,"style":154},[109,113,147],[28,2126,62],{"className":2127},[158,147],[28,2129,65],{"className":2130},[109,113,147],[28,2132,75],{"className":2133},[186,147],[28,2135,166],{"className":2136},[165],[28,2138,2140],{"className":2139},[127],[28,2141,2143],{"className":2142,"style":600},[131],[28,2144],{},[28,2146],{"className":2147},[186,513],[28,2149],{"className":2150,"style":191},[190],[28,2152,78],{"className":2153},[195],[28,2155],{"className":2156,"style":191},[190],[28,2158,2160,2163,2231,2234,2303,2306],{"className":2159},[100],[28,2161],{"className":2162,"style":1576},[104],[28,2164,2166,2169,2228],{"className":2165},[109],[28,2167],{"className":2168},[179,513],[28,2170,2172],{"className":2171},[390],[28,2173,2175,2220],{"className":2174},[122,123],[28,2176,2178,2217],{"className":2177},[127],[28,2179,2181,2195,2203],{"className":2180,"style":1595},[131],[28,2182,2183,2186],{"style":529},[28,2184],{"className":2185,"style":533},[139],[28,2187,2189],{"className":2188},[144,145,146,147],[28,2190,2192],{"className":2191},[109,147],[28,2193,1373],{"className":2194},[109,113,147],[28,2196,2197,2200],{"style":549},[28,2198],{"className":2199,"style":533},[139],[28,2201],{"className":2202,"style":557},[556],[28,2204,2205,2208],{"style":839},[28,2206],{"className":2207,"style":533},[139],[28,2209,2211],{"className":2210},[144,145,146,147],[28,2212,2214],{"className":2213},[109,147],[28,2215,1370],{"className":2216},[109,147],[28,2218,166],{"className":2219},[165],[28,2221,2223],{"className":2222},[127],[28,2224,2226],{"className":2225,"style":600},[131],[28,2227],{},[28,2229],{"className":2230},[186,513],[28,2232],{"className":2233,"style":293},[190],[28,2235,2237,2240],{"className":2236},[1652],[28,2238,1379],{"className":2239,"style":1658},[1652,1656,1657],[28,2241,2243],{"className":2242},[118],[28,2244,2246,2295],{"className":2245},[122,123],[28,2247,2249,2292],{"className":2248},[127],[28,2250,2252,2272],{"className":2251,"style":1671},[131],[28,2253,2254,2257],{"style":1674},[28,2255],{"className":2256,"style":140},[139],[28,2258,2260],{"className":2259},[144,145,146,147],[28,2261,2263,2266,2269],{"className":2262},[109,147],[28,2264,1384],{"className":2265},[109,113,147],[28,2267,78],{"className":2268},[195,147],[28,2270,1389],{"className":2271},[109,147],[28,2273,2274,2277],{"style":1695},[28,2275],{"className":2276,"style":140},[139],[28,2278,2280],{"className":2279},[144,145,146,147],[28,2281,2283,2286,2289],{"className":2282},[109,147],[28,2284,1373],{"className":2285},[109,113,147],[28,2287,385],{"className":2288},[219,147],[28,2290,1370],{"className":2291},[109,147],[28,2293,166],{"className":2294},[165],[28,2296,2298],{"className":2297},[127],[28,2299,2301],{"className":2300,"style":1723},[131],[28,2302],{},[28,2304],{"className":2305,"style":293},[190],[28,2307,2309,2315,2364,2367,2405,2408,2411,2414,2417,2455],{"className":2308},[1732],[28,2310,2312],{"className":2311,"style":1737},[179,1736],[28,2313,69],{"className":2314},[1741,1742],[28,2316,2318,2321],{"className":2317},[109],[28,2319,52],{"className":2320,"style":114},[109,113],[28,2322,2324],{"className":2323},[118],[28,2325,2327,2356],{"className":2326},[122,123],[28,2328,2330,2353],{"className":2329},[127],[28,2331,2333],{"className":2332,"style":132},[131],[28,2334,2335,2338],{"style":135},[28,2336],{"className":2337,"style":140},[139],[28,2339,2341],{"className":2340},[144,145,146,147],[28,2342,2344,2347,2350],{"className":2343},[109,147],[28,2345,57],{"className":2346,"style":154},[109,113,147],[28,2348,62],{"className":2349},[158,147],[28,2351,65],{"className":2352},[109,113,147],[28,2354,166],{"className":2355},[165],[28,2357,2359],{"className":2358},[127],[28,2360,2362],{"className":2361,"style":173},[131],[28,2363],{},[28,2365,69],{"className":2366},[179],[28,2368,2370,2373],{"className":2369},[109],[28,2371,72],{"className":2372},[109,113],[28,2374,2376],{"className":2375},[118],[28,2377,2379],{"className":2378},[122],[28,2380,2382],{"className":2381},[127],[28,2383,2385],{"className":2384,"style":1813},[131],[28,2386,2387,2390],{"style":1816},[28,2388],{"className":2389,"style":140},[139],[28,2391,2393],{"className":2392},[144,145,146,147],[28,2394,2396,2399,2402],{"className":2395},[109,147],[28,2397,69],{"className":2398},[179,147],[28,2400,1384],{"className":2401},[109,113,147],[28,2403,75],{"className":2404},[186,147],[28,2406,75],{"className":2407},[186],[28,2409],{"className":2410,"style":215},[190],[28,2412,385],{"className":2413},[219],[28,2415],{"className":2416,"style":215},[190],[28,2418,2420,2423],{"className":2419},[109],[28,2421,1437],{"className":2422,"style":1853},[109,113],[28,2424,2426],{"className":2425},[118],[28,2427,2429],{"className":2428},[122],[28,2430,2432],{"className":2431},[127],[28,2433,2435],{"className":2434,"style":1813},[131],[28,2436,2437,2440],{"style":1816},[28,2438],{"className":2439,"style":140},[139],[28,2441,2443],{"className":2442},[144,145,146,147],[28,2444,2446,2449,2452],{"className":2445},[109,147],[28,2447,69],{"className":2448},[179,147],[28,2450,1384],{"className":2451},[109,113,147],[28,2453,75],{"className":2454},[186,147],[28,2456,2458],{"className":2457,"style":1737},[186,1736],[28,2459,75],{"className":2460},[1741,1742],[11,2462,2463,2464,2492,2493,2567,2568,2596,2597,2625,2626,2654,2655,2683],{},"Repara que as duas são quase gêmeas: a de ",[28,2465,2467,2480],{"className":2466},[31],[28,2468,2470],{"className":2469},[35],[37,2471,2472],{"xmlns":39},[41,2473,2474,2478],{},[44,2475,2476],{},[50,2477,57],{},[89,2479,57],{"encoding":91},[28,2481,2483],{"className":2482,"ariaHidden":61},[96],[28,2484,2486,2489],{"className":2485},[100],[28,2487],{"className":2488,"style":465},[104],[28,2490,57],{"className":2491,"style":154},[109,113]," tem um ",[28,2494,2496,2520],{"className":2495},[31],[28,2497,2499],{"className":2498},[35],[37,2500,2501],{"xmlns":39},[41,2502,2503,2517],{},[44,2504,2505],{},[1417,2506,2507,2509],{},[50,2508,72],{},[44,2510,2511,2513,2515],{},[59,2512,69],{"stretchy":68},[50,2514,1384],{},[59,2516,75],{"stretchy":68},[89,2518,2519],{"encoding":91},"x^{(i)}",[28,2521,2523],{"className":2522,"ariaHidden":61},[96],[28,2524,2526,2529],{"className":2525},[100],[28,2527],{"className":2528,"style":1813},[104],[28,2530,2532,2535],{"className":2531},[109],[28,2533,72],{"className":2534},[109,113],[28,2536,2538],{"className":2537},[118],[28,2539,2541],{"className":2540},[122],[28,2542,2544],{"className":2543},[127],[28,2545,2547],{"className":2546,"style":1813},[131],[28,2548,2549,2552],{"style":1816},[28,2550],{"className":2551,"style":140},[139],[28,2553,2555],{"className":2554},[144,145,146,147],[28,2556,2558,2561,2564],{"className":2557},[109,147],[28,2559,69],{"className":2560},[179,147],[28,2562,1384],{"className":2563},[109,113,147],[28,2565,75],{"className":2566},[186,147]," multiplicando o erro, a de ",[28,2569,2571,2584],{"className":2570},[31],[28,2572,2574],{"className":2573},[35],[37,2575,2576],{"xmlns":39},[41,2577,2578,2582],{},[44,2579,2580],{},[50,2581,65],{},[89,2583,65],{"encoding":91},[28,2585,2587],{"className":2586,"ariaHidden":61},[96],[28,2588,2590,2593],{"className":2589},[100],[28,2591],{"className":2592,"style":229},[104],[28,2594,65],{"className":2595},[109,113]," não. Faz sentido pensando geometricamente: mudar ",[28,2598,2600,2613],{"className":2599},[31],[28,2601,2603],{"className":2602},[35],[37,2604,2605],{"xmlns":39},[41,2606,2607,2611],{},[44,2608,2609],{},[50,2610,57],{},[89,2612,57],{"encoding":91},[28,2614,2616],{"className":2615,"ariaHidden":61},[96],[28,2617,2619,2622],{"className":2618},[100],[28,2620],{"className":2621,"style":465},[104],[28,2623,57],{"className":2624,"style":154},[109,113]," afeta mais forte os exemplos com ",[28,2627,2629,2642],{"className":2628},[31],[28,2630,2632],{"className":2631},[35],[37,2633,2634],{"xmlns":39},[41,2635,2636,2640],{},[44,2637,2638],{},[50,2639,72],{},[89,2641,72],{"encoding":91},[28,2643,2645],{"className":2644,"ariaHidden":61},[96],[28,2646,2648,2651],{"className":2647},[100],[28,2649],{"className":2650,"style":465},[104],[28,2652,72],{"className":2653},[109,113]," grande (a inclinação pesa mais longe da origem), enquanto ",[28,2656,2658,2671],{"className":2657},[31],[28,2659,2661],{"className":2660},[35],[37,2662,2663],{"xmlns":39},[41,2664,2665,2669],{},[44,2666,2667],{},[50,2668,65],{},[89,2670,65],{"encoding":91},[28,2672,2674],{"className":2673,"ariaHidden":61},[96],[28,2675,2677,2680],{"className":2676},[100],[28,2678],{"className":2679,"style":229},[104],[28,2681,65],{"className":2682},[109,113]," desloca a reta inteira igualzinho pra todo mundo.",[11,2685,2686,2687,2723,2724,2726],{},"E aquele \"2\" que a gente colocou em ",[28,2688,2690,2707],{"className":2689},[31],[28,2691,2693],{"className":2692},[35],[37,2694,2695],{"xmlns":39},[41,2696,2697,2704],{},[44,2698,2699,2702],{},[1368,2700,2701],{},"2",[50,2703,1373],{},[89,2705,2706],{"encoding":91},"2m",[28,2708,2710],{"className":2709,"ariaHidden":61},[96],[28,2711,2713,2717,2720],{"className":2712},[100],[28,2714],{"className":2715,"style":2716},[104],"height:0.6444em;",[28,2718,2701],{"className":2719},[109],[28,2721,1373],{"className":2722},[109,113]," no ",[22,2725,749],{"href":236},", lembra que eu disse que era só pra simplificar conta? É aqui que ele paga a dívida: ao derivar o termo ao quadrado, sobra um fator 2 que cancela exatamente com o 2 do denominador. Sem aquele 2 lá atrás, essas fórmulas aqui teriam um 2 sobrando.",[11,2728,2729,2732,2733,2761,2762,2790,2791,2819,2820,2848],{},[913,2730,2731],{},"Atualização simultânea importa."," Você calcula as duas derivadas primeiro, usando os valores atuais de ",[28,2734,2736,2749],{"className":2735},[31],[28,2737,2739],{"className":2738},[35],[37,2740,2741],{"xmlns":39},[41,2742,2743,2747],{},[44,2744,2745],{},[50,2746,57],{},[89,2748,57],{"encoding":91},[28,2750,2752],{"className":2751,"ariaHidden":61},[96],[28,2753,2755,2758],{"className":2754},[100],[28,2756],{"className":2757,"style":465},[104],[28,2759,57],{"className":2760,"style":154},[109,113]," e ",[28,2763,2765,2778],{"className":2764},[31],[28,2766,2768],{"className":2767},[35],[37,2769,2770],{"xmlns":39},[41,2771,2772,2776],{},[44,2773,2774],{},[50,2775,65],{},[89,2777,65],{"encoding":91},[28,2779,2781],{"className":2780,"ariaHidden":61},[96],[28,2782,2784,2787],{"className":2783},[100],[28,2785],{"className":2786,"style":229},[104],[28,2788,65],{"className":2789},[109,113],", e só depois troca os dois parâmetros ao mesmo tempo. Usar o ",[28,2792,2794,2807],{"className":2793},[31],[28,2795,2797],{"className":2796},[35],[37,2798,2799],{"xmlns":39},[41,2800,2801,2805],{},[44,2802,2803],{},[50,2804,57],{},[89,2806,57],{"encoding":91},[28,2808,2810],{"className":2809,"ariaHidden":61},[96],[28,2811,2813,2816],{"className":2812},[100],[28,2814],{"className":2815,"style":465},[104],[28,2817,57],{"className":2818,"style":154},[109,113]," novo pra calcular a derivada de ",[28,2821,2823,2836],{"className":2822},[31],[28,2824,2826],{"className":2825},[35],[37,2827,2828],{"xmlns":39},[41,2829,2830,2834],{},[44,2831,2832],{},[50,2833,65],{},[89,2835,65],{"encoding":91},[28,2837,2839],{"className":2838,"ariaHidden":61},[96],[28,2840,2842,2845],{"className":2841},[100],[28,2843],{"className":2844,"style":229},[104],[28,2846,65],{"className":2847},[109,113]," é um erro clássico que muda o comportamento do algoritmo.",[740,2850,2852],{"id":2851},"colocando-isso-em-código","Colocando isso em código",[2854,2855,2860],"pre",{"className":2856,"code":2857,"language":2858,"meta":2859,"style":2859},"language-python shiki shiki-themes github-light github-dark","def compute_gradient(x, y, w, b):\n    \"\"\"\n    Calcula o gradiente da função de custo para regressão linear.\n\n    Args:\n      x (ndarray (m,)) : dados de entrada, m exemplos\n      y (ndarray (m,)) : valores-alvo\n      w, b (scalar)    : parâmetros do modelo\n\n    Returns:\n      dj_dw (scalar): derivada parcial do custo em relação a w\n      dj_db (scalar): derivada parcial do custo em relação a b\n    \"\"\"\n    m = x.shape[0]\n\n    dj_dw = 0\n    dj_db = 0\n\n    for i in range(m):\n        f_wb = w * x[i] + b\n        dj_dw_i = (f_wb - y[i]) * x[i]   # contribuição do exemplo i pra dj_dw\n        dj_db_i = f_wb - y[i]            # contribuição do exemplo i pra dj_db\n        dj_db += dj_db_i\n        dj_dw += dj_dw_i\n\n    dj_dw = dj_dw \u002F m\n    dj_db = dj_db \u002F m\n\n    return dj_dw, dj_db\n","python","",[2861,2862,2863,2870,2876,2882,2889,2895,2901,2907,2913,2918,2924,2930,2936,2941,2947,2952,2958,2964,2969,2975,2981,2987,2993,2999,3005,3010,3016,3022,3027],"code",{"__ignoreMap":2859},[28,2864,2867],{"class":2865,"line":2866},"line",1,[28,2868,2869],{},"def compute_gradient(x, y, w, b):\n",[28,2871,2873],{"class":2865,"line":2872},2,[28,2874,2875],{},"    \"\"\"\n",[28,2877,2879],{"class":2865,"line":2878},3,[28,2880,2881],{},"    Calcula o gradiente da função de custo para regressão linear.\n",[28,2883,2885],{"class":2865,"line":2884},4,[28,2886,2888],{"emptyLinePlaceholder":2887},true,"\n",[28,2890,2892],{"class":2865,"line":2891},5,[28,2893,2894],{},"    Args:\n",[28,2896,2898],{"class":2865,"line":2897},6,[28,2899,2900],{},"      x (ndarray (m,)) : dados de entrada, m exemplos\n",[28,2902,2904],{"class":2865,"line":2903},7,[28,2905,2906],{},"      y (ndarray (m,)) : valores-alvo\n",[28,2908,2910],{"class":2865,"line":2909},8,[28,2911,2912],{},"      w, b (scalar)    : parâmetros do modelo\n",[28,2914,2916],{"class":2865,"line":2915},9,[28,2917,2888],{"emptyLinePlaceholder":2887},[28,2919,2921],{"class":2865,"line":2920},10,[28,2922,2923],{},"    Returns:\n",[28,2925,2927],{"class":2865,"line":2926},11,[28,2928,2929],{},"      dj_dw (scalar): derivada parcial do custo em relação a w\n",[28,2931,2933],{"class":2865,"line":2932},12,[28,2934,2935],{},"      dj_db (scalar): derivada parcial do custo em relação a b\n",[28,2937,2939],{"class":2865,"line":2938},13,[28,2940,2875],{},[28,2942,2944],{"class":2865,"line":2943},14,[28,2945,2946],{},"    m = x.shape[0]\n",[28,2948,2950],{"class":2865,"line":2949},15,[28,2951,2888],{"emptyLinePlaceholder":2887},[28,2953,2955],{"class":2865,"line":2954},16,[28,2956,2957],{},"    dj_dw = 0\n",[28,2959,2961],{"class":2865,"line":2960},17,[28,2962,2963],{},"    dj_db = 0\n",[28,2965,2967],{"class":2865,"line":2966},18,[28,2968,2888],{"emptyLinePlaceholder":2887},[28,2970,2972],{"class":2865,"line":2971},19,[28,2973,2974],{},"    for i in range(m):\n",[28,2976,2978],{"class":2865,"line":2977},20,[28,2979,2980],{},"        f_wb = w * x[i] + b\n",[28,2982,2984],{"class":2865,"line":2983},21,[28,2985,2986],{},"        dj_dw_i = (f_wb - y[i]) * x[i]   # contribuição do exemplo i pra dj_dw\n",[28,2988,2990],{"class":2865,"line":2989},22,[28,2991,2992],{},"        dj_db_i = f_wb - y[i]            # contribuição do exemplo i pra dj_db\n",[28,2994,2996],{"class":2865,"line":2995},23,[28,2997,2998],{},"        dj_db += dj_db_i\n",[28,3000,3002],{"class":2865,"line":3001},24,[28,3003,3004],{},"        dj_dw += dj_dw_i\n",[28,3006,3008],{"class":2865,"line":3007},25,[28,3009,2888],{"emptyLinePlaceholder":2887},[28,3011,3013],{"class":2865,"line":3012},26,[28,3014,3015],{},"    dj_dw = dj_dw \u002F m\n",[28,3017,3019],{"class":2865,"line":3018},27,[28,3020,3021],{},"    dj_db = dj_db \u002F m\n",[28,3023,3025],{"class":2865,"line":3024},28,[28,3026,2888],{"emptyLinePlaceholder":2887},[28,3028,3030],{"class":2865,"line":3029},29,[28,3031,3032],{},"    return dj_dw, dj_db\n",[11,3034,3035],{},"E o laço principal, que repete a atualização até acabar as iterações:",[2854,3037,3039],{"className":2856,"code":3038,"language":2858,"meta":2859,"style":2859},"def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function):\n    \"\"\"\n    Executa o gradiente descendente pra ajustar w e b.\n\n    Args:\n      x, y                : dados de treino\n      w_in, b_in (scalar) : valores INICIAIS dos parâmetros\n      alpha (float)       : taxa de aprendizado\n      num_iters (int)     : quantas iterações executar\n      cost_function       : função pra calcular o custo\n      gradient_function   : função pra calcular o gradiente\n\n    Returns:\n      w, b (scalar)    : parâmetros depois do treino\n      J_history (list) : custo a cada iteração\n    \"\"\"\n    J_history = []\n    w = w_in\n    b = b_in\n\n    for i in range(num_iters):\n        dj_dw, dj_db = gradient_function(x, y, w, b)\n\n        b = b - alpha * dj_db   # atualização simultânea: as duas derivadas\n        w = w - alpha * dj_dw   # já foram calculadas com os valores antigos\n\n        J_history.append(cost_function(x, y, w, b))\n\n    return w, b, J_history\n",[2861,3040,3041,3046,3050,3055,3059,3063,3068,3073,3078,3083,3088,3093,3097,3101,3106,3111,3115,3120,3125,3130,3134,3139,3144,3148,3153,3158,3162,3167,3171],{"__ignoreMap":2859},[28,3042,3043],{"class":2865,"line":2866},[28,3044,3045],{},"def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function):\n",[28,3047,3048],{"class":2865,"line":2872},[28,3049,2875],{},[28,3051,3052],{"class":2865,"line":2878},[28,3053,3054],{},"    Executa o gradiente descendente pra ajustar w e b.\n",[28,3056,3057],{"class":2865,"line":2884},[28,3058,2888],{"emptyLinePlaceholder":2887},[28,3060,3061],{"class":2865,"line":2891},[28,3062,2894],{},[28,3064,3065],{"class":2865,"line":2897},[28,3066,3067],{},"      x, y                : dados de treino\n",[28,3069,3070],{"class":2865,"line":2903},[28,3071,3072],{},"      w_in, b_in (scalar) : valores INICIAIS dos parâmetros\n",[28,3074,3075],{"class":2865,"line":2909},[28,3076,3077],{},"      alpha (float)       : taxa de aprendizado\n",[28,3079,3080],{"class":2865,"line":2915},[28,3081,3082],{},"      num_iters (int)     : quantas iterações executar\n",[28,3084,3085],{"class":2865,"line":2920},[28,3086,3087],{},"      cost_function       : função pra calcular o custo\n",[28,3089,3090],{"class":2865,"line":2926},[28,3091,3092],{},"      gradient_function   : função pra calcular o gradiente\n",[28,3094,3095],{"class":2865,"line":2932},[28,3096,2888],{"emptyLinePlaceholder":2887},[28,3098,3099],{"class":2865,"line":2938},[28,3100,2923],{},[28,3102,3103],{"class":2865,"line":2943},[28,3104,3105],{},"      w, b (scalar)    : parâmetros depois do treino\n",[28,3107,3108],{"class":2865,"line":2949},[28,3109,3110],{},"      J_history (list) : custo a cada iteração\n",[28,3112,3113],{"class":2865,"line":2954},[28,3114,2875],{},[28,3116,3117],{"class":2865,"line":2960},[28,3118,3119],{},"    J_history = []\n",[28,3121,3122],{"class":2865,"line":2966},[28,3123,3124],{},"    w = w_in\n",[28,3126,3127],{"class":2865,"line":2971},[28,3128,3129],{},"    b = b_in\n",[28,3131,3132],{"class":2865,"line":2977},[28,3133,2888],{"emptyLinePlaceholder":2887},[28,3135,3136],{"class":2865,"line":2983},[28,3137,3138],{},"    for i in range(num_iters):\n",[28,3140,3141],{"class":2865,"line":2989},[28,3142,3143],{},"        dj_dw, dj_db = gradient_function(x, y, w, b)\n",[28,3145,3146],{"class":2865,"line":2995},[28,3147,2888],{"emptyLinePlaceholder":2887},[28,3149,3150],{"class":2865,"line":3001},[28,3151,3152],{},"        b = b - alpha * dj_db   # atualização simultânea: as duas derivadas\n",[28,3154,3155],{"class":2865,"line":3007},[28,3156,3157],{},"        w = w - alpha * dj_dw   # já foram calculadas com os valores antigos\n",[28,3159,3160],{"class":2865,"line":3012},[28,3161,2888],{"emptyLinePlaceholder":2887},[28,3163,3164],{"class":2865,"line":3018},[28,3165,3166],{},"        J_history.append(cost_function(x, y, w, b))\n",[28,3168,3169],{"class":2865,"line":3024},[28,3170,2888],{"emptyLinePlaceholder":2887},[28,3172,3173],{"class":2865,"line":3029},[28,3174,3175],{},"    return w, b, J_history\n",[740,3177,3179],{"id":3178},"agora-você-mesmo-mas-com-o-algoritmo-fazendo-o-trabalho","Agora você mesmo, mas com o algoritmo fazendo o trabalho",[11,3181,3182],{},"Chega de arrastar slider até achar o valor certo na mão. Aqui embaixo tem o algoritmo de verdade rodando, com controle total: escolhe uma taxa de aprendizado, dá um passo de cada vez ou roda vários de uma vez, e observa o pontinho vermelho descendo a ladeira sozinho no mapa de calor, na superfície 3D, ou na parábola.",[11,3184,3185,3186,238,3237,3288],{},"Começa em ",[28,3187,3189,3207],{"className":3188},[31],[28,3190,3192],{"className":3191},[35],[37,3193,3194],{"xmlns":39},[41,3195,3196,3204],{},[44,3197,3198,3200,3202],{},[50,3199,57],{},[59,3201,78],{},[1368,3203,1389],{},[89,3205,3206],{"encoding":91},"w = 0",[28,3208,3210,3228],{"className":3209,"ariaHidden":61},[96],[28,3211,3213,3216,3219,3222,3225],{"className":3212},[100],[28,3214],{"className":3215,"style":465},[104],[28,3217,57],{"className":3218,"style":154},[109,113],[28,3220],{"className":3221,"style":191},[190],[28,3223,78],{"className":3224},[195],[28,3226],{"className":3227,"style":191},[190],[28,3229,3231,3234],{"className":3230},[100],[28,3232],{"className":3233,"style":2716},[104],[28,3235,1389],{"className":3236},[109],[28,3238,3240,3258],{"className":3239},[31],[28,3241,3243],{"className":3242},[35],[37,3244,3245],{"xmlns":39},[41,3246,3247,3255],{},[44,3248,3249,3251,3253],{},[50,3250,65],{},[59,3252,78],{},[1368,3254,1389],{},[89,3256,3257],{"encoding":91},"b = 0",[28,3259,3261,3279],{"className":3260,"ariaHidden":61},[96],[28,3262,3264,3267,3270,3273,3276],{"className":3263},[100],[28,3265],{"className":3266,"style":229},[104],[28,3268,65],{"className":3269},[109,113],[28,3271],{"className":3272,"style":191},[190],[28,3274,78],{"className":3275},[195],[28,3277],{"className":3278,"style":191},[190],[28,3280,3282,3285],{"className":3281},[100],[28,3283],{"className":3284,"style":2716},[104],[28,3286,1389],{"className":3287},[109]," (bem longe da resposta) e clica em \"Rodar 2000\" algumas vezes com o alpha padrão de 0.01. Repara como o custo despenca rápido no começo e depois desacelera sozinho, sem você mexer em nada.",[3290,3291],"gradient-descent-simulator",{":b-range":3292,":initial-b":1389,":initial-w":1389,":w-range":3293,"b-label":65,"w-label":57,":x-train":3294,":y-train":3295},"[-200, 400]","[-100, 500]","[1, 2]","[300, 500]",[740,3297,3299],{"id":3298},"quando-a-taxa-de-aprendizado-é-grande-demais","Quando a taxa de aprendizado é grande demais",[11,3301,3302,3303,2761,3331,3359],{},"Agora clica no preset de alpha 0.8 (bem maior que o 0.01 que funcionou) e roda alguns passos. Você vai ver os números de ",[28,3304,3306,3319],{"className":3305},[31],[28,3307,3309],{"className":3308},[35],[37,3310,3311],{"xmlns":39},[41,3312,3313,3317],{},[44,3314,3315],{},[50,3316,57],{},[89,3318,57],{"encoding":91},[28,3320,3322],{"className":3321,"ariaHidden":61},[96],[28,3323,3325,3328],{"className":3324},[100],[28,3326],{"className":3327,"style":465},[104],[28,3329,57],{"className":3330,"style":154},[109,113],[28,3332,3334,3347],{"className":3333},[31],[28,3335,3337],{"className":3336},[35],[37,3338,3339],{"xmlns":39},[41,3340,3341,3345],{},[44,3342,3343],{},[50,3344,65],{},[89,3346,65],{"encoding":91},[28,3348,3350],{"className":3349,"ariaHidden":61},[96],[28,3351,3353,3356],{"className":3352},[100],[28,3354],{"className":3355,"style":229},[104],[28,3357,65],{"className":3358},[109,113]," ficarem cada vez mais absurdos, e o custo, em vez de cair, sobe.",[11,3361,3362,3363,3367,3368,3396],{},"Isso é ",[358,3364,3366],{"definition":3365},"quando o gradiente descendente, em vez de se aproximar do mínimo, se afasta cada vez mais dele porque o passo é grande demais","divergência",", e o motivo é simples de visualizar: o passo é proporcional à derivada. Se ",[28,3369,3371,3384],{"className":3370},[31],[28,3372,3374],{"className":3373},[35],[37,3375,3376],{"xmlns":39},[41,3377,3378,3382],{},[44,3379,3380],{},[50,3381,388],{},[89,3383,886],{"encoding":91},[28,3385,3387],{"className":3386,"ariaHidden":61},[96],[28,3388,3390,3393],{"className":3389},[100],[28,3391],{"className":3392,"style":465},[104],[28,3394,388],{"className":3395,"style":506},[109,113]," é grande, o passo ultrapassa o fundo da tigela e pousa do outro lado, só que mais alto do que estava antes. Do lado novo, a derivada é ainda maior (em módulo) e de sinal trocado, então o próximo passo é ainda maior na direção contrária. Vira um ciclo que se alimenta e explode, tipo empurrar um balanço cada vez com mais força até ele virar de cabeça pra baixo.",[11,3398,3399,3400,3428],{},"Na prática, se você tá treinando um modelo de verdade e vê o custo subindo ou indo pra frente e pra trás sem parar, a primeira coisa que eu tento é diminuir ",[28,3401,3403,3416],{"className":3402},[31],[28,3404,3406],{"className":3405},[35],[37,3407,3408],{"xmlns":39},[41,3409,3410,3414],{},[44,3411,3412],{},[50,3413,388],{},[89,3415,886],{"encoding":91},[28,3417,3419],{"className":3418,"ariaHidden":61},[96],[28,3420,3422,3425],{"className":3421},[100],[28,3423],{"className":3424,"style":465},[104],[28,3426,388],{"className":3427,"style":506},[109,113]," (dividir por 3 ou por 10, por exemplo). O curso sugere testar uma sequência tipo 0.001, 0.003, 0.01, 0.03, 0.1 e comparar as curvas de custo até achar uma que desça de forma estável.",[922,3430,3431,3441],{},[925,3432,3433],{},[928,3434,3435,3438],{},[931,3436,3437],{"align":937},"Alpha",[931,3439,3440],{"align":933},"O que acontece (depois de 1000 passos, começando em w=0, b=0)",[1082,3442,3443,3451,3459,3467,3475,3483],{},[928,3444,3445,3448],{},[1087,3446,3447],{"align":937},"0.0001",[1087,3449,3450],{"align":933},"lento demais, mal saiu do ponto inicial",[928,3452,3453,3456],{},[1087,3454,3455],{"align":937},"0.001",[1087,3457,3458],{"align":933},"ainda longe do alvo",[928,3460,3461,3464],{},[1087,3462,3463],{"align":937},"0.01",[1087,3465,3466],{"align":933},"bom equilíbrio, é o que a gente usou acima",[928,3468,3469,3472],{},[1087,3470,3471],{"align":937},"0.1",[1087,3473,3474],{"align":933},"converge rápido",[928,3476,3477,3480],{},[1087,3478,3479],{"align":937},"0.3",[1087,3481,3482],{"align":933},"ainda converge, mas já perto do limite",[928,3484,3485,3488],{},[1087,3486,3487],{"align":937},"0.8",[1087,3489,3490],{"align":933},"diverge",[11,3492,3493],{},"Testa esses valores você mesmo no simulador acima e compara com a tabela.",[740,3495,3497],{"id":3496},"bônus-nem-toda-tigela-é-bonitinha-assim","Bônus: nem toda tigela é bonitinha assim",[11,3499,3500,3501,3503],{},"Toda superfície de custo que a gente desenhou até aqui tem a mesma cara de tigela de sopa, porque vem de erro elevado ao quadrado, e isso garante convexidade (",[22,3502,749],{"href":236},"). Mas gradiente descendente não vive só de tigela bem-comportada. Aqui vão dois clássicos que todo mundo que estuda otimização esbarra cedo ou tarde, só pra você ver que a dificuldade que a gente viu com o alpha grande é só a ponta do iceberg.",[3505,3506,3508],"h3",{"id":3507},"o-vale-banana-de-rosenbrock","O vale-banana de Rosenbrock",[11,3510,3511],{},"Essa aqui é praticamente um teste de estresse padrão da área, tem até nome próprio: função de Rosenbrock.",[11,3513,3514],{},[28,3515,3517,3580],{"className":3516},[31],[28,3518,3520],{"className":3519},[35],[37,3521,3522],{"xmlns":39},[41,3523,3524,3577],{},[44,3525,3526,3528,3530,3532,3534,3536,3538,3540,3542,3544,3546,3548,3554,3556,3559,3561,3563,3565,3571],{},[50,3527,52],{},[59,3529,69],{"stretchy":68},[50,3531,57],{},[59,3533,62],{"separator":61},[50,3535,65],{},[59,3537,75],{"stretchy":68},[59,3539,78],{},[59,3541,69],{"stretchy":68},[1368,3543,1370],{},[59,3545,385],{},[50,3547,57],{},[1417,3549,3550,3552],{},[59,3551,75],{"stretchy":68},[1368,3553,2701],{},[59,3555,85],{},[1368,3557,3558],{},"100",[59,3560,69],{"stretchy":68},[50,3562,65],{},[59,3564,385],{},[1417,3566,3567,3569],{},[50,3568,57],{},[1368,3570,2701],{},[1417,3572,3573,3575],{},[59,3574,75],{"stretchy":68},[1368,3576,2701],{},[89,3578,3579],{"encoding":91},"f(w,b) = (1-w)^2 + 100(b - w^2)^2",[28,3581,3583,3619,3640,3689,3713],{"className":3582,"ariaHidden":61},[96],[28,3584,3586,3589,3592,3595,3598,3601,3604,3607,3610,3613,3616],{"className":3585},[100],[28,3587],{"className":3588,"style":276},[104],[28,3590,52],{"className":3591,"style":114},[109,113],[28,3593,69],{"className":3594},[179],[28,3596,57],{"className":3597,"style":154},[109,113],[28,3599,62],{"className":3600},[158],[28,3602],{"className":3603,"style":293},[190],[28,3605,65],{"className":3606},[109,113],[28,3608,75],{"className":3609},[186],[28,3611],{"className":3612,"style":191},[190],[28,3614,78],{"className":3615},[195],[28,3617],{"className":3618,"style":191},[190],[28,3620,3622,3625,3628,3631,3634,3637],{"className":3621},[100],[28,3623],{"className":3624,"style":276},[104],[28,3626,69],{"className":3627},[179],[28,3629,1370],{"className":3630},[109],[28,3632],{"className":3633,"style":215},[190],[28,3635,385],{"className":3636},[219],[28,3638],{"className":3639,"style":215},[190],[28,3641,3643,3647,3650,3680,3683,3686],{"className":3642},[100],[28,3644],{"className":3645,"style":3646},[104],"height:1.0641em;vertical-align:-0.25em;",[28,3648,57],{"className":3649,"style":154},[109,113],[28,3651,3653,3656],{"className":3652},[186],[28,3654,75],{"className":3655},[186],[28,3657,3659],{"className":3658},[118],[28,3660,3662],{"className":3661},[122],[28,3663,3665],{"className":3664},[127],[28,3666,3669],{"className":3667,"style":3668},[131],"height:0.8141em;",[28,3670,3671,3674],{"style":1816},[28,3672],{"className":3673,"style":140},[139],[28,3675,3677],{"className":3676},[144,145,146,147],[28,3678,2701],{"className":3679},[109,147],[28,3681],{"className":3682,"style":215},[190],[28,3684,85],{"className":3685},[219],[28,3687],{"className":3688,"style":215},[190],[28,3690,3692,3695,3698,3701,3704,3707,3710],{"className":3691},[100],[28,3693],{"className":3694,"style":276},[104],[28,3696,3558],{"className":3697},[109],[28,3699,69],{"className":3700},[179],[28,3702,65],{"className":3703},[109,113],[28,3705],{"className":3706,"style":215},[190],[28,3708,385],{"className":3709},[219],[28,3711],{"className":3712,"style":215},[190],[28,3714,3716,3719,3748],{"className":3715},[100],[28,3717],{"className":3718,"style":3646},[104],[28,3720,3722,3725],{"className":3721},[109],[28,3723,57],{"className":3724,"style":154},[109,113],[28,3726,3728],{"className":3727},[118],[28,3729,3731],{"className":3730},[122],[28,3732,3734],{"className":3733},[127],[28,3735,3737],{"className":3736,"style":3668},[131],[28,3738,3739,3742],{"style":1816},[28,3740],{"className":3741,"style":140},[139],[28,3743,3745],{"className":3744},[144,145,146,147],[28,3746,2701],{"className":3747},[109,147],[28,3749,3751,3754],{"className":3750},[186],[28,3752,75],{"className":3753},[186],[28,3755,3757],{"className":3756},[118],[28,3758,3760],{"className":3759},[122],[28,3761,3763],{"className":3762},[127],[28,3764,3766],{"className":3765,"style":3668},[131],[28,3767,3768,3771],{"style":1816},[28,3769],{"className":3770,"style":140},[139],[28,3772,3774],{"className":3773},[144,145,146,147],[28,3775,2701],{"className":3776},[109,147],[11,3778,3779,3780,3832],{},"O mínimo global é em ",[28,3781,3783,3805],{"className":3782},[31],[28,3784,3786],{"className":3785},[35],[37,3787,3788],{"xmlns":39},[41,3789,3790,3802],{},[44,3791,3792,3794,3796,3798,3800],{},[59,3793,69],{"stretchy":68},[1368,3795,1370],{},[59,3797,62],{"separator":61},[1368,3799,1370],{},[59,3801,75],{"stretchy":68},[89,3803,3804],{"encoding":91},"(1,1)",[28,3806,3808],{"className":3807,"ariaHidden":61},[96],[28,3809,3811,3814,3817,3820,3823,3826,3829],{"className":3810},[100],[28,3812],{"className":3813,"style":276},[104],[28,3815,69],{"className":3816},[179],[28,3818,1370],{"className":3819},[109],[28,3821,62],{"className":3822},[158],[28,3824],{"className":3825,"style":293},[190],[28,3827,1370],{"className":3828},[109],[28,3830,75],{"className":3831},[186],", custo zero, mas repara na forma:",[3834,3835],"cost-surface3d",{":b-max":3836,":b-min":3837,":w-max":2701,":w-min":3838,"fn":3839},"3","-1","-2","rosenbrock",[11,3841,3842],{},"Não é uma tigela redonda, é um vale curvo, tipo uma banana. Isso é um problema de verdade pro gradiente descendente: a direção que desce mais rápido quase nunca aponta pro fundo do vale, aponta pra parede mais próxima. O algoritmo fica ricocheteando de um lado pro outro da banana, avançando bem pouco a cada zigue-zague, mesmo perto do fundo.",[11,3844,3845],{},"Testa o alpha 0.01 aqui (o mesmo que funcionou liso no nosso exemplo de imóveis) e olha o que acontece:",[3290,3847],{":b-range":3848,":initial-b":1370,":initial-w":3837,":w-range":3849,"b-label":65,"w-label":57,":alpha-presets":3850,":initial-alpha":3851,"fn":3839},"[-1, 3]","[-2, 2]","[0.0001, 0.0005, 0.001, 0.002, 0.005, 0.01]","0.002",[11,3853,3854,3855,362],{},"Alpha 0.01 diverge quase na hora aqui, mesmo valor que era o \"bom equilíbrio\" lá em cima. Não existe alpha universal, ele depende inteiro do formato da superfície que você tá descendo. Baixa pra 0.002 e roda \"Rodar 2000\" algumas vezes: agora sim, o ponto vermelho serpenteia devagar pelo vale até chegar perto de ",[28,3856,3858,3879],{"className":3857},[31],[28,3859,3861],{"className":3860},[35],[37,3862,3863],{"xmlns":39},[41,3864,3865,3877],{},[44,3866,3867,3869,3871,3873,3875],{},[59,3868,69],{"stretchy":68},[1368,3870,1370],{},[59,3872,62],{"separator":61},[1368,3874,1370],{},[59,3876,75],{"stretchy":68},[89,3878,3804],{"encoding":91},[28,3880,3882],{"className":3881,"ariaHidden":61},[96],[28,3883,3885,3888,3891,3894,3897,3900,3903],{"className":3884},[100],[28,3886],{"className":3887,"style":276},[104],[28,3889,69],{"className":3890},[179],[28,3892,1370],{"className":3893},[109],[28,3895,62],{"className":3896},[158],[28,3898],{"className":3899,"style":293},[190],[28,3901,1370],{"className":3902},[109],[28,3904,75],{"className":3905},[186],[3505,3907,3909],{"id":3908},"o-ponto-de-sela","O ponto de sela",[11,3911,3912],{},[28,3913,3915,3955],{"className":3914},[31],[28,3916,3918],{"className":3917},[35],[37,3919,3920],{"xmlns":39},[41,3921,3922,3952],{},[44,3923,3924,3926,3928,3930,3932,3934,3936,3938,3944,3946],{},[50,3925,52],{},[59,3927,69],{"stretchy":68},[50,3929,57],{},[59,3931,62],{"separator":61},[50,3933,65],{},[59,3935,75],{"stretchy":68},[59,3937,78],{},[1417,3939,3940,3942],{},[50,3941,57],{},[1368,3943,2701],{},[59,3945,385],{},[1417,3947,3948,3950],{},[50,3949,65],{},[1368,3951,2701],{},[89,3953,3954],{"encoding":91},"f(w,b) = w^2 - b^2",[28,3956,3958,3994,4039],{"className":3957,"ariaHidden":61},[96],[28,3959,3961,3964,3967,3970,3973,3976,3979,3982,3985,3988,3991],{"className":3960},[100],[28,3962],{"className":3963,"style":276},[104],[28,3965,52],{"className":3966,"style":114},[109,113],[28,3968,69],{"className":3969},[179],[28,3971,57],{"className":3972,"style":154},[109,113],[28,3974,62],{"className":3975},[158],[28,3977],{"className":3978,"style":293},[190],[28,3980,65],{"className":3981},[109,113],[28,3983,75],{"className":3984},[186],[28,3986],{"className":3987,"style":191},[190],[28,3989,78],{"className":3990},[195],[28,3992],{"className":3993,"style":191},[190],[28,3995,3997,4001,4030,4033,4036],{"className":3996},[100],[28,3998],{"className":3999,"style":4000},[104],"height:0.8974em;vertical-align:-0.0833em;",[28,4002,4004,4007],{"className":4003},[109],[28,4005,57],{"className":4006,"style":154},[109,113],[28,4008,4010],{"className":4009},[118],[28,4011,4013],{"className":4012},[122],[28,4014,4016],{"className":4015},[127],[28,4017,4019],{"className":4018,"style":3668},[131],[28,4020,4021,4024],{"style":1816},[28,4022],{"className":4023,"style":140},[139],[28,4025,4027],{"className":4026},[144,145,146,147],[28,4028,2701],{"className":4029},[109,147],[28,4031],{"className":4032,"style":215},[190],[28,4034,385],{"className":4035},[219],[28,4037],{"className":4038,"style":215},[190],[28,4040,4042,4045],{"className":4041},[100],[28,4043],{"className":4044,"style":3668},[104],[28,4046,4048,4051],{"className":4047},[109],[28,4049,65],{"className":4050},[109,113],[28,4052,4054],{"className":4053},[118],[28,4055,4057],{"className":4056},[122],[28,4058,4060],{"className":4059},[127],[28,4061,4063],{"className":4062,"style":3668},[131],[28,4064,4065,4068],{"style":1816},[28,4066],{"className":4067,"style":140},[139],[28,4069,4071],{"className":4070},[144,145,146,147],[28,4072,2701],{"className":4073},[109,147],[3834,4075],{":b-max":2701,":b-min":3838,":w-max":2701,":w-min":3838,"fn":4076,":marker-b":1389,":marker-w":1389},"saddle",[11,4078,4079,4080,4108,4109,4137,4138,4142],{},"Gira essa aqui com calma. É um mínimo se você olhar só pro eixo ",[28,4081,4083,4096],{"className":4082},[31],[28,4084,4086],{"className":4085},[35],[37,4087,4088],{"xmlns":39},[41,4089,4090,4094],{},[44,4091,4092],{},[50,4093,57],{},[89,4095,57],{"encoding":91},[28,4097,4099],{"className":4098,"ariaHidden":61},[96],[28,4100,4102,4105],{"className":4101},[100],[28,4103],{"className":4104,"style":465},[104],[28,4106,57],{"className":4107,"style":154},[109,113],", e um máximo se olhar só pro eixo ",[28,4110,4112,4125],{"className":4111},[31],[28,4113,4115],{"className":4114},[35],[37,4116,4117],{"xmlns":39},[41,4118,4119,4123],{},[44,4120,4121],{},[50,4122,65],{},[89,4124,65],{"encoding":91},[28,4126,4128],{"className":4127,"ariaHidden":61},[96],[28,4129,4131,4134],{"className":4130},[100],[28,4132],{"className":4133,"style":229},[104],[28,4135,65],{"className":4136},[109,113],", ao mesmo tempo, no mesmo ponto. Isso se chama ",[358,4139,4141],{"definition":4140},"um ponto onde o gradiente é zero, mas que não é mínimo nem máximo, é mínimo numa direção e máximo em outra ao mesmo tempo, tipo o meio de uma sela de cavalo","ponto de sela",", o ponto vermelho no centro marca exatamente ele.",[11,4144,4145,4146,4174],{},"Lembra da regra \"quando a derivada zera, o algoritmo para sozinho\"? Pois é, nesse ponto ela zera igualzinho. Se o gradiente descendente chegasse exatamente ali, ia achar que tinha terminado, sem ter terminado nada, só tá equilibrado no topo de um pico de cavalo. Qualquer empurrãozinho pra fora do centro exato, e ele escorrega ladeira abaixo na direção que desce (o eixo ",[28,4147,4149,4162],{"className":4148},[31],[28,4150,4152],{"className":4151},[35],[37,4153,4154],{"xmlns":39},[41,4155,4156,4160],{},[44,4157,4158],{},[50,4159,65],{},[89,4161,65],{"encoding":91},[28,4163,4165],{"className":4164,"ariaHidden":61},[96],[28,4166,4168,4171],{"className":4167},[100],[28,4169],{"className":4170,"style":229},[104],[28,4172,65],{"className":4173},[109,113],"), longe de qualquer mínimo de verdade.",[11,4176,4177],{},"Na nossa regressão isso nunca acontece (a tigela é sempre convexa, sem sela nenhuma escondida), mas é exatamente esse tipo de superfície que aparece direto em modelos mais complexos, tipo rede neural. Guarda esse nome, ele volta.",[740,4179,4181],{"id":4180},"fechando-a-trilogia","Fechando a trilogia",[922,4183,4184,4194],{},[925,4185,4186],{},[928,4187,4188,4191],{},[931,4189,4190],{"align":933},"Post",[931,4192,4193],{"align":933},"O que ficou pronto",[1082,4195,4196,4354,4420],{},[928,4197,4198,4203],{},[1087,4199,4200],{"align":933},[22,4201,4202],{"href":24},"Lab 02",[1087,4204,4205,4206],{"align":933},"o modelo, ",[28,4207,4209,4248],{"className":4208},[31],[28,4210,4212],{"className":4211},[35],[37,4213,4214],{"xmlns":39},[41,4215,4216,4246],{},[44,4217,4218,4230,4232,4234,4236,4238,4240,4242,4244],{},[47,4219,4220,4222],{},[50,4221,52],{},[44,4223,4224,4226,4228],{},[50,4225,57],{},[59,4227,62],{"separator":61},[50,4229,65],{},[59,4231,69],{"stretchy":68},[50,4233,72],{},[59,4235,75],{"stretchy":68},[59,4237,78],{},[50,4239,57],{},[50,4241,72],{},[59,4243,85],{},[50,4245,65],{},[89,4247,92],{"encoding":91},[28,4249,4251,4324,4345],{"className":4250,"ariaHidden":61},[96],[28,4252,4254,4257,4306,4309,4312,4315,4318,4321],{"className":4253},[100],[28,4255],{"className":4256,"style":105},[104],[28,4258,4260,4263],{"className":4259},[109],[28,4261,52],{"className":4262,"style":114},[109,113],[28,4264,4266],{"className":4265},[118],[28,4267,4269,4298],{"className":4268},[122,123],[28,4270,4272,4295],{"className":4271},[127],[28,4273,4275],{"className":4274,"style":132},[131],[28,4276,4277,4280],{"style":135},[28,4278],{"className":4279,"style":140},[139],[28,4281,4283],{"className":4282},[144,145,146,147],[28,4284,4286,4289,4292],{"className":4285},[109,147],[28,4287,57],{"className":4288,"style":154},[109,113,147],[28,4290,62],{"className":4291},[158,147],[28,4293,65],{"className":4294},[109,113,147],[28,4296,166],{"className":4297},[165],[28,4299,4301],{"className":4300},[127],[28,4302,4304],{"className":4303,"style":173},[131],[28,4305],{},[28,4307,69],{"className":4308},[179],[28,4310,72],{"className":4311},[109,113],[28,4313,75],{"className":4314},[186],[28,4316],{"className":4317,"style":191},[190],[28,4319,78],{"className":4320},[195],[28,4322],{"className":4323,"style":191},[190],[28,4325,4327,4330,4333,4336,4339,4342],{"className":4326},[100],[28,4328],{"className":4329,"style":205},[104],[28,4331,57],{"className":4332,"style":154},[109,113],[28,4334,72],{"className":4335},[109,113],[28,4337],{"className":4338,"style":215},[190],[28,4340,85],{"className":4341},[219],[28,4343],{"className":4344,"style":215},[190],[28,4346,4348,4351],{"className":4347},[100],[28,4349],{"className":4350,"style":229},[104],[28,4352,65],{"className":4353},[109,113],[928,4355,4356,4361],{},[1087,4357,4358],{"align":933},[22,4359,4360],{"href":236},"Lab 03",[1087,4362,4363,4364],{"align":933},"a medida do erro, ",[28,4365,4367,4390],{"className":4366},[31],[28,4368,4370],{"className":4369},[35],[37,4371,4372],{"xmlns":39},[41,4373,4374,4388],{},[44,4375,4376,4378,4380,4382,4384,4386],{},[50,4377,253],{},[59,4379,69],{"stretchy":68},[50,4381,57],{},[59,4383,62],{"separator":61},[50,4385,65],{},[59,4387,75],{"stretchy":68},[89,4389,266],{"encoding":91},[28,4391,4393],{"className":4392,"ariaHidden":61},[96],[28,4394,4396,4399,4402,4405,4408,4411,4414,4417],{"className":4395},[100],[28,4397],{"className":4398,"style":276},[104],[28,4400,253],{"className":4401,"style":280},[109,113],[28,4403,69],{"className":4404},[179],[28,4406,57],{"className":4407,"style":154},[109,113],[28,4409,62],{"className":4410},[158],[28,4412],{"className":4413,"style":293},[190],[28,4415,65],{"className":4416},[109,113],[28,4418,75],{"className":4419},[186],[928,4421,4422,4425],{},[1087,4423,4424],{"align":933},"Lab 04 (esse aqui)",[1087,4426,4427],{"align":933},"o algoritmo que minimiza esse erro sozinho, gradiente descendente",[11,4429,4430],{},"Três ideias pra levar:",[4432,4433,4434,4441,4447],"ol",{},[4435,4436,4437,4440],"li",{},[913,4438,4439],{},"O gradiente aponta pra onde o custo cresce",", então o algoritmo sempre anda no sentido contrário.",[4435,4442,4443,4446],{},[913,4444,4445],{},"A atualização é simultânea",", calcula as duas derivadas primeiro, troca os parâmetros depois.",[4435,4448,4449,4452],{},[913,4450,4451],{},"A taxa de aprendizado é o parâmetro mais sensível que você vai mexer",": pequena demais é lento, grande demais diverge.",[11,4454,4455,4458,4459,4462,4463,4467],{},[913,4456,4457],{},"No próximo post:"," tudo que você viu até aqui foi com uma feature só (o tamanho da casa). Na Semana 2 do curso, o modelo ganha várias features de uma vez, e fazer conta com um laço ",[2861,4460,4461],{},"for"," deixa de dar conta do recado. Antes de mexer no modelo com várias features, ",[22,4464,4466],{"href":4465},"\u002Fplaylists\u002Fmachine-learning-specialization\u002Fw2-lab01-numpy-vectorization","o próximo post"," é sobre a ferramenta que torna isso viável: NumPy e vetorização.",[740,4469,4471],{"id":4470},"aplicação-prática","Aplicação prática",[11,4473,4474,4475,4481,4482,2761,4484,4486],{},"Mesmo dataset real de imóveis dos dois posts anteriores (",[22,4476,4480],{"href":4477,"rel":4478},"https:\u002F\u002Fwww.kaggle.com\u002Fdatasets\u002Fdenkuznetz\u002Fhousing-prices-regression",[4479],"nofollow","Housing Prices Regression, Kaggle","), mesma escala (tamanho em \"centenas de pés²\", preço em \"milhares de dólares\"). Bora ver o algoritmo achar sozinho, em dado real, o ajuste que nos posts ",[22,4483,1370],{"href":24},[22,4485,2701],{"href":236}," você foi atrás na mão.",[2854,4488,4490],{"className":2856,"code":4489,"language":2858,"meta":2859,"style":2859},"w, b, J_hist = gradient_descent(\n    x_sqft, y_price,          # as 50 casas reais\n    w_in=0, b_in=0,           # começando do zero, igual no exemplo de brinquedo\n    alpha=0.01, num_iters=4000,\n    cost_function=compute_cost, gradient_function=compute_gradient)\n\nprint(f\"(w, b) encontrados: ({w:.1f}, {b:.1f})\")\n",[2861,4491,4492,4497,4502,4507,4512,4517,4521],{"__ignoreMap":2859},[28,4493,4494],{"class":2865,"line":2866},[28,4495,4496],{},"w, b, J_hist = gradient_descent(\n",[28,4498,4499],{"class":2865,"line":2872},[28,4500,4501],{},"    x_sqft, y_price,          # as 50 casas reais\n",[28,4503,4504],{"class":2865,"line":2878},[28,4505,4506],{},"    w_in=0, b_in=0,           # começando do zero, igual no exemplo de brinquedo\n",[28,4508,4509],{"class":2865,"line":2884},[28,4510,4511],{},"    alpha=0.01, num_iters=4000,\n",[28,4513,4514],{"class":2865,"line":2891},[28,4515,4516],{},"    cost_function=compute_cost, gradient_function=compute_gradient)\n",[28,4518,4519],{"class":2865,"line":2897},[28,4520,2888],{"emptyLinePlaceholder":2887},[28,4522,4523],{"class":2865,"line":2903},[28,4524,4525],{},"print(f\"(w, b) encontrados: ({w:.1f}, {b:.1f})\")\n",[4527,4528,4529],"blockquote",{},[11,4530,4531,26,4534],{},[913,4532,4533],{},"Saída:",[2861,4535,4536],{},"(w, b) encontrados: (116.5, 398.3)",[11,4538,4539],{},"Bate certinho com o ajuste que a gente citou nos dois posts anteriores. Clica em \"Rodar 2000\" duas vezes no simulador abaixo e confere ao vivo:",[4541,4542],"housing-gradient-descent-simulator",{},[11,4544,4545,4546,2761,4574,4602],{},"Repara que a convergência aqui é bem mais devagar que no exemplo de brinquedo de 2 pontos, mesmo já usando a mesma escala pequena de sempre. Isso acontece porque ",[28,4547,4549,4562],{"className":4548},[31],[28,4550,4552],{"className":4551},[35],[37,4553,4554],{"xmlns":39},[41,4555,4556,4560],{},[44,4557,4558],{},[50,4559,57],{},[89,4561,57],{"encoding":91},[28,4563,4565],{"className":4564,"ariaHidden":61},[96],[28,4566,4568,4571],{"className":4567},[100],[28,4569],{"className":4570,"style":465},[104],[28,4572,57],{"className":4573,"style":154},[109,113],[28,4575,4577,4590],{"className":4576},[31],[28,4578,4580],{"className":4579},[35],[37,4581,4582],{"xmlns":39},[41,4583,4584,4588],{},[44,4585,4586],{},[50,4587,65],{},[89,4589,65],{"encoding":91},[28,4591,4593],{"className":4592,"ariaHidden":61},[96],[28,4594,4596,4599],{"className":4595},[100],[28,4597],{"className":4598,"style":229},[104],[28,4600,65],{"className":4601},[109,113]," ainda vivem em faixas bem diferentes uma da outra (um vai até 300, o outro até 600), o que estica o vale de custo. É exatamente esse tipo de situação que a normalização de features, mais pra frente no curso, resolve de vez.",[4604,4605,4606],"style",{},"html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":2859,"searchDepth":2872,"depth":2872,"links":4608},[4609,4610,4611,4612,4613,4614,4615,4619,4620],{"id":742,"depth":2872,"text":743},{"id":907,"depth":2872,"text":908},{"id":1320,"depth":2872,"text":1321},{"id":2851,"depth":2872,"text":2852},{"id":3178,"depth":2872,"text":3179},{"id":3298,"depth":2872,"text":3299},{"id":3496,"depth":2872,"text":3497,"children":4616},[4617,4618],{"id":3507,"depth":2878,"text":3508},{"id":3908,"depth":2878,"text":3909},{"id":4180,"depth":2872,"text":4181},{"id":4470,"depth":2872,"text":4471},null,"2026-08-18","O algoritmo que desce sozinho até o fundo da tigela de custo: a matemática por trás do gradiente descendente, o que acontece quando a taxa de aprendizado é grande demais, e por que ele para sozinho perto do mínimo.","md",{},"\u002Fpt\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent","machine-learning-specialization",{"title":6,"description":4623},"published","pt\u002Fplaylists\u002Fmachine-learning-specialization\u002Flab04-gradient-descent",[4632,4633,4634],"gradiente-descendente","otimizacao","fundamentos","dPZR4SOlZIhg6S2-xD1g-RDgMsuyf5eAfVMCCPFYZlw",1787338983640]