[{"data":1,"prerenderedAt":6473},["ShallowReactive",2],{"\u002Fblog\u002FIntroduction-to-Machine-Learning":3,"post-count":6065,"series-global-data":6066,"authors-all":6176,"series-sidebar-none":6371,"sidebar-authors":6372},{"id":4,"title":5,"author":6,"body":7,"date":6054,"description":2688,"draft":6055,"edited_at":6054,"extension":6056,"featured_image":6057,"meta":6058,"navigation":6059,"path":6060,"pinned":6055,"seo":6061,"sitemap":6062,"stem":6063,"tags":6057,"__hash__":6064},"blog\u002Fblog\u002FIntroduction-to-Machine-Learning.md","Introduction to Machine Learning","chinono",{"type":8,"value":9,"toc":6030},"minimark",[10,15,24,32,35,51,55,58,61,91,98,102,105,111,117,123,129,133,138,141,173,177,180,194,198,201,221,288,294,298,301,328,332,335,339,422,763,770,774,777,1199,1202,1548,1619,1623,1634,1638,1641,2008,2065,5256,5259,5270,5276,5479,5688,5692,5695,5721,5736,5889,5893,5896,5902,5908,5914,5920,5923,5927,5930,5936,5942,5945,5949,5952,5990,5994,6026],[11,12,14],"h2",{"id":13},"what-even-is-learning","What Even Is \"Learning\"?",[16,17,18,19,23],"p",{},"Before we talk about ",[20,21,22],"em",{},"machine"," learning, let's think about what learning means in general.",[16,25,26,27,31],{},"Herbert Simon, a Nobel Prize-winning scientist, once described learning as ",[28,29,30],"strong",{},"any process by which a system improves its performance from experience",". That's a beautifully simple definition, and it applies just as well to computers as it does to humans.",[16,33,34],{},"When we talk about learning in the context of machines, the \"tasks\" we want them to improve at generally fall into two buckets:",[36,37,38,45],"ul",{},[39,40,41,44],"li",{},[28,42,43],{},"Classification"," — assigning things to categories (e.g., \"Is this email spam or not?\")",[39,46,47,50],{},[28,48,49],{},"Problem solving \u002F Planning \u002F Control"," — taking actions to achieve a goal (e.g., \"How should a robot navigate a maze?\")",[11,52,54],{"id":53},"where-does-machine-learning-fit-in-the-ai-landscape","Where Does Machine Learning Fit in the AI Landscape?",[16,56,57],{},"You've probably heard the terms AI, Machine Learning, Deep Learning, and Data Science thrown around interchangeably. They're related, but they're not the same thing.",[16,59,60],{},"Think of it as a set of nested circles:",[36,62,63,69,75,81],{},[39,64,65,68],{},[28,66,67],{},"Artificial Intelligence (AI)"," is the broadest concept. It's about creating machines that can mimic intelligent human behaviour.",[39,70,71,74],{},[28,72,73],{},"Machine Learning (ML)"," is a subset of AI. Instead of being explicitly programmed with rules, ML systems learn patterns from data and use those patterns to make predictions or decisions.",[39,76,77,80],{},[28,78,79],{},"Deep Learning (DL)"," is a subset of ML that uses multi-layered neural networks to tackle complex problems like image recognition and natural language processing.",[39,82,83,86,87,90],{},[28,84,85],{},"Data Science"," overlaps with all of these. It's the broader discipline of extracting insights from data using statistics, scientific methods, and algorithms.\nThe key takeaway: ",[28,88,89],{},"ML is about building models from training data to make predictions",", rather than writing rules by hand.",[16,92,93],{},[94,95],"img",{"alt":96,"src":97},"0.83","https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1777198853679-1775145963610-Screenshot_2026-04-03_000510.png",[11,99,101],{"id":100},"the-main-flavours-of-machine-learning","The Main Flavours of Machine Learning",[16,103,104],{},"Machine learning approaches can be grouped into several categories based on how the system learns:",[16,106,107,110],{},[28,108,109],{},"Supervised Learning"," — The model learns from labeled examples. You give it inputs paired with the correct outputs, and it learns the mapping between them. This includes regression (predicting a continuous value, like house prices) and classification (predicting a category, like spam vs. not spam).",[16,112,113,116],{},[28,114,115],{},"Unsupervised Learning"," — The model receives data without labels and must find structure on its own. The most common task here is clustering — grouping similar data points together.",[16,118,119,122],{},[28,120,121],{},"Reinforcement Learning"," — The model learns by interacting with an environment. It takes actions, receives rewards or penalties, and gradually figures out the best strategy. Think of it like training a dog with treats.",[16,124,125,128],{},[28,126,127],{},"Self-Supervised Learning"," — A newer paradigm where the model generates its own labels from the data itself (for example, masking a word in a sentence and learning to predict it).",[11,130,132],{"id":131},"real-world-applications","Real-World Applications",[134,135,137],"h3",{"id":136},"classification-examples","Classification Examples",[16,139,140],{},"Classification is everywhere in daily life:",[36,142,143,149,155,161,167],{},[39,144,145,148],{},[28,146,147],{},"Medical diagnosis"," — Is this X-ray showing signs of pneumonia?",[39,150,151,154],{},[28,152,153],{},"Spam filtering"," — Should this email go to your inbox or junk folder?",[39,156,157,160],{},[28,158,159],{},"Fraud detection"," — Is this credit card transaction suspicious?",[39,162,163,166],{},[28,164,165],{},"Recommendation systems"," — Which movies, books, or songs might you enjoy?",[39,168,169,172],{},[28,170,171],{},"Speech and handwriting recognition"," — Converting spoken words or handwritten text into digital text.",[134,174,176],{"id":175},"problem-solving-planning-control-examples","Problem Solving \u002F Planning \u002F Control Examples",[16,178,179],{},"These are tasks where an agent takes actions in an environment to achieve a goal:",[36,181,182,185,188,191],{},[39,183,184],{},"Playing board games like chess or checkers",[39,186,187],{},"Self-driving cars navigating roads",[39,189,190],{},"Controlling robots or video game characters",[39,192,193],{},"Flying drones or helicopters autonomously",[11,195,197],{"id":196},"defining-a-learning-task-t-p-e","Defining a Learning Task: T, P, E",[16,199,200],{},"One of the most useful frameworks for thinking about ML problems comes from Tom Mitchell's classic definition. Every learning task can be described by three components:",[36,202,203,209,215],{},[39,204,205,208],{},[28,206,207],{},"T (Task)"," — What is the system trying to do?",[39,210,211,214],{},[28,212,213],{},"P (Performance)"," — How do we measure success?",[39,216,217,220],{},[28,218,219],{},"E (Experience)"," — What data does the system learn from?\nHere are a few examples to make this concrete:",[222,223,224,240],"table",{},[225,226,227],"thead",{},[228,229,230,234,237],"tr",{},[231,232,233],"th",{},"Task (T)",[231,235,236],{},"Performance (P)",[231,238,239],{},"Experience (E)",[241,242,243,255,266,277],"tbody",{},[228,244,245,249,252],{},[246,247,248],"td",{},"Playing checkers",[246,250,251],{},"% of games won",[246,253,254],{},"Self-play practice games",[228,256,257,260,263],{},[246,258,259],{},"Recognizing handwritten words",[246,261,262],{},"% of words correctly classified",[246,264,265],{},"Database of labeled handwriting images",[228,267,268,271,274],{},[246,269,270],{},"Driving on highways",[246,272,273],{},"Average distance before a human-judged error",[246,275,276],{},"Recorded images and steering commands from a human driver",[228,278,279,282,285],{},[246,280,281],{},"Spam classification",[246,283,284],{},"% of emails correctly classified",[246,286,287],{},"Database of emails with human labels",[16,289,290,291],{},"This framework is great for getting clarity before you start any ML project. Ask yourself: ",[20,292,293],{},"What's my T, P, and E?",[11,295,297],{"id":296},"designing-a-learning-system","Designing a Learning System",[16,299,300],{},"When you set out to build an ML system, there are four key design decisions:",[302,303,304,310,316,322],"ol",{},[39,305,306,309],{},[28,307,308],{},"Choose the training experience"," — What kind of data will the system learn from? Is it direct (labeled input-output pairs) or indirect (like game outcomes where individual moves aren't labeled)?",[39,311,312,315],{},[28,313,314],{},"Choose the target function"," — What exactly should the system learn? For a checkers player, this might be an evaluation function that scores how favorable a board position is.",[39,317,318,321],{},[28,319,320],{},"Choose a representation"," — How will the target function be expressed? Options include lookup tables, linear functions, decision trees, neural networks, and many more.",[39,323,324,327],{},[28,325,326],{},"Choose a learning algorithm"," — How will the system search for the best function? This could be gradient descent, dynamic programming, evolutionary algorithms, etc.",[11,329,331],{"id":330},"a-concrete-example-learning-to-play-checkers","A Concrete Example: Learning to Play Checkers",[16,333,334],{},"To tie everything together, let's walk through a classic example: Arthur Samuel's checkers-playing program from 1959, one of the earliest ML systems ever built.",[134,336,338],{"id":337},"the-target-function","The Target Function",[16,340,341,342,345,346,421],{},"We want to learn an ",[28,343,344],{},"evaluation function"," ",[347,348,352],"mjx-container",{"className":349,"jax":351},[350],"MathJax","SVG",[353,354,362,382],"svg",{"style":355,"xmlns":356,"width":357,"height":358,"role":94,"focusable":359,"viewBox":360,"xmlnsXLink":361},"vertical-align: -0.566ex;","http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","4.471ex","2.262ex","false","0 -750 1976 1000","http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink",[363,364,365,370,374,378],"defs",{},[366,367],"path",{"id":368,"d":369},"MJX-1-TEX-I-1D449","M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z",[366,371],{"id":372,"d":373},"MJX-1-TEX-N-28","M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z",[366,375],{"id":376,"d":377},"MJX-1-TEX-I-1D44F","M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z",[366,379],{"id":380,"d":381},"MJX-1-TEX-N-29","M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z",[383,384,388],"g",{"stroke":385,"fill":385,"stroke-width":386,"transform":387},"currentColor","0","scale(1,-1)",[383,389,391,399,407,414],{"dataMmlNode":390},"math",[383,392,394],{"dataMmlNode":393},"mi",[395,396],"use",{"dataC":397,"xLinkHref":398},"1D449","#MJX-1-TEX-I-1D449",[383,400,403],{"dataMmlNode":401,"transform":402},"mo","translate(769,0)",[395,404],{"dataC":405,"xLinkHref":406},"28","#MJX-1-TEX-N-28",[383,408,410],{"dataMmlNode":393,"transform":409},"translate(1158,0)",[395,411],{"dataC":412,"xLinkHref":413},"1D44F","#MJX-1-TEX-I-1D44F",[383,415,417],{"dataMmlNode":401,"transform":416},"translate(1587,0)",[395,418],{"dataC":419,"xLinkHref":420},"29","#MJX-1-TEX-N-29"," that takes a board state and returns a score indicating how favorable it is. 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if ",[347,508,510],{"className":509,"jax":351},[350],[353,511,516,521],{"style":512,"xmlns":356,"width":513,"height":514,"role":94,"focusable":359,"viewBox":515,"xmlnsXLink":361},"vertical-align: -0.025ex;","0.971ex","1.595ex","0 -694 429 705",[363,517,518],{},[366,519],{"id":520,"d":377},"MJX-3-TEX-I-1D44F",[383,522,523],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,524,525],{"dataMmlNode":390},[383,526,527],{"dataMmlNode":393},[395,528],{"dataC":412,"xLinkHref":529},"#MJX-3-TEX-I-1D44F"," is a winning position",[39,532,533,506,613,632],{},[347,534,536],{"className":535,"jax":351},[350],[353,537,540,567],{"style":355,"xmlns":356,"width":538,"height":358,"role":94,"focusable":359,"viewBox":539,"xmlnsXLink":361},"12.642ex","0 -750 5587.6 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is a losing position",[39,634,635,506,696,715],{},[347,636,638],{"className":637,"jax":351},[350],[353,639,642,662],{"style":355,"xmlns":356,"width":640,"height":358,"role":94,"focusable":359,"viewBox":641,"xmlnsXLink":361},"8.619ex","0 -750 3809.6 1000",[363,643,644,647,650,653,656,659],{},[366,645],{"id":646,"d":369},"MJX-6-TEX-I-1D449",[366,648],{"id":649,"d":373},"MJX-6-TEX-N-28",[366,651],{"id":652,"d":377},"MJX-6-TEX-I-1D44F",[366,654],{"id":655,"d":381},"MJX-6-TEX-N-29",[366,657],{"id":658,"d":450},"MJX-6-TEX-N-3D",[366,660],{"id":661,"d":458},"MJX-6-TEX-N-30",[383,663,664],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,665,666,671,676,681,686,691],{"dataMmlNode":390},[383,667,668],{"dataMmlNode":393},[395,669],{"dataC":397,"xLinkHref":670},"#MJX-6-TEX-I-1D449",[383,672,673],{"dataMmlNode":401,"transform":402},[395,674],{"dataC":405,"xLinkHref":675},"#MJX-6-TEX-N-28",[383,677,678],{"dataMmlNode":393,"transform":409},[395,679],{"dataC":412,"xLinkHref":680},"#MJX-6-TEX-I-1D44F",[383,682,683],{"dataMmlNode":401,"transform":416},[395,684],{"dataC":419,"xLinkHref":685},"#MJX-6-TEX-N-29",[383,687,688],{"dataMmlNode":401,"transform":485},[395,689],{"dataC":488,"xLinkHref":690},"#MJX-6-TEX-N-3D",[383,692,693],{"dataMmlNode":492,"transform":493},[395,694],{"dataC":500,"xLinkHref":695},"#MJX-6-TEX-N-30",[347,697,699],{"className":698,"jax":351},[350],[353,700,701,706],{"style":512,"xmlns":356,"width":513,"height":514,"role":94,"focusable":359,"viewBox":515,"xmlnsXLink":361},[363,702,703],{},[366,704],{"id":705,"d":377},"MJX-7-TEX-I-1D44F",[383,707,708],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,709,710],{"dataMmlNode":390},[383,711,712],{"dataMmlNode":393},[395,713],{"dataC":412,"xLinkHref":714},"#MJX-7-TEX-I-1D44F"," is a draw",[39,717,718,719,762],{},"Otherwise, ",[347,720,722],{"className":721,"jax":351},[350],[353,723,724,738],{"style":355,"xmlns":356,"width":357,"height":358,"role":94,"focusable":359,"viewBox":360,"xmlnsXLink":361},[363,725,726,729,732,735],{},[366,727],{"id":728,"d":369},"MJX-8-TEX-I-1D449",[366,730],{"id":731,"d":373},"MJX-8-TEX-N-28",[366,733],{"id":734,"d":377},"MJX-8-TEX-I-1D44F",[366,736],{"id":737,"d":381},"MJX-8-TEX-N-29",[383,739,740],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,741,742,747,752,757],{"dataMmlNode":390},[383,743,744],{"dataMmlNode":393},[395,745],{"dataC":397,"xLinkHref":746},"#MJX-8-TEX-I-1D449",[383,748,749],{"dataMmlNode":401,"transform":402},[395,750],{"dataC":405,"xLinkHref":751},"#MJX-8-TEX-N-28",[383,753,754],{"dataMmlNode":393,"transform":409},[395,755],{"dataC":412,"xLinkHref":756},"#MJX-8-TEX-I-1D44F",[383,758,759],{"dataMmlNode":401,"transform":416},[395,760],{"dataC":419,"xLinkHref":761},"#MJX-8-TEX-N-29"," equals the value of the best reachable final state under optimal play",[16,764,765,766,769],{},"The problem? Computing this perfectly requires searching the entire game tree, which is astronomically large. 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1000",[363,1270,1271,1274,1277,1280,1283],{},[366,1272],{"id":1273,"d":831},"MJX-11-TEX-I-1D45F",[366,1275],{"id":1276,"d":823},"MJX-11-TEX-I-1D45D",[366,1278],{"id":1279,"d":373},"MJX-11-TEX-N-28",[366,1281],{"id":1282,"d":377},"MJX-11-TEX-I-1D44F",[366,1284],{"id":1285,"d":381},"MJX-11-TEX-N-29",[383,1287,1288],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1289,1290,1295,1301,1307,1313],{"dataMmlNode":390},[383,1291,1292],{"dataMmlNode":393},[395,1293],{"dataC":981,"xLinkHref":1294},"#MJX-11-TEX-I-1D45F",[383,1296,1298],{"dataMmlNode":393,"transform":1297},"translate(451,0)",[395,1299],{"dataC":936,"xLinkHref":1300},"#MJX-11-TEX-I-1D45D",[383,1302,1304],{"dataMmlNode":401,"transform":1303},"translate(954,0)",[395,1305],{"dataC":405,"xLinkHref":1306},"#MJX-11-TEX-N-28",[383,1308,1310],{"dataMmlNode":393,"transform":1309},"translate(1343,0)",[395,1311],{"dataC":412,"xLinkHref":1312},"#MJX-11-TEX-I-1D44F",[383,1314,1316],{"dataMmlNode":401,"transform":1315},"translate(1772,0)",[395,1317],{"dataC":419,"xLinkHref":1318},"#MJX-11-TEX-N-29"," = number of red pieces",[39,1321,1322,1374],{},[347,1323,1325],{"className":1324,"jax":351},[350],[353,1326,1329,1343],{"style":355,"xmlns":356,"width":1327,"height":358,"role":94,"focusable":359,"viewBox":1328,"xmlnsXLink":361},"4.88ex","0 -750 2157 1000",[363,1330,1331,1334,1337,1340],{},[366,1332],{"id":1333,"d":377},"MJX-12-TEX-I-1D44F",[366,1335],{"id":1336,"d":839},"MJX-12-TEX-I-1D458",[366,1338],{"id":1339,"d":373},"MJX-12-TEX-N-28",[366,1341],{"id":1342,"d":381},"MJX-12-TEX-N-29",[383,1344,1345],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1346,1347,1352,1357,1363,1368],{"dataMmlNode":390},[383,1348,1349],{"dataMmlNode":393},[395,1350],{"dataC":412,"xLinkHref":1351},"#MJX-12-TEX-I-1D44F",[383,1353,1354],{"dataMmlNode":393,"transform":1238},[395,1355],{"dataC":1036,"xLinkHref":1356},"#MJX-12-TEX-I-1D458",[383,1358,1360],{"dataMmlNode":401,"transform":1359},"translate(950,0)",[395,1361],{"dataC":405,"xLinkHref":1362},"#MJX-12-TEX-N-28",[383,1364,1366],{"dataMmlNode":393,"transform":1365},"translate(1339,0)",[395,1367],{"dataC":412,"xLinkHref":1351},[383,1369,1371],{"dataMmlNode":401,"transform":1370},"translate(1768,0)",[395,1372],{"dataC":419,"xLinkHref":1373},"#MJX-12-TEX-N-29"," = number of black kings",[39,1376,1377,1433],{},[347,1378,1380],{"className":1379,"jax":351},[350],[353,1381,1384,1401],{"style":355,"xmlns":356,"width":1382,"height":358,"role":94,"focusable":359,"viewBox":1383,"xmlnsXLink":361},"4.93ex","0 -750 2179 1000",[363,1385,1386,1389,1392,1395,1398],{},[366,1387],{"id":1388,"d":831},"MJX-13-TEX-I-1D45F",[366,1390],{"id":1391,"d":839},"MJX-13-TEX-I-1D458",[366,1393],{"id":1394,"d":373},"MJX-13-TEX-N-28",[366,1396],{"id":1397,"d":377},"MJX-13-TEX-I-1D44F",[366,1399],{"id":1400,"d":381},"MJX-13-TEX-N-29",[383,1402,1403],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1404,1405,1410,1415,1421,1427],{"dataMmlNode":390},[383,1406,1407],{"dataMmlNode":393},[395,1408],{"dataC":981,"xLinkHref":1409},"#MJX-13-TEX-I-1D45F",[383,1411,1412],{"dataMmlNode":393,"transform":1297},[395,1413],{"dataC":1036,"xLinkHref":1414},"#MJX-13-TEX-I-1D458",[383,1416,1418],{"dataMmlNode":401,"transform":1417},"translate(972,0)",[395,1419],{"dataC":405,"xLinkHref":1420},"#MJX-13-TEX-N-28",[383,1422,1424],{"dataMmlNode":393,"transform":1423},"translate(1361,0)",[395,1425],{"dataC":412,"xLinkHref":1426},"#MJX-13-TEX-I-1D44F",[383,1428,1430],{"dataMmlNode":401,"transform":1429},"translate(1790,0)",[395,1431],{"dataC":419,"xLinkHref":1432},"#MJX-13-TEX-N-29"," = number of red kings",[39,1435,1436,1488],{},[347,1437,1439],{"className":1438,"jax":351},[350],[353,1440,1443,1457],{"style":355,"xmlns":356,"width":1441,"height":358,"role":94,"focusable":359,"viewBox":1442,"xmlnsXLink":361},"4.518ex","0 -750 1997 1000",[363,1444,1445,1448,1451,1454],{},[366,1446],{"id":1447,"d":377},"MJX-14-TEX-I-1D44F",[366,1449],{"id":1450,"d":851},"MJX-14-TEX-I-1D461",[366,1452],{"id":1453,"d":373},"MJX-14-TEX-N-28",[366,1455],{"id":1456,"d":381},"MJX-14-TEX-N-29",[383,1458,1459],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1460,1461,1466,1471,1477,1482],{"dataMmlNode":390},[383,1462,1463],{"dataMmlNode":393},[395,1464],{"dataC":412,"xLinkHref":1465},"#MJX-14-TEX-I-1D44F",[383,1467,1468],{"dataMmlNode":393,"transform":1238},[395,1469],{"dataC":1134,"xLinkHref":1470},"#MJX-14-TEX-I-1D461",[383,1472,1474],{"dataMmlNode":401,"transform":1473},"translate(790,0)",[395,1475],{"dataC":405,"xLinkHref":1476},"#MJX-14-TEX-N-28",[383,1478,1480],{"dataMmlNode":393,"transform":1479},"translate(1179,0)",[395,1481],{"dataC":412,"xLinkHref":1465},[383,1483,1485],{"dataMmlNode":401,"transform":1484},"translate(1608,0)",[395,1486],{"dataC":419,"xLinkHref":1487},"#MJX-14-TEX-N-29"," = number of black pieces under threat",[39,1490,1491,1547],{},[347,1492,1494],{"className":1493,"jax":351},[350],[353,1495,1498,1515],{"style":355,"xmlns":356,"width":1496,"height":358,"role":94,"focusable":359,"viewBox":1497,"xmlnsXLink":361},"4.568ex","0 -750 2019 1000",[363,1499,1500,1503,1506,1509,1512],{},[366,1501],{"id":1502,"d":831},"MJX-15-TEX-I-1D45F",[366,1504],{"id":1505,"d":851},"MJX-15-TEX-I-1D461",[366,1507],{"id":1508,"d":373},"MJX-15-TEX-N-28",[366,1510],{"id":1511,"d":377},"MJX-15-TEX-I-1D44F",[366,1513],{"id":1514,"d":381},"MJX-15-TEX-N-29",[383,1516,1517],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1518,1519,1524,1529,1535,1541],{"dataMmlNode":390},[383,1520,1521],{"dataMmlNode":393},[395,1522],{"dataC":981,"xLinkHref":1523},"#MJX-15-TEX-I-1D45F",[383,1525,1526],{"dataMmlNode":393,"transform":1297},[395,1527],{"dataC":1134,"xLinkHref":1528},"#MJX-15-TEX-I-1D461",[383,1530,1532],{"dataMmlNode":401,"transform":1531},"translate(812,0)",[395,1533],{"dataC":405,"xLinkHref":1534},"#MJX-15-TEX-N-28",[383,1536,1538],{"dataMmlNode":393,"transform":1537},"translate(1201,0)",[395,1539],{"dataC":412,"xLinkHref":1540},"#MJX-15-TEX-I-1D44F",[383,1542,1544],{"dataMmlNode":401,"transform":1543},"translate(1630,0)",[395,1545],{"dataC":419,"xLinkHref":1546},"#MJX-15-TEX-N-29"," = number of red pieces under threat",[16,1549,1550,1551,1588,1589,1615,1616,769],{},"The weights (",[347,1552,1554],{"className":1553,"jax":351},[350],[353,1555,1560,1565],{"style":1556,"xmlns":356,"width":1557,"height":1558,"role":94,"focusable":359,"viewBox":1559,"xmlnsXLink":361},"vertical-align: -0.452ex;","2.977ex","2.149ex","0 -750 1316 950",[363,1561,1562],{},[366,1563],{"id":1564,"d":805},"MJX-16-TEX-I-1D464",[383,1566,1567],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1568,1569,1574],{"dataMmlNode":390},[383,1570,1571],{"dataMmlNode":393},[395,1572],{"dataC":892,"xLinkHref":1573},"#MJX-16-TEX-I-1D464",[383,1575,1579],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":1578},"TeXAtom","ORD","translate(716,0)",[383,1580,1581],{"dataMmlNode":401},[1582,1583,1587],"text",{"dataVariant":1584,"transform":387,"font-size":1585,"font-family":1586},"normal","884px","serif","₀"," through ",[347,1590,1592],{"className":1591,"jax":351},[350],[353,1593,1594,1599],{"style":1556,"xmlns":356,"width":1557,"height":1558,"role":94,"focusable":359,"viewBox":1559,"xmlnsXLink":361},[363,1595,1596],{},[366,1597],{"id":1598,"d":805},"MJX-17-TEX-I-1D464",[383,1600,1601],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1602,1603,1608],{"dataMmlNode":390},[383,1604,1605],{"dataMmlNode":393},[395,1606],{"dataC":892,"xLinkHref":1607},"#MJX-17-TEX-I-1D464",[383,1609,1610],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":1578},[383,1611,1612],{"dataMmlNode":401},[1582,1613,1614],{"dataVariant":1584,"transform":387,"font-size":1585,"font-family":1586},"₆",") are what the system needs to ",[20,1617,1618],{},"learn",[134,1620,1622],{"id":1621},"training-with-indirect-experience","Training with Indirect Experience",[16,1624,1625,1626,1629,1630,1633],{},"Since we're learning from self-play, we don't have direct labels for every board position. Instead, we use ",[28,1627,1628],{},"temporal difference learning",": the estimated value of a board position is updated to be closer to the estimated value of the ",[20,1631,1632],{},"next"," board position in actual play. Over many games, accurate values from end-game positions gradually \"back up\" to earlier positions.",[134,1635,1637],{"id":1636},"the-lms-least-mean-squares-algorithm","The LMS (Least Mean Squares) Algorithm",[16,1639,1640],{},"To adjust the weights, we use gradient descent. For each training example:",[302,1642,1643,1838],{},[39,1644,1645,1646],{},"Compute the error: ",[347,1647,1649],{"className":1648,"jax":351},[350],[353,1650,1653,1699],{"style":355,"xmlns":356,"width":1651,"height":358,"role":94,"focusable":359,"viewBox":1652,"xmlnsXLink":361},"26.092ex","0 -750 11532.4 1000",[363,1654,1655,1659,1662,1666,1669,1672,1675,1678,1681,1684,1688,1692,1696],{},[366,1656],{"id":1657,"d":1658},"MJX-18-TEX-I-1D452","M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z",[366,1660],{"id":1661,"d":831},"MJX-18-TEX-I-1D45F",[366,1663],{"id":1664,"d":1665},"MJX-18-TEX-I-1D45C","M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z",[366,1667],{"id":1668,"d":373},"MJX-18-TEX-N-28",[366,1670],{"id":1671,"d":377},"MJX-18-TEX-I-1D44F",[366,1673],{"id":1674,"d":381},"MJX-18-TEX-N-29",[366,1676],{"id":1677,"d":450},"MJX-18-TEX-N-3D",[366,1679],{"id":1680,"d":369},"MJX-18-TEX-I-1D449",[366,1682],{"id":1683,"d":851},"MJX-18-TEX-I-1D461",[366,1685],{"id":1686,"d":1687},"MJX-18-TEX-I-1D44E","M33 157Q33 258 109 349T280 441Q331 441 370 392Q386 422 416 422Q429 422 439 414T449 394Q449 381 412 234T374 68Q374 43 381 35T402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487Q506 153 506 144Q506 138 501 117T481 63T449 13Q436 0 417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z",[366,1689],{"id":1690,"d":1691},"MJX-18-TEX-I-1D456","M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z",[366,1693],{"id":1694,"d":1695},"MJX-18-TEX-I-1D45B","M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",[366,1697],{"id":1698,"d":560},"MJX-18-TEX-N-2212",[383,1700,1701],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,1702,1703,1709,1715,1720,1727,1732,1738,1744,1750,1756,1797,1802,1807,1812,1818,1823,1828,1833],{"dataMmlNode":390},[383,1704,1705],{"dataMmlNode":393},[395,1706],{"dataC":1707,"xLinkHref":1708},"1D452","#MJX-18-TEX-I-1D452",[383,1710,1712],{"dataMmlNode":393,"transform":1711},"translate(466,0)",[395,1713],{"dataC":981,"xLinkHref":1714},"#MJX-18-TEX-I-1D45F",[383,1716,1718],{"dataMmlNode":393,"transform":1717},"translate(917,0)",[395,1719],{"dataC":981,"xLinkHref":1714},[383,1721,1723],{"dataMmlNode":393,"transform":1722},"translate(1368,0)",[395,1724],{"dataC":1725,"xLinkHref":1726},"1D45C","#MJX-18-TEX-I-1D45C",[383,1728,1730],{"dataMmlNode":393,"transform":1729},"translate(1853,0)",[395,1731],{"dataC":981,"xLinkHref":1714},[383,1733,1735],{"dataMmlNode":401,"transform":1734},"translate(2304,0)",[395,1736],{"dataC":405,"xLinkHref":1737},"#MJX-18-TEX-N-28",[383,1739,1741],{"dataMmlNode":393,"transform":1740},"translate(2693,0)",[395,1742],{"dataC":412,"xLinkHref":1743},"#MJX-18-TEX-I-1D44F",[383,1745,1747],{"dataMmlNode":401,"transform":1746},"translate(3122,0)",[395,1748],{"dataC":419,"xLinkHref":1749},"#MJX-18-TEX-N-29",[383,1751,1753],{"dataMmlNode":401,"transform":1752},"translate(3788.8,0)",[395,1754],{"dataC":488,"xLinkHref":1755},"#MJX-18-TEX-N-3D",[383,1757,1759,1764],{"dataMmlNode":887,"transform":1758},"translate(4844.6,0)",[383,1760,1761],{"dataMmlNode":393},[395,1762],{"dataC":397,"xLinkHref":1763},"#MJX-18-TEX-I-1D449",[383,1765,1767,1772,1777,1783,1790],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},"translate(616,-150) scale(0.707)",[383,1768,1769],{"dataMmlNode":393},[395,1770],{"dataC":1134,"xLinkHref":1771},"#MJX-18-TEX-I-1D461",[383,1773,1775],{"dataMmlNode":393,"transform":1774},"translate(361,0)",[395,1776],{"dataC":981,"xLinkHref":1714},[383,1778,1779],{"dataMmlNode":393,"transform":1531},[395,1780],{"dataC":1781,"xLinkHref":1782},"1D44E","#MJX-18-TEX-I-1D44E",[383,1784,1786],{"dataMmlNode":393,"transform":1785},"translate(1341,0)",[395,1787],{"dataC":1788,"xLinkHref":1789},"1D456","#MJX-18-TEX-I-1D456",[383,1791,1793],{"dataMmlNode":393,"transform":1792},"translate(1686,0)",[395,1794],{"dataC":1795,"xLinkHref":1796},"1D45B","#MJX-18-TEX-I-1D45B",[383,1798,1800],{"dataMmlNode":401,"transform":1799},"translate(7127,0)",[395,1801],{"dataC":405,"xLinkHref":1737},[383,1803,1805],{"dataMmlNode":393,"transform":1804},"translate(7516,0)",[395,1806],{"dataC":412,"xLinkHref":1743},[383,1808,1810],{"dataMmlNode":401,"transform":1809},"translate(7945,0)",[395,1811],{"dataC":419,"xLinkHref":1749},[383,1813,1815],{"dataMmlNode":401,"transform":1814},"translate(8556.2,0)",[395,1816],{"dataC":600,"xLinkHref":1817},"#MJX-18-TEX-N-2212",[383,1819,1821],{"dataMmlNode":393,"transform":1820},"translate(9556.4,0)",[395,1822],{"dataC":397,"xLinkHref":1763},[383,1824,1826],{"dataMmlNode":401,"transform":1825},"translate(10325.4,0)",[395,1827],{"dataC":405,"xLinkHref":1737},[383,1829,1831],{"dataMmlNode":393,"transform":1830},"translate(10714.4,0)",[395,1832],{"dataC":412,"xLinkHref":1743},[383,1834,1836],{"dataMmlNode":401,"transform":1835},"translate(11143.4,0)",[395,1837],{"dataC":419,"xLinkHref":1749},[39,1839,1840,1841],{},"Update each weight: ",[347,1842,1844],{"className":1843,"jax":351},[350],[353,1845,1848,1891],{"style":355,"xmlns":356,"width":1846,"height":358,"role":94,"focusable":359,"viewBox":1847,"xmlnsXLink":361},"24.542ex","0 -750 10847.7 1000",[363,1849,1850,1853,1856,1859,1862,1866,1869,1873,1876,1879,1882,1885,1888],{},[366,1851],{"id":1852,"d":805},"MJX-19-TEX-I-1D464",[366,1854],{"id":1855,"d":1691},"MJX-19-TEX-I-1D456",[366,1857],{"id":1858,"d":450},"MJX-19-TEX-N-3D",[366,1860],{"id":1861,"d":812},"MJX-19-TEX-N-2B",[366,1863],{"id":1864,"d":1865},"MJX-19-TEX-I-1D450","M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 408 306T360 285Q341 285 330 295T319 325T330 359T352 380T366 386H367Q367 388 361 392T340 400T306 404Q276 404 249 390Q228 381 206 359Q162 315 142 235T121 119Q121 73 147 50Q169 26 205 26H209Q321 26 394 111Q403 121 406 121Q410 121 419 112T429 98T420 83T391 55T346 25T282 0T202 -11Q127 -11 81 37T34 159Z",[366,1867],{"id":1868,"d":819},"MJX-19-TEX-N-22C5",[366,1870],{"id":1871,"d":1872},"MJX-19-TEX-I-1D453","M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 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scale(0.707)",[395,1956],{"dataC":1788,"xLinkHref":1906},[383,1958,1960],{"dataMmlNode":401,"transform":1959},"translate(6836.5,0)",[395,1961],{"dataC":924,"xLinkHref":1942},[383,1963,1965],{"dataMmlNode":393,"transform":1964},"translate(7336.7,0)",[395,1966],{"dataC":1707,"xLinkHref":1967},"#MJX-19-TEX-I-1D452",[383,1969,1971],{"dataMmlNode":393,"transform":1970},"translate(7802.7,0)",[395,1972],{"dataC":981,"xLinkHref":1973},"#MJX-19-TEX-I-1D45F",[383,1975,1977],{"dataMmlNode":393,"transform":1976},"translate(8253.7,0)",[395,1978],{"dataC":981,"xLinkHref":1973},[383,1980,1982],{"dataMmlNode":393,"transform":1981},"translate(8704.7,0)",[395,1983],{"dataC":1725,"xLinkHref":1984},"#MJX-19-TEX-I-1D45C",[383,1986,1988],{"dataMmlNode":393,"transform":1987},"translate(9189.7,0)",[395,1989],{"dataC":981,"xLinkHref":1973},[383,1991,1993],{"dataMmlNode":401,"transform":1992},"translate(9640.7,0)",[395,1994],{"dataC":405,"xLinkHref":1995},"#MJX-19-TEX-N-28",[383,1997,1999],{"dataMmlNode":393,"transform":1998},"translate(10029.7,0)",[395,2000],{"dataC":412,"xLinkHref":2001},"#MJX-19-TEX-I-1D44F",[383,2003,2005],{"dataMmlNode":401,"transform":2004},"translate(10458.7,0)",[395,2006],{"dataC":419,"xLinkHref":2007},"#MJX-19-TEX-N-29",[16,2009,2010,2011,2033,2034,2064],{},"Here, ",[347,2012,2014],{"className":2013,"jax":351},[350],[353,2015,2019,2024],{"style":512,"xmlns":356,"width":2016,"height":2017,"role":94,"focusable":359,"viewBox":2018,"xmlnsXLink":361},"0.98ex","1.025ex","0 -442 433 453",[363,2020,2021],{},[366,2022],{"id":2023,"d":1865},"MJX-20-TEX-I-1D450",[383,2025,2026],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2027,2028],{"dataMmlNode":390},[383,2029,2030],{"dataMmlNode":393},[395,2031],{"dataC":1935,"xLinkHref":2032},"#MJX-20-TEX-I-1D450"," is a small learning rate, and ",[347,2035,2037],{"className":2036,"jax":351},[350],[353,2038,2043,2048],{"style":2039,"xmlns":356,"width":2040,"height":2041,"role":94,"focusable":359,"viewBox":2042,"xmlnsXLink":361},"vertical-align: -0.464ex;","2.602ex","2.161ex","0 -750 1150 955",[363,2044,2045],{},[366,2046],{"id":2047,"d":1872},"MJX-21-TEX-I-1D453",[383,2049,2050],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2051,2052,2057],{"dataMmlNode":390},[383,2053,2054],{"dataMmlNode":393},[395,2055],{"dataC":1950,"xLinkHref":2056},"#MJX-21-TEX-I-1D453",[383,2058,2060],{"dataMmlNode":393,"transform":2059},"translate(550,0)",[1582,2061,2063],{"dataVariant":2062,"transform":387,"font-size":1585,"font-family":1586,"font-style":2062},"italic","ᵢ"," is the value of the i-th feature for board b.",[2066,2067,2071,2075],"details",{"className":2068},[2069,2070],"info-box","info-box-info",[2072,2073,2074],"summary",{},"Deriving LMS",[2076,2077,2080,2130,2388,2459,2486,2635,2638,2641,2839,2842,2883,2886,2999,3046,3112,3187,3199,3202,3345,3643,3646,3872,3875,4049,4055,4078,4214,4217,4391,4394,4550,4553,4645,4746,4749,4826,4828,4835,4855,4858,4863,4943,4949,5100,5105,5249],"div",{"className":2078},[2079],"info-box-content",[16,2081,2082,2083,769,2126,2129],{},"Let's take the guess from our AI, and call it ",[347,2084,2086],{"className":2085,"jax":351},[350],[353,2087,2088,2102],{"style":355,"xmlns":356,"width":357,"height":358,"role":94,"focusable":359,"viewBox":360,"xmlnsXLink":361},[363,2089,2090,2093,2096,2099],{},[366,2091],{"id":2092,"d":369},"MJX-22-TEX-I-1D449",[366,2094],{"id":2095,"d":373},"MJX-22-TEX-N-28",[366,2097],{"id":2098,"d":377},"MJX-22-TEX-I-1D44F",[366,2100],{"id":2101,"d":381},"MJX-22-TEX-N-29",[383,2103,2104],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2105,2106,2111,2116,2121],{"dataMmlNode":390},[383,2107,2108],{"dataMmlNode":393},[395,2109],{"dataC":397,"xLinkHref":2110},"#MJX-22-TEX-I-1D449",[383,2112,2113],{"dataMmlNode":401,"transform":402},[395,2114],{"dataC":405,"xLinkHref":2115},"#MJX-22-TEX-N-28",[383,2117,2118],{"dataMmlNode":393,"transform":409},[395,2119],{"dataC":412,"xLinkHref":2120},"#MJX-22-TEX-I-1D44F",[383,2122,2123],{"dataMmlNode":401,"transform":416},[395,2124],{"dataC":419,"xLinkHref":2125},"#MJX-22-TEX-N-29",[2127,2128],"br",{},"\nAI is just taking an approximation here, or just guessing random number, we can't really tell, so we can't rely on it entirely.",[16,2131,2132,2133,2225,2226,2228,2229,769],{},"So, we define another variable, ",[347,2134,2136],{"className":2135,"jax":351},[350],[353,2137,2140,2169],{"style":355,"xmlns":356,"width":2138,"height":358,"role":94,"focusable":359,"viewBox":2139,"xmlnsXLink":361},"7.895ex","0 -750 3489.4 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that represents the answer that the AI should have guessed.",[2127,2227],{},"\nAnd the raw mistake is just ",[347,2230,2232],{"className":2231,"jax":351},[350],[353,2233,2234,2275],{"style":355,"xmlns":356,"width":1651,"height":358,"role":94,"focusable":359,"viewBox":1652,"xmlnsXLink":361},[363,2235,2236,2239,2242,2245,2248,2251,2254,2257,2260,2263,2266,2269,2272],{},[366,2237],{"id":2238,"d":1658},"MJX-24-TEX-I-1D452",[366,2240],{"id":2241,"d":831},"MJX-24-TEX-I-1D45F",[366,2243],{"id":2244,"d":1665},"MJX-24-TEX-I-1D45C",[366,2246],{"id":2247,"d":373},"MJX-24-TEX-N-28",[366,2249],{"id":2250,"d":377},"MJX-24-TEX-I-1D44F",[366,2252],{"id":2253,"d":381},"MJX-24-TEX-N-29",[366,2255],{"id":2256,"d":450},"MJX-24-TEX-N-3D",[366,2258],{"id":2259,"d":369},"MJX-24-TEX-I-1D449",[366,2261],{"id":2262,"d":851},"MJX-24-TEX-I-1D461",[366,2264],{"id":2265,"d":1687},"MJX-24-TEX-I-1D44E",[366,2267],{"id":2268,"d":1691},"MJX-24-TEX-I-1D456",[366,2270],{"id":2271,"d":1695},"MJX-24-TEX-I-1D45B",[366,2273],{"id":2274,"d":560},"MJX-24-TEX-N-2212",[383,2276,2277],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2278,2279,2284,2289,2293,2298,2302,2307,2312,2317,2322,2355,2359,2363,2367,2372,2376,2380,2384],{"dataMmlNode":390},[383,2280,2281],{"dataMmlNode":393},[395,2282],{"dataC":1707,"xLinkHref":2283},"#MJX-24-TEX-I-1D452",[383,2285,2286],{"dataMmlNode":393,"transform":1711},[395,2287],{"dataC":981,"xLinkHref":2288},"#MJX-24-TEX-I-1D45F",[383,2290,2291],{"dataMmlNode":393,"transform":1717},[395,2292],{"dataC":981,"xLinkHref":2288},[383,2294,2295],{"dataMmlNode":393,"transform":1722},[395,2296],{"dataC":1725,"xLinkHref":2297},"#MJX-24-TEX-I-1D45C",[383,2299,2300],{"dataMmlNode":393,"transform":1729},[395,2301],{"dataC":981,"xLinkHref":2288},[383,2303,2304],{"dataMmlNode":401,"transform":1734},[395,2305],{"dataC":405,"xLinkHref":2306},"#MJX-24-TEX-N-28",[383,2308,2309],{"dataMmlNode":393,"transform":1740},[395,2310],{"dataC":412,"xLinkHref":2311},"#MJX-24-TEX-I-1D44F",[383,2313,2314],{"dataMmlNode":401,"transform":1746},[395,2315],{"dataC":419,"xLinkHref":2316},"#MJX-24-TEX-N-29",[383,2318,2319],{"dataMmlNode":401,"transform":1752},[395,2320],{"dataC":488,"xLinkHref":2321},"#MJX-24-TEX-N-3D",[383,2323,2324,2329],{"dataMmlNode":887,"transform":1758},[383,2325,2326],{"dataMmlNode":393},[395,2327],{"dataC":397,"xLinkHref":2328},"#MJX-24-TEX-I-1D449",[383,2330,2331,2336,2340,2345,2350],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,2332,2333],{"dataMmlNode":393},[395,2334],{"dataC":1134,"xLinkHref":2335},"#MJX-24-TEX-I-1D461",[383,2337,2338],{"dataMmlNode":393,"transform":1774},[395,2339],{"dataC":981,"xLinkHref":2288},[383,2341,2342],{"dataMmlNode":393,"transform":1531},[395,2343],{"dataC":1781,"xLinkHref":2344},"#MJX-24-TEX-I-1D44E",[383,2346,2347],{"dataMmlNode":393,"transform":1785},[395,2348],{"dataC":1788,"xLinkHref":2349},"#MJX-24-TEX-I-1D456",[383,2351,2352],{"dataMmlNode":393,"transform":1792},[395,2353],{"dataC":1795,"xLinkHref":2354},"#MJX-24-TEX-I-1D45B",[383,2356,2357],{"dataMmlNode":401,"transform":1799},[395,2358],{"dataC":405,"xLinkHref":2306},[383,2360,2361],{"dataMmlNode":393,"transform":1804},[395,2362],{"dataC":412,"xLinkHref":2311},[383,2364,2365],{"dataMmlNode":401,"transform":1809},[395,2366],{"dataC":419,"xLinkHref":2316},[383,2368,2369],{"dataMmlNode":401,"transform":1814},[395,2370],{"dataC":600,"xLinkHref":2371},"#MJX-24-TEX-N-2212",[383,2373,2374],{"dataMmlNode":393,"transform":1820},[395,2375],{"dataC":397,"xLinkHref":2328},[383,2377,2378],{"dataMmlNode":401,"transform":1825},[395,2379],{"dataC":405,"xLinkHref":2306},[383,2381,2382],{"dataMmlNode":393,"transform":1830},[395,2383],{"dataC":412,"xLinkHref":2311},[383,2385,2386],{"dataMmlNode":401,"transform":1835},[395,2387],{"dataC":419,"xLinkHref":2316},[16,2389,2390,2391,2458],{},"Let's place ",[347,2392,2394],{"className":2393,"jax":351},[350],[353,2395,2400,2420],{"style":2396,"xmlns":356,"width":2397,"height":2398,"role":94,"focusable":359,"viewBox":2399,"xmlnsXLink":361},"vertical-align: -0.357ex;","5.164ex","1.902ex","0 -683 2282.4 840.8",[363,2401,2402,2405,2408,2411,2414,2417],{},[366,2403],{"id":2404,"d":369},"MJX-25-TEX-I-1D449",[366,2406],{"id":2407,"d":851},"MJX-25-TEX-I-1D461",[366,2409],{"id":2410,"d":831},"MJX-25-TEX-I-1D45F",[366,2412],{"id":2413,"d":1687},"MJX-25-TEX-I-1D44E",[366,2415],{"id":2416,"d":1691},"MJX-25-TEX-I-1D456",[366,2418],{"id":2419,"d":1695},"MJX-25-TEX-I-1D45B",[383,2421,2422],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2423,2424],{"dataMmlNode":390},[383,2425,2426,2431],{"dataMmlNode":887},[383,2427,2428],{"dataMmlNode":393},[395,2429],{"dataC":397,"xLinkHref":2430},"#MJX-25-TEX-I-1D449",[383,2432,2433,2438,2443,2448,2453],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,2434,2435],{"dataMmlNode":393},[395,2436],{"dataC":1134,"xLinkHref":2437},"#MJX-25-TEX-I-1D461",[383,2439,2440],{"dataMmlNode":393,"transform":1774},[395,2441],{"dataC":981,"xLinkHref":2442},"#MJX-25-TEX-I-1D45F",[383,2444,2445],{"dataMmlNode":393,"transform":1531},[395,2446],{"dataC":1781,"xLinkHref":2447},"#MJX-25-TEX-I-1D44E",[383,2449,2450],{"dataMmlNode":393,"transform":1785},[395,2451],{"dataC":1788,"xLinkHref":2452},"#MJX-25-TEX-I-1D456",[383,2454,2455],{"dataMmlNode":393,"transform":1792},[395,2456],{"dataC":1795,"xLinkHref":2457},"#MJX-25-TEX-I-1D45B"," aside first, and just pretend that it's a magical function that spits out the accurate score every time.",[16,2460,2461,2462,769],{},"Now, we need a way to tell AI how bad it is doing overall. That's our cost function, let's call it ",[347,2463,2465],{"className":2464,"jax":351},[350],[353,2466,2470,2476],{"style":2467,"xmlns":356,"width":2468,"height":514,"role":94,"focusable":359,"viewBox":2469,"xmlnsXLink":361},"vertical-align: -0.05ex;","1.432ex","0 -683 633 705",[363,2471,2472],{},[366,2473],{"id":2474,"d":2475},"MJX-26-TEX-I-1D43D","M447 625Q447 637 354 637H329Q323 642 323 645T325 664Q329 677 335 683H352Q393 681 498 681Q541 681 568 681T605 682T619 682Q633 682 633 672Q633 670 630 658Q626 642 623 640T604 637Q552 637 545 623Q541 610 483 376Q420 128 419 127Q397 64 333 21T195 -22Q137 -22 97 8T57 88Q57 130 80 152T132 174Q177 174 182 130Q182 98 164 80T123 56Q115 54 115 53T122 44Q148 15 197 15Q235 15 271 47T324 130Q328 142 387 380T447 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this creates a problem: A huge positive error (guessing too low) and a huge negative error (guessing too high) will cancel each other out, making it look like the model is doing a great job when it isn't.",[16,2639,2640],{},"By squaring the error:",[347,2642,2644],{"className":2643,"jax":351,"display":780},[350],[353,2645,2650,2698],{"style":2646,"xmlns":356,"width":2647,"height":2648,"role":94,"focusable":359,"viewBox":2649,"xmlnsXLink":361},"vertical-align: -1.552ex;","26.203ex","4.588ex","0 -1342 11581.6 2028",[363,2651,2652,2655,2658,2661,2664,2667,2670,2673,2676,2679,2682,2685,2689,2692,2695],{},[366,2653],{"id":2654,"d":2475},"MJX-28-TEX-I-1D43D",[366,2656],{"id":2657,"d":450},"MJX-28-TEX-N-3D",[366,2659],{"id":2660,"d":454},"MJX-28-TEX-N-31",[366,2662],{"id":2663,"d":827},"MJX-28-TEX-N-32",[366,2665],{"id":2666,"d":373},"MJX-28-TEX-N-28",[366,2668],{"id":2669,"d":369},"MJX-28-TEX-I-1D449",[366,2671],{"id":2672,"d":851},"MJX-28-TEX-I-1D461",[366,2674],{"id":2675,"d":831},"MJX-28-TEX-I-1D45F",[366,2677],{"id":2678,"d":1687},"MJX-28-TEX-I-1D44E",[366,2680],{"id":2681,"d":1691},"MJX-28-TEX-I-1D456",[366,2683],{"id":2684,"d":1695},"MJX-28-TEX-I-1D45B",[366,2686],{"id":2687,"d":2688},"MJX-28-TEX-N-200B","",[366,2690],{"id":2691,"d":377},"MJX-28-TEX-I-1D44F",[366,2693],{"id":2694,"d":381},"MJX-28-TEX-N-29",[366,2696],{"id":2697,"d":560},"MJX-28-TEX-N-2212",[383,2699,2700],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2701,2702,2707,2712,2734,2740,2746,2783,2788,2794,2800,2806,2811,2816,2821,2826],{"dataMmlNode":390},[383,2703,2704],{"dataMmlNode":393},[395,2705],{"dataC":2484,"xLinkHref":2706},"#MJX-28-TEX-I-1D43D",[383,2708,2709],{"dataMmlNode":401,"transform":2542},[395,2710],{"dataC":488,"xLinkHref":2711},"#MJX-28-TEX-N-3D",[383,2713,2715,2721,2727],{"dataMmlNode":2714,"transform":2548},"mfrac",[383,2716,2718],{"dataMmlNode":492,"transform":2717},"translate(220,676)",[395,2719],{"dataC":496,"xLinkHref":2720},"#MJX-28-TEX-N-31",[383,2722,2724],{"dataMmlNode":492,"transform":2723},"translate(220,-686)",[395,2725],{"dataC":969,"xLinkHref":2726},"#MJX-28-TEX-N-32",[2728,2729],"rect",{"width":2730,"height":2731,"x":2732,"y":2733},700,60,"120","220",[383,2735,2737],{"dataMmlNode":401,"transform":2736},"translate(2906.6,0)",[395,2738],{"dataC":405,"xLinkHref":2739},"#MJX-28-TEX-N-28",[383,2741,2743],{"dataMmlNode":393,"transform":2742},"translate(3295.6,0)",[395,2744],{"dataC":397,"xLinkHref":2745},"#MJX-28-TEX-I-1D449",[383,2747,2749,2754,2759,2764,2769,2774],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":2748},"translate(4064.6,0)",[383,2750,2751],{"dataMmlNode":393},[395,2752],{"dataC":1134,"xLinkHref":2753},"#MJX-28-TEX-I-1D461",[383,2755,2756],{"dataMmlNode":393,"transform":1774},[395,2757],{"dataC":981,"xLinkHref":2758},"#MJX-28-TEX-I-1D45F",[383,2760,2761],{"dataMmlNode":393,"transform":1531},[395,2762],{"dataC":1781,"xLinkHref":2763},"#MJX-28-TEX-I-1D44E",[383,2765,2766],{"dataMmlNode":393,"transform":1785},[395,2767],{"dataC":1788,"xLinkHref":2768},"#MJX-28-TEX-I-1D456",[383,2770,2771],{"dataMmlNode":393,"transform":1792},[395,2772],{"dataC":1795,"xLinkHref":2773},"#MJX-28-TEX-I-1D45B",[383,2775,2777],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":2776},"translate(2286,0)",[383,2778,2779],{"dataMmlNode":401},[395,2780],{"dataC":2781,"xLinkHref":2782},"200B","#MJX-28-TEX-N-200B",[383,2784,2786],{"dataMmlNode":401,"transform":2785},"translate(6350.6,0)",[395,2787],{"dataC":405,"xLinkHref":2739},[383,2789,2791],{"dataMmlNode":393,"transform":2790},"translate(6739.6,0)",[395,2792],{"dataC":412,"xLinkHref":2793},"#MJX-28-TEX-I-1D44F",[383,2795,2797],{"dataMmlNode":401,"transform":2796},"translate(7168.6,0)",[395,2798],{"dataC":419,"xLinkHref":2799},"#MJX-28-TEX-N-29",[383,2801,2803],{"dataMmlNode":401,"transform":2802},"translate(7779.8,0)",[395,2804],{"dataC":600,"xLinkHref":2805},"#MJX-28-TEX-N-2212",[383,2807,2809],{"dataMmlNode":393,"transform":2808},"translate(8780,0)",[395,2810],{"dataC":397,"xLinkHref":2745},[383,2812,2814],{"dataMmlNode":401,"transform":2813},"translate(9549,0)",[395,2815],{"dataC":405,"xLinkHref":2739},[383,2817,2819],{"dataMmlNode":393,"transform":2818},"translate(9938,0)",[395,2820],{"dataC":412,"xLinkHref":2793},[383,2822,2824],{"dataMmlNode":401,"transform":2823},"translate(10367,0)",[395,2825],{"dataC":419,"xLinkHref":2799},[383,2827,2830,2834],{"dataMmlNode":2828,"transform":2829},"msup","translate(10756,0)",[383,2831,2832],{"dataMmlNode":401},[395,2833],{"dataC":419,"xLinkHref":2799},[383,2835,2837],{"dataMmlNode":492,"transform":2836},"translate(422,413) scale(0.707)",[395,2838],{"dataC":969,"xLinkHref":2726},[16,2840,2841],{},"...we ensure that all errors are positive, and larger errors are heavily penalised.",[16,2843,2844,2845,769],{},"When you use calculus to find the derivative (gradient) of that squared error equation to figure out how to adjust the weights, the 2 from the exponent drops down, cancels out the ",[347,2846,2848],{"className":2847,"jax":351},[350],[353,2849,2854,2862],{"style":2850,"xmlns":356,"width":2851,"height":2852,"role":94,"focusable":359,"viewBox":2853,"xmlnsXLink":361},"vertical-align: -0.781ex;","1.795ex","2.737ex","0 -864.9 793.6 1209.9",[363,2855,2856,2859],{},[366,2857],{"id":2858,"d":454},"MJX-29-TEX-N-31",[366,2860],{"id":2861,"d":827},"MJX-29-TEX-N-32",[383,2863,2864],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2865,2866],{"dataMmlNode":390},[383,2867,2868,2874,2880],{"dataMmlNode":2714},[383,2869,2871],{"dataMmlNode":492,"transform":2870},"translate(220,394) scale(0.707)",[395,2872],{"dataC":496,"xLinkHref":2873},"#MJX-29-TEX-N-31",[383,2875,2877],{"dataMmlNode":492,"transform":2876},"translate(220,-345) scale(0.707)",[395,2878],{"dataC":969,"xLinkHref":2879},"#MJX-29-TEX-N-32",[2728,2881],{"width":2882,"height":2731,"x":2732,"y":2733},553.6,[16,2884,2885],{},"Your mission is now to make J as close to zero as possible.",[2887,2888,2889,2924],"blockquote",{},[16,2890,2891,2892,2923],{},"You might ask, why is ",[347,2893,2895],{"className":2894,"jax":351},[350],[353,2896,2897,2905],{"style":2850,"xmlns":356,"width":2851,"height":2852,"role":94,"focusable":359,"viewBox":2853,"xmlnsXLink":361},[363,2898,2899,2902],{},[366,2900],{"id":2901,"d":454},"MJX-30-TEX-N-31",[366,2903],{"id":2904,"d":827},"MJX-30-TEX-N-32",[383,2906,2907],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2908,2909],{"dataMmlNode":390},[383,2910,2911,2916,2921],{"dataMmlNode":2714},[383,2912,2913],{"dataMmlNode":492,"transform":2870},[395,2914],{"dataC":496,"xLinkHref":2915},"#MJX-30-TEX-N-31",[383,2917,2918],{"dataMmlNode":492,"transform":2876},[395,2919],{"dataC":969,"xLinkHref":2920},"#MJX-30-TEX-N-32",[2728,2922],{"width":2882,"height":2731,"x":2732,"y":2733},"  allowed here?",[16,2925,2926,2927,2946,2947,2966,2967,2998],{},"As our aim is to minimise ",[347,2928,2930],{"className":2929,"jax":351},[350],[353,2931,2932,2937],{"style":2467,"xmlns":356,"width":2468,"height":514,"role":94,"focusable":359,"viewBox":2469,"xmlnsXLink":361},[363,2933,2934],{},[366,2935],{"id":2936,"d":2475},"MJX-31-TEX-I-1D43D",[383,2938,2939],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2940,2941],{"dataMmlNode":390},[383,2942,2943],{"dataMmlNode":393},[395,2944],{"dataC":2484,"xLinkHref":2945},"#MJX-31-TEX-I-1D43D"," (turning it to 0), although we are halving the hill's height and the gradient here, but it doesn't matter as long as we can get to the bottom of the hill. And we also utilise a learning rate ",[347,2948,2950],{"className":2949,"jax":351},[350],[353,2951,2952,2957],{"style":512,"xmlns":356,"width":2016,"height":2017,"role":94,"focusable":359,"viewBox":2018,"xmlnsXLink":361},[363,2953,2954],{},[366,2955],{"id":2956,"d":1865},"MJX-32-TEX-I-1D450",[383,2958,2959],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2960,2961],{"dataMmlNode":390},[383,2962,2963],{"dataMmlNode":393},[395,2964],{"dataC":1935,"xLinkHref":2965},"#MJX-32-TEX-I-1D450"," later in the equation too, which can be anything the user wants to be. So this ",[347,2968,2970],{"className":2969,"jax":351},[350],[353,2971,2972,2980],{"style":2850,"xmlns":356,"width":2851,"height":2852,"role":94,"focusable":359,"viewBox":2853,"xmlnsXLink":361},[363,2973,2974,2977],{},[366,2975],{"id":2976,"d":454},"MJX-33-TEX-N-31",[366,2978],{"id":2979,"d":827},"MJX-33-TEX-N-32",[383,2981,2982],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,2983,2984],{"dataMmlNode":390},[383,2985,2986,2991,2996],{"dataMmlNode":2714},[383,2987,2988],{"dataMmlNode":492,"transform":2870},[395,2989],{"dataC":496,"xLinkHref":2990},"#MJX-33-TEX-N-31",[383,2992,2993],{"dataMmlNode":492,"transform":2876},[395,2994],{"dataC":969,"xLinkHref":2995},"#MJX-33-TEX-N-32",[2728,2997],{"width":2882,"height":2731,"x":2732,"y":2733}," gets absorbed into the learning rate anyways.",[16,3000,3001,3002,3045],{},"To make J smaller, you have to tweak your weights (",[347,3003,3005],{"className":3004,"jax":351},[350],[353,3006,3010,3021],{"style":2396,"xmlns":356,"width":3007,"height":3008,"role":94,"focusable":359,"viewBox":3009,"xmlnsXLink":361},"2.36ex","1.359ex","0 -443 1043 600.8",[363,3011,3012,3015,3018],{},[366,3013],{"id":3014,"d":805},"MJX-34-TEX-I-1D464",[366,3016],{"id":3017,"d":1691},"MJX-34-TEX-I-1D456",[366,3019],{"id":3020,"d":2688},"MJX-34-TEX-N-200B",[383,3022,3023],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3024,3025,3037],{"dataMmlNode":390},[383,3026,3027,3032],{"dataMmlNode":887},[383,3028,3029],{"dataMmlNode":393},[395,3030],{"dataC":892,"xLinkHref":3031},"#MJX-34-TEX-I-1D464",[383,3033,3034],{"dataMmlNode":393,"transform":896},[395,3035],{"dataC":1788,"xLinkHref":3036},"#MJX-34-TEX-I-1D456",[383,3038,3040],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3039},"translate(1043,0)",[383,3041,3042],{"dataMmlNode":401},[395,3043],{"dataC":2781,"xLinkHref":3044},"#MJX-34-TEX-N-200B","). But do you tweak them up or down?",[16,3047,3048,3049],{},"You ask: ",[20,3050,3051,3052,3091,3092,3111],{},"\"If I bump up a specific weight (",[347,3053,3055],{"className":3054,"jax":351},[350],[353,3056,3057,3068],{"style":2396,"xmlns":356,"width":3007,"height":3008,"role":94,"focusable":359,"viewBox":3009,"xmlnsXLink":361},[363,3058,3059,3062,3065],{},[366,3060],{"id":3061,"d":805},"MJX-35-TEX-I-1D464",[366,3063],{"id":3064,"d":1691},"MJX-35-TEX-I-1D456",[366,3066],{"id":3067,"d":2688},"MJX-35-TEX-N-200B",[383,3069,3070],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3071,3072,3084],{"dataMmlNode":390},[383,3073,3074,3079],{"dataMmlNode":887},[383,3075,3076],{"dataMmlNode":393},[395,3077],{"dataC":892,"xLinkHref":3078},"#MJX-35-TEX-I-1D464",[383,3080,3081],{"dataMmlNode":393,"transform":896},[395,3082],{"dataC":1788,"xLinkHref":3083},"#MJX-35-TEX-I-1D456",[383,3085,3086],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3039},[383,3087,3088],{"dataMmlNode":401},[395,3089],{"dataC":2781,"xLinkHref":3090},"#MJX-35-TEX-N-200B",") by a tiny amount, does my total error (",[347,3093,3095],{"className":3094,"jax":351},[350],[353,3096,3097,3102],{"style":2467,"xmlns":356,"width":2468,"height":514,"role":94,"focusable":359,"viewBox":2469,"xmlnsXLink":361},[363,3098,3099],{},[366,3100],{"id":3101,"d":2475},"MJX-36-TEX-I-1D43D",[383,3103,3104],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3105,3106],{"dataMmlNode":390},[383,3107,3108],{"dataMmlNode":393},[395,3109],{"dataC":2484,"xLinkHref":3110},"#MJX-36-TEX-I-1D43D",") go up or down, and by how much?\"",[16,3113,3114,3115,769],{},"So, you take the derivative of your Cost function with respect to that specific weight: ",[347,3116,3118],{"className":3117,"jax":351},[350],[353,3119,3124,3139],{"style":3120,"xmlns":356,"width":3121,"height":3122,"role":94,"focusable":359,"viewBox":3123,"xmlnsXLink":361},"vertical-align: -1.034ex;","3.569ex","3.07ex","0 -899.6 1577.7 1356.7",[363,3125,3126,3130,3133,3136],{},[366,3127],{"id":3128,"d":3129},"MJX-37-TEX-I-1D715","M202 508Q179 508 169 520T158 547Q158 557 164 577T185 624T230 675T301 710L333 715H345Q378 715 384 714Q447 703 489 661T549 568T566 457Q566 362 519 240T402 53Q321 -22 223 -22Q123 -22 73 56Q42 102 42 148V159Q42 276 129 370T322 465Q383 465 414 434T455 367L458 378Q478 461 478 515Q478 603 437 639T344 676Q266 676 223 612Q264 606 264 572Q264 547 246 528T202 508ZM430 306Q430 372 401 400T333 428Q270 428 222 382Q197 354 183 323T150 221Q132 149 132 116Q132 21 232 21Q244 21 250 22Q327 35 374 112Q389 137 409 196T430 306Z",[366,3131],{"id":3132,"d":2475},"MJX-37-TEX-I-1D43D",[366,3134],{"id":3135,"d":805},"MJX-37-TEX-I-1D464",[366,3137],{"id":3138,"d":1691},"MJX-37-TEX-I-1D456",[383,3140,3141],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3142,3143],{"dataMmlNode":390},[383,3144,3145,3163,3184],{"dataMmlNode":2714},[383,3146,3149,3155],{"dataMmlNode":3147,"transform":3148},"mrow","translate(364.9,394) scale(0.707)",[383,3150,3151],{"dataMmlNode":393},[395,3152],{"dataC":3153,"xLinkHref":3154},"1D715","#MJX-37-TEX-I-1D715",[383,3156,3158],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3157},"translate(566,0)",[383,3159,3160],{"dataMmlNode":393},[395,3161],{"dataC":2484,"xLinkHref":3162},"#MJX-37-TEX-I-1D43D",[383,3164,3166,3170],{"dataMmlNode":3147,"transform":3165},"translate(220,-345.6) scale(0.707)",[383,3167,3168],{"dataMmlNode":393},[395,3169],{"dataC":3153,"xLinkHref":3154},[383,3171,3172],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3157},[383,3173,3174,3179],{"dataMmlNode":887},[383,3175,3176],{"dataMmlNode":393},[395,3177],{"dataC":892,"xLinkHref":3178},"#MJX-37-TEX-I-1D464",[383,3180,3181],{"dataMmlNode":393,"transform":896},[395,3182],{"dataC":1788,"xLinkHref":3183},"#MJX-37-TEX-I-1D456",[2728,3185],{"width":3186,"height":2731,"x":2732,"y":2733},1337.7,[2887,3188,3189],{},[16,3190,3191,3192,769],{},"Learn more about partial derivatives ",[3193,3194,3198],"a",{"href":3195,"rel":3196},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002FArtificial-Neural-Networks-and-Backpropagation#partial-derivative",[3197],"nofollow","here",[16,3200,3201],{},"Now we can use chain rule on our cost function.",[16,3203,3204,3205],{},"Outside: ",[347,3206,3208],{"className":3207,"jax":351},[350],[353,3209,3212,3247],{"style":355,"xmlns":356,"width":3210,"height":358,"role":94,"focusable":359,"viewBox":3211,"xmlnsXLink":361},"16.891ex","0 -750 7465.9 1000",[363,3213,3214,3217,3220,3223,3226,3229,3232,3235,3238,3241,3244],{},[366,3215],{"id":3216,"d":373},"MJX-38-TEX-N-28",[366,3218],{"id":3219,"d":369},"MJX-38-TEX-I-1D449",[366,3221],{"id":3222,"d":851},"MJX-38-TEX-I-1D461",[366,3224],{"id":3225,"d":831},"MJX-38-TEX-I-1D45F",[366,3227],{"id":3228,"d":1687},"MJX-38-TEX-I-1D44E",[366,3230],{"id":3231,"d":1691},"MJX-38-TEX-I-1D456",[366,3233],{"id":3234,"d":1695},"MJX-38-TEX-I-1D45B",[366,3236],{"id":3237,"d":2688},"MJX-38-TEX-N-200B",[366,3239],{"id":3240,"d":377},"MJX-38-TEX-I-1D44F",[366,3242],{"id":3243,"d":381},"MJX-38-TEX-N-29",[366,3245],{"id":3246,"d":560},"MJX-38-TEX-N-2212",[383,3248,3249],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3250,3251,3256,3298,3302,3308,3314,3320,3325,3330,3335,3340],{"dataMmlNode":390},[383,3252,3253],{"dataMmlNode":401},[395,3254],{"dataC":405,"xLinkHref":3255},"#MJX-38-TEX-N-28",[383,3257,3259,3264],{"dataMmlNode":887,"transform":3258},"translate(389,0)",[383,3260,3261],{"dataMmlNode":393},[395,3262],{"dataC":397,"xLinkHref":3263},"#MJX-38-TEX-I-1D449",[383,3265,3266,3271,3276,3281,3286,3291],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,3267,3268],{"dataMmlNode":393},[395,3269],{"dataC":1134,"xLinkHref":3270},"#MJX-38-TEX-I-1D461",[383,3272,3273],{"dataMmlNode":393,"transform":1774},[395,3274],{"dataC":981,"xLinkHref":3275},"#MJX-38-TEX-I-1D45F",[383,3277,3278],{"dataMmlNode":393,"transform":1531},[395,3279],{"dataC":1781,"xLinkHref":3280},"#MJX-38-TEX-I-1D44E",[383,3282,3283],{"dataMmlNode":393,"transform":1785},[395,3284],{"dataC":1788,"xLinkHref":3285},"#MJX-38-TEX-I-1D456",[383,3287,3288],{"dataMmlNode":393,"transform":1792},[395,3289],{"dataC":1795,"xLinkHref":3290},"#MJX-38-TEX-I-1D45B",[383,3292,3293],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":2776},[383,3294,3295],{"dataMmlNode":401},[395,3296],{"dataC":2781,"xLinkHref":3297},"#MJX-38-TEX-N-200B",[383,3299,3300],{"dataMmlNode":401,"transform":2215},[395,3301],{"dataC":405,"xLinkHref":3255},[383,3303,3305],{"dataMmlNode":393,"transform":3304},"translate(3060.4,0)",[395,3306],{"dataC":412,"xLinkHref":3307},"#MJX-38-TEX-I-1D44F",[383,3309,3311],{"dataMmlNode":401,"transform":3310},"translate(3489.4,0)",[395,3312],{"dataC":419,"xLinkHref":3313},"#MJX-38-TEX-N-29",[383,3315,3317],{"dataMmlNode":401,"transform":3316},"translate(4100.7,0)",[395,3318],{"dataC":600,"xLinkHref":3319},"#MJX-38-TEX-N-2212",[383,3321,3323],{"dataMmlNode":393,"transform":3322},"translate(5100.9,0)",[395,3324],{"dataC":397,"xLinkHref":3263},[383,3326,3328],{"dataMmlNode":401,"transform":3327},"translate(5869.9,0)",[395,3329],{"dataC":405,"xLinkHref":3255},[383,3331,3333],{"dataMmlNode":393,"transform":3332},"translate(6258.9,0)",[395,3334],{"dataC":412,"xLinkHref":3307},[383,3336,3338],{"dataMmlNode":401,"transform":3337},"translate(6687.9,0)",[395,3339],{"dataC":419,"xLinkHref":3313},[383,3341,3343],{"dataMmlNode":401,"transform":3342},"translate(7076.9,0)",[395,3344],{"dataC":419,"xLinkHref":3313},[16,3346,3347,3348,3391,3392,3535,3536,3565,3566,3597,3598,3601,3602,3642],{},"Inside: The guess ",[347,3349,3351],{"className":3350,"jax":351},[350],[353,3352,3353,3367],{"style":355,"xmlns":356,"width":357,"height":358,"role":94,"focusable":359,"viewBox":360,"xmlnsXLink":361},[363,3354,3355,3358,3361,3364],{},[366,3356],{"id":3357,"d":369},"MJX-39-TEX-I-1D449",[366,3359],{"id":3360,"d":373},"MJX-39-TEX-N-28",[366,3362],{"id":3363,"d":377},"MJX-39-TEX-I-1D44F",[366,3365],{"id":3366,"d":381},"MJX-39-TEX-N-29",[383,3368,3369],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3370,3371,3376,3381,3386],{"dataMmlNode":390},[383,3372,3373],{"dataMmlNode":393},[395,3374],{"dataC":397,"xLinkHref":3375},"#MJX-39-TEX-I-1D449",[383,3377,3378],{"dataMmlNode":401,"transform":402},[395,3379],{"dataC":405,"xLinkHref":3380},"#MJX-39-TEX-N-28",[383,3382,3383],{"dataMmlNode":393,"transform":409},[395,3384],{"dataC":412,"xLinkHref":3385},"#MJX-39-TEX-I-1D44F",[383,3387,3388],{"dataMmlNode":401,"transform":416},[395,3389],{"dataC":419,"xLinkHref":3390},"#MJX-39-TEX-N-29"," is made of ",[347,3393,3395],{"className":3394,"jax":351},[350],[353,3396,3400,3427],{"style":2039,"xmlns":356,"width":3397,"height":3398,"role":94,"focusable":359,"viewBox":3399,"xmlnsXLink":361},"20.575ex","2.059ex","0 -705 9094.3 910",[363,3401,3402,3405,3408,3411,3414,3417,3420,3423],{},[366,3403],{"id":3404,"d":805},"MJX-40-TEX-I-1D464",[366,3406],{"id":3407,"d":458},"MJX-40-TEX-N-30",[366,3409],{"id":3410,"d":2688},"MJX-40-TEX-N-200B",[366,3412],{"id":3413,"d":812},"MJX-40-TEX-N-2B",[366,3415],{"id":3416,"d":454},"MJX-40-TEX-N-31",[366,3418],{"id":3419,"d":1872},"MJX-40-TEX-I-1D453",[366,3421],{"id":3422,"d":827},"MJX-40-TEX-N-32",[366,3424],{"id":3425,"d":3426},"MJX-40-TEX-N-2026","M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z",[383,3428,3429],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3430,3431,3443,3451,3457,3469,3476,3487,3494,3499,3511,3518,3528],{"dataMmlNode":390},[383,3432,3433,3438],{"dataMmlNode":887},[383,3434,3435],{"dataMmlNode":393},[395,3436],{"dataC":892,"xLinkHref":3437},"#MJX-40-TEX-I-1D464",[383,3439,3440],{"dataMmlNode":492,"transform":896},[395,3441],{"dataC":500,"xLinkHref":3442},"#MJX-40-TEX-N-30",[383,3444,3446],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3445},"translate(1152.6,0)",[383,3447,3448],{"dataMmlNode":401},[395,3449],{"dataC":2781,"xLinkHref":3450},"#MJX-40-TEX-N-200B",[383,3452,3454],{"dataMmlNode":401,"transform":3453},"translate(1374.8,0)",[395,3455],{"dataC":905,"xLinkHref":3456},"#MJX-40-TEX-N-2B",[383,3458,3460,3464],{"dataMmlNode":887,"transform":3459},"translate(2375,0)",[383,3461,3462],{"dataMmlNode":393},[395,3463],{"dataC":892,"xLinkHref":3437},[383,3465,3466],{"dataMmlNode":492,"transform":896},[395,3467],{"dataC":496,"xLinkHref":3468},"#MJX-40-TEX-N-31",[383,3470,3472],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3471},"translate(3527.6,0)",[383,3473,3474],{"dataMmlNode":401},[395,3475],{"dataC":2781,"xLinkHref":3450},[383,3477,3478,3483],{"dataMmlNode":887,"transform":3471},[383,3479,3480],{"dataMmlNode":393},[395,3481],{"dataC":1950,"xLinkHref":3482},"#MJX-40-TEX-I-1D453",[383,3484,3485],{"dataMmlNode":492,"transform":1954},[395,3486],{"dataC":496,"xLinkHref":3468},[383,3488,3490],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3489},"translate(4454.1,0)",[383,3491,3492],{"dataMmlNode":401},[395,3493],{"dataC":2781,"xLinkHref":3450},[383,3495,3497],{"dataMmlNode":401,"transform":3496},"translate(4676.3,0)",[395,3498],{"dataC":905,"xLinkHref":3456},[383,3500,3502,3506],{"dataMmlNode":887,"transform":3501},"translate(5676.5,0)",[383,3503,3504],{"dataMmlNode":393},[395,3505],{"dataC":892,"xLinkHref":3437},[383,3507,3508],{"dataMmlNode":492,"transform":896},[395,3509],{"dataC":969,"xLinkHref":3510},"#MJX-40-TEX-N-32",[383,3512,3514],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":3513},"translate(6829.1,0)",[383,3515,3516],{"dataMmlNode":401},[395,3517],{"dataC":2781,"xLinkHref":3450},[383,3519,3520,3524],{"dataMmlNode":887,"transform":3513},[383,3521,3522],{"dataMmlNode":393},[395,3523],{"dataC":1950,"xLinkHref":3482},[383,3525,3526],{"dataMmlNode":492,"transform":1954},[395,3527],{"dataC":969,"xLinkHref":3510},[383,3529,3531],{"dataMmlNode":401,"transform":3530},"translate(7922.3,0)",[395,3532],{"dataC":3533,"xLinkHref":3534},"2026","#MJX-40-TEX-N-2026"," etc. If you are taking the derivative for just one specific weight (",[347,3537,3539],{"className":3538,"jax":351},[350],[353,3540,3541,3549],{"style":2396,"xmlns":356,"width":3007,"height":3008,"role":94,"focusable":359,"viewBox":3009,"xmlnsXLink":361},[363,3542,3543,3546],{},[366,3544],{"id":3545,"d":805},"MJX-41-TEX-I-1D464",[366,3547],{"id":3548,"d":1691},"MJX-41-TEX-I-1D456",[383,3550,3551],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3552,3553],{"dataMmlNode":390},[383,3554,3555,3560],{"dataMmlNode":887},[383,3556,3557],{"dataMmlNode":393},[395,3558],{"dataC":892,"xLinkHref":3559},"#MJX-41-TEX-I-1D464",[383,3561,3562],{"dataMmlNode":393,"transform":896},[395,3563],{"dataC":1788,"xLinkHref":3564},"#MJX-41-TEX-I-1D456","​), all the other weights vanish because they are constants. The only thing left is the feature attached to it (",[347,3567,3569],{"className":3568,"jax":351},[350],[353,3570,3573,3581],{"style":2039,"xmlns":356,"width":3571,"height":3398,"role":94,"focusable":359,"viewBox":3572,"xmlnsXLink":361},"1.848ex","0 -705 817 910",[363,3574,3575,3578],{},[366,3576],{"id":3577,"d":1872},"MJX-42-TEX-I-1D453",[366,3579],{"id":3580,"d":1691},"MJX-42-TEX-I-1D456",[383,3582,3583],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3584,3585],{"dataMmlNode":390},[383,3586,3587,3592],{"dataMmlNode":887},[383,3588,3589],{"dataMmlNode":393},[395,3590],{"dataC":1950,"xLinkHref":3591},"#MJX-42-TEX-I-1D453",[383,3593,3594],{"dataMmlNode":393,"transform":1954},[395,3595],{"dataC":1788,"xLinkHref":3596},"#MJX-42-TEX-I-1D456","). Because the guess is being ",[20,3599,3600],{},"subtracted"," in the raw error, a negative sign pops out: ",[347,3603,3605],{"className":3604,"jax":351},[350],[353,3606,3609,3620],{"style":2039,"xmlns":356,"width":3607,"height":3398,"role":94,"focusable":359,"viewBox":3608,"xmlnsXLink":361},"3.608ex","0 -705 1595 910",[363,3610,3611,3614,3617],{},[366,3612],{"id":3613,"d":560},"MJX-43-TEX-N-2212",[366,3615],{"id":3616,"d":1872},"MJX-43-TEX-I-1D453",[366,3618],{"id":3619,"d":1691},"MJX-43-TEX-I-1D456",[383,3621,3622],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,3623,3624,3629],{"dataMmlNode":390},[383,3625,3626],{"dataMmlNode":401},[395,3627],{"dataC":600,"xLinkHref":3628},"#MJX-43-TEX-N-2212",[383,3630,3632,3637],{"dataMmlNode":887,"transform":3631},"translate(778,0)",[383,3633,3634],{"dataMmlNode":393},[395,3635],{"dataC":1950,"xLinkHref":3636},"#MJX-43-TEX-I-1D453",[383,3638,3639],{"dataMmlNode":393,"transform":1954},[395,3640],{"dataC":1788,"xLinkHref":3641},"#MJX-43-TEX-I-1D456","​.",[16,3644,3645],{},"Multiply the outside and the inside together, and you get the 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the \"true\" score.",[16,4747,4748],{},"There is no human sitting there labelling every single move with a perfect 1 to 100 score.",[16,4750,4751,4752,4825],{},"So, how does the AI generate its own ",[347,4753,4755],{"className":4754,"jax":351},[350],[353,4756,4757,4780],{"style":2396,"xmlns":356,"width":2397,"height":2398,"role":94,"focusable":359,"viewBox":2399,"xmlnsXLink":361},[363,4758,4759,4762,4765,4768,4771,4774,4777],{},[366,4760],{"id":4761,"d":369},"MJX-52-TEX-I-1D449",[366,4763],{"id":4764,"d":851},"MJX-52-TEX-I-1D461",[366,4766],{"id":4767,"d":831},"MJX-52-TEX-I-1D45F",[366,4769],{"id":4770,"d":1687},"MJX-52-TEX-I-1D44E",[366,4772],{"id":4773,"d":1691},"MJX-52-TEX-I-1D456",[366,4775],{"id":4776,"d":1695},"MJX-52-TEX-I-1D45B",[366,4778],{"id":4779,"d":2688},"MJX-52-TEX-N-200B",[383,4781,4782],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,4783,4784],{"dataMmlNode":390},[383,4785,4786,4791],{"dataMmlNode":887},[383,4787,4788],{"dataMmlNode":393},[395,4789],{"dataC":397,"xLinkHref":4790},"#MJX-52-TEX-I-1D449",[383,4792,4793,4798,4803,4808,4813,4818],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,4794,4795],{"dataMmlNode":393},[395,4796],{"dataC":1134,"xLinkHref":4797},"#MJX-52-TEX-I-1D461",[383,4799,4800],{"dataMmlNode":393,"transform":1774},[395,4801],{"dataC":981,"xLinkHref":4802},"#MJX-52-TEX-I-1D45F",[383,4804,4805],{"dataMmlNode":393,"transform":1531},[395,4806],{"dataC":1781,"xLinkHref":4807},"#MJX-52-TEX-I-1D44E",[383,4809,4810],{"dataMmlNode":393,"transform":1785},[395,4811],{"dataC":1788,"xLinkHref":4812},"#MJX-52-TEX-I-1D456",[383,4814,4815],{"dataMmlNode":393,"transform":1792},[395,4816],{"dataC":1795,"xLinkHref":4817},"#MJX-52-TEX-I-1D45B",[383,4819,4820],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":2776},[383,4821,4822],{"dataMmlNode":401},[395,4823],{"dataC":2781,"xLinkHref":4824},"#MJX-52-TEX-N-200B","?",[2127,4827],{},[16,4829,4830,4831,4834],{},"The AI doesn't know the exact value of a mid-game board, but the rules of Checkers provide an absolute, undeniable mathematical truth at the very end of the game. These are called ",[28,4832,4833],{},"Terminal States",":",[36,4836,4837,4843,4849],{},[39,4838,4839,4842],{},[28,4840,4841],{},"Win"," = 100",[39,4844,4845,4848],{},[28,4846,4847],{},"Loss"," = −100",[39,4850,4851,4854],{},[28,4852,4853],{},"Draw"," = 0",[16,4856,4857],{},"The AI is not allowed to guess the score of a Terminal State. The game environment forces these numbers to be the absolute truth. Everything the AI learns is anchored to these final outcomes.",[4859,4860,4862],"h4",{"id":4861},"temporal-difference-td-learning","Temporal Difference (TD) Learning",[16,4864,4865,4866,4939,4940],{},"Since the AI lacks a true ",[347,4867,4869],{"className":4868,"jax":351},[350],[353,4870,4871,4894],{"style":2396,"xmlns":356,"width":2397,"height":2398,"role":94,"focusable":359,"viewBox":2399,"xmlnsXLink":361},[363,4872,4873,4876,4879,4882,4885,4888,4891],{},[366,4874],{"id":4875,"d":369},"MJX-53-TEX-I-1D449",[366,4877],{"id":4878,"d":851},"MJX-53-TEX-I-1D461",[366,4880],{"id":4881,"d":831},"MJX-53-TEX-I-1D45F",[366,4883],{"id":4884,"d":1687},"MJX-53-TEX-I-1D44E",[366,4886],{"id":4887,"d":1691},"MJX-53-TEX-I-1D456",[366,4889],{"id":4890,"d":1695},"MJX-53-TEX-I-1D45B",[366,4892],{"id":4893,"d":2688},"MJX-53-TEX-N-200B",[383,4895,4896],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,4897,4898],{"dataMmlNode":390},[383,4899,4900,4905],{"dataMmlNode":887},[383,4901,4902],{"dataMmlNode":393},[395,4903],{"dataC":397,"xLinkHref":4904},"#MJX-53-TEX-I-1D449",[383,4906,4907,4912,4917,4922,4927,4932],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,4908,4909],{"dataMmlNode":393},[395,4910],{"dataC":1134,"xLinkHref":4911},"#MJX-53-TEX-I-1D461",[383,4913,4914],{"dataMmlNode":393,"transform":1774},[395,4915],{"dataC":981,"xLinkHref":4916},"#MJX-53-TEX-I-1D45F",[383,4918,4919],{"dataMmlNode":393,"transform":1531},[395,4920],{"dataC":1781,"xLinkHref":4921},"#MJX-53-TEX-I-1D44E",[383,4923,4924],{"dataMmlNode":393,"transform":1785},[395,4925],{"dataC":1788,"xLinkHref":4926},"#MJX-53-TEX-I-1D456",[383,4928,4929],{"dataMmlNode":393,"transform":1792},[395,4930],{"dataC":1795,"xLinkHref":4931},"#MJX-53-TEX-I-1D45B",[383,4933,4934],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":2776},[383,4935,4936],{"dataMmlNode":401},[395,4937],{"dataC":2781,"xLinkHref":4938},"#MJX-53-TEX-N-200B"," for intermediate moves (like Move 10), it uses a clever trick: ",[28,4941,4942],{},"It uses its own prediction from Move 11 as the \"truth\" for Move 10.",[16,4944,4945,4946],{},"This is Temporal Difference learning. The AI essentially says: ",[20,4947,4948],{},"\"I have better, more updated information after making a move than I did before making it. Therefore, my guess for the next state is a better target than my current guess.\"",[347,4950,4952],{"className":4951,"jax":351,"display":780},[350],[353,4953,4956,4995],{"style":355,"xmlns":356,"width":4954,"height":358,"role":94,"focusable":359,"viewBox":4955,"xmlnsXLink":361},"18.347ex","0 -750 8109.5 1000",[363,4957,4958,4961,4964,4967,4970,4973,4976,4979,4982,4985,4988,4991],{},[366,4959],{"id":4960,"d":369},"MJX-54-TEX-I-1D449",[366,4962],{"id":4963,"d":851},"MJX-54-TEX-I-1D461",[366,4965],{"id":4966,"d":831},"MJX-54-TEX-I-1D45F",[366,4968],{"id":4969,"d":1687},"MJX-54-TEX-I-1D44E",[366,4971],{"id":4972,"d":1691},"MJX-54-TEX-I-1D456",[366,4974],{"id":4975,"d":1695},"MJX-54-TEX-I-1D45B",[366,4977],{"id":4978,"d":373},"MJX-54-TEX-N-28",[366,4980],{"id":4981,"d":377},"MJX-54-TEX-I-1D44F",[366,4983],{"id":4984,"d":381},"MJX-54-TEX-N-29",[366,4986],{"id":4987,"d":450},"MJX-54-TEX-N-3D",[366,4989],{"id":4990,"d":1658},"MJX-54-TEX-I-1D452",[366,4992],{"id":4993,"d":4994},"MJX-54-TEX-I-1D465","M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",[383,4996,4997],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,4998,4999,5033,5038,5043,5048,5054,5085,5090,5095],{"dataMmlNode":390},[383,5000,5001,5006],{"dataMmlNode":887},[383,5002,5003],{"dataMmlNode":393},[395,5004],{"dataC":397,"xLinkHref":5005},"#MJX-54-TEX-I-1D449",[383,5007,5008,5013,5018,5023,5028],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,5009,5010],{"dataMmlNode":393},[395,5011],{"dataC":1134,"xLinkHref":5012},"#MJX-54-TEX-I-1D461",[383,5014,5015],{"dataMmlNode":393,"transform":1774},[395,5016],{"dataC":981,"xLinkHref":5017},"#MJX-54-TEX-I-1D45F",[383,5019,5020],{"dataMmlNode":393,"transform":1531},[395,5021],{"dataC":1781,"xLinkHref":5022},"#MJX-54-TEX-I-1D44E",[383,5024,5025],{"dataMmlNode":393,"transform":1785},[395,5026],{"dataC":1788,"xLinkHref":5027},"#MJX-54-TEX-I-1D456",[383,5029,5030],{"dataMmlNode":393,"transform":1792},[395,5031],{"dataC":1795,"xLinkHref":5032},"#MJX-54-TEX-I-1D45B",[383,5034,5035],{"dataMmlNode":401,"transform":2209},[395,5036],{"dataC":405,"xLinkHref":5037},"#MJX-54-TEX-N-28",[383,5039,5040],{"dataMmlNode":393,"transform":2215},[395,5041],{"dataC":412,"xLinkHref":5042},"#MJX-54-TEX-I-1D44F",[383,5044,5045],{"dataMmlNode":401,"transform":2221},[395,5046],{"dataC":419,"xLinkHref":5047},"#MJX-54-TEX-N-29",[383,5049,5051],{"dataMmlNode":401,"transform":5050},"translate(3767.2,0)",[395,5052],{"dataC":488,"xLinkHref":5053},"#MJX-54-TEX-N-3D",[383,5055,5057,5061],{"dataMmlNode":887,"transform":5056},"translate(4823,0)",[383,5058,5059],{"dataMmlNode":393},[395,5060],{"dataC":397,"xLinkHref":5005},[383,5062,5063,5067,5073,5080],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,5064,5065],{"dataMmlNode":393},[395,5066],{"dataC":1795,"xLinkHref":5032},[383,5068,5070],{"dataMmlNode":393,"transform":5069},"translate(600,0)",[395,5071],{"dataC":1707,"xLinkHref":5072},"#MJX-54-TEX-I-1D452",[383,5074,5076],{"dataMmlNode":393,"transform":5075},"translate(1066,0)",[395,5077],{"dataC":5078,"xLinkHref":5079},"1D465","#MJX-54-TEX-I-1D465",[383,5081,5083],{"dataMmlNode":393,"transform":5082},"translate(1638,0)",[395,5084],{"dataC":1134,"xLinkHref":5012},[383,5086,5088],{"dataMmlNode":401,"transform":5087},"translate(6902.5,0)",[395,5089],{"dataC":405,"xLinkHref":5037},[383,5091,5093],{"dataMmlNode":393,"transform":5092},"translate(7291.5,0)",[395,5094],{"dataC":412,"xLinkHref":5042},[383,5096,5098],{"dataMmlNode":401,"transform":5097},"translate(7720.5,0)",[395,5099],{"dataC":419,"xLinkHref":5047},[16,5101,5102],{},[28,5103,5104],{},"How it works in practice:",[302,5106,5107,5113,5119,5125,5205,5229],{},[39,5108,5109,5112],{},[28,5110,5111],{},"The Guess:"," At Step 4, the AI evaluates the board and guesses a score of 90.",[39,5114,5115,5118],{},[28,5116,5117],{},"The Move:"," The AI makes a move and immediately wins the game (Step 5).",[39,5120,5121,5124],{},[28,5122,5123],{},"The Correction:"," The environment declares Step 5 is a Terminal State worth 100.",[39,5126,5127,5130,5131,5204],{},[28,5128,5129],{},"The Update:"," The AI looks back at Step 4. It realizes its guess of 90 was wrong, because Step 4 directly led to a 100. It sets ",[347,5132,5134],{"className":5133,"jax":351},[350],[353,5135,5136,5159],{"style":2396,"xmlns":356,"width":2397,"height":2398,"role":94,"focusable":359,"viewBox":2399,"xmlnsXLink":361},[363,5137,5138,5141,5144,5147,5150,5153,5156],{},[366,5139],{"id":5140,"d":369},"MJX-55-TEX-I-1D449",[366,5142],{"id":5143,"d":851},"MJX-55-TEX-I-1D461",[366,5145],{"id":5146,"d":831},"MJX-55-TEX-I-1D45F",[366,5148],{"id":5149,"d":1687},"MJX-55-TEX-I-1D44E",[366,5151],{"id":5152,"d":1691},"MJX-55-TEX-I-1D456",[366,5154],{"id":5155,"d":1695},"MJX-55-TEX-I-1D45B",[366,5157],{"id":5158,"d":2688},"MJX-55-TEX-N-200B",[383,5160,5161],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,5162,5163],{"dataMmlNode":390},[383,5164,5165,5170],{"dataMmlNode":887},[383,5166,5167],{"dataMmlNode":393},[395,5168],{"dataC":397,"xLinkHref":5169},"#MJX-55-TEX-I-1D449",[383,5171,5172,5177,5182,5187,5192,5197],{"dataMmlNode":1576,"transform":1766,"dataMjxTexclass":1577},[383,5173,5174],{"dataMmlNode":393},[395,5175],{"dataC":1134,"xLinkHref":5176},"#MJX-55-TEX-I-1D461",[383,5178,5179],{"dataMmlNode":393,"transform":1774},[395,5180],{"dataC":981,"xLinkHref":5181},"#MJX-55-TEX-I-1D45F",[383,5183,5184],{"dataMmlNode":393,"transform":1531},[395,5185],{"dataC":1781,"xLinkHref":5186},"#MJX-55-TEX-I-1D44E",[383,5188,5189],{"dataMmlNode":393,"transform":1785},[395,5190],{"dataC":1788,"xLinkHref":5191},"#MJX-55-TEX-I-1D456",[383,5193,5194],{"dataMmlNode":393,"transform":1792},[395,5195],{"dataC":1795,"xLinkHref":5196},"#MJX-55-TEX-I-1D45B",[383,5198,5199],{"dataMmlNode":1576,"dataMjxTexclass":1577,"transform":2776},[383,5200,5201],{"dataMmlNode":401},[395,5202],{"dataC":2781,"xLinkHref":5203},"#MJX-55-TEX-N-200B"," for Step 4 to 100, and the LMS algorithm kicks in to adjust the weights up.",[39,5206,5207,5210,5211],{},[28,5208,5209],{},"The Win (Pushing Up):"," Let's say the AI evaluates the state at 90. It wins, so the target is 100.\n",[36,5212,5213,5216,5219],{},[39,5214,5215],{},"Error=+10",[39,5217,5218],{},"Adjustment=0.1⋅10=+1",[39,5220,5221,5224,5225,5228],{},[28,5222,5223],{},"New Value = 91"," (It steps ",[20,5226,5227],{},"towards"," 100, but doesn't jump all the way there).",[39,5230,5231,5234,5235],{},[28,5232,5233],{},"The Loss (Dialling Back):"," The next game, it reaches that same state, confidently guesses 91, but falls into a trap and loses. The target is now −100.\n",[36,5236,5237,5240,5243],{},[39,5238,5239],{},"Error=−100−91=−191",[39,5241,5242],{},"Adjustment=0.1⋅(−191)=−19.1",[39,5244,5245,5248],{},[28,5246,5247],{},"New Value = 71.9"," (It takes a massive hit and dials way back).",[16,5250,5251,5252,5255],{},"Over thousands of games, the absolute certainty of the end-game (100 or -100) slowly ripples backward through the moves. Step 4 learns from the Win, then Step 3 learns from Step 4, and so on. Eventually, the evaluation function perfectly maps out the true probability of winning from ",[20,5253,5254],{},"any"," starting board state.",[16,5257,5258],{},"The intuition is simple:",[36,5260,5261,5264,5267],{},[39,5262,5263],{},"If the prediction is correct → no change",[39,5265,5266],{},"If the prediction is too high → decrease weights proportionally",[39,5268,5269],{},"If the prediction is too low → increase weights proportionally",[16,5271,5272,5273,4834],{},"Under reasonable conditions, LMS is guaranteed to converge to the weights that minimise the ",[28,5274,5275],{},"Mean Squared Error (MSE)",[347,5277,5279],{"className":5278,"jax":351,"display":780},[350],[353,5280,5285,5335],{"style":5281,"xmlns":356,"width":5282,"height":5283,"role":94,"focusable":359,"viewBox":5284,"xmlnsXLink":361},"vertical-align: -2.819ex;","24.202ex","6.354ex","0 -1562.5 10697.1 2808.5",[363,5286,5287,5291,5295,5299,5302,5305,5308,5312,5315,5318,5322,5325,5329,5332],{},[366,5288],{"id":5289,"d":5290},"MJX-56-TEX-I-1D440","M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 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560Z",[366,5330],{"id":5331,"d":381},"MJX-56-TEX-N-29",[366,5333],{"id":5334,"d":827},"MJX-56-TEX-N-32",[383,5336,5337],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,5338,5339,5345,5352,5359,5365,5382,5417,5423,5437,5443,5466],{"dataMmlNode":390},[383,5340,5341],{"dataMmlNode":393},[395,5342],{"dataC":5343,"xLinkHref":5344},"1D440","#MJX-56-TEX-I-1D440",[383,5346,5348],{"dataMmlNode":393,"transform":5347},"translate(1051,0)",[395,5349],{"dataC":5350,"xLinkHref":5351},"1D446","#MJX-56-TEX-I-1D446",[383,5353,5355],{"dataMmlNode":393,"transform":5354},"translate(1696,0)",[395,5356],{"dataC":5357,"xLinkHref":5358},"1D438","#MJX-56-TEX-I-1D438",[383,5360,5362],{"dataMmlNode":401,"transform":5361},"translate(2737.8,0)",[395,5363],{"dataC":488,"xLinkHref":5364},"#MJX-56-TEX-N-3D",[383,5366,5368,5374,5379],{"dataMmlNode":2714,"transform":5367},"translate(3793.6,0)",[383,5369,5371],{"dataMmlNode":492,"transform":5370},"translate(270,676)",[395,5372],{"dataC":496,"xLinkHref":5373},"#MJX-56-TEX-N-31",[383,5375,5376],{"dataMmlNode":393,"transform":2723},[395,5377],{"dataC":1795,"xLinkHref":5378},"#MJX-56-TEX-I-1D45B",[2728,5380],{"width":5381,"height":2731,"x":2732,"y":2733},800,[383,5383,5386,5392,5410],{"dataMmlNode":5384,"transform":5385},"munderover","translate(5000.2,0)",[383,5387,5388],{"dataMmlNode":401},[395,5389],{"dataC":5390,"xLinkHref":5391},"2211","#MJX-56-TEX-LO-2211",[383,5393,5395,5400,5405],{"dataMmlNode":1576,"transform":5394,"dataMjxTexclass":1577},"translate(148.2,-1087.9) scale(0.707)",[383,5396,5397],{"dataMmlNode":393},[395,5398],{"dataC":1788,"xLinkHref":5399},"#MJX-56-TEX-I-1D456",[383,5401,5403],{"dataMmlNode":401,"transform":5402},"translate(345,0)",[395,5404],{"dataC":488,"xLinkHref":5364},[383,5406,5408],{"dataMmlNode":492,"transform":5407},"translate(1123,0)",[395,5409],{"dataC":496,"xLinkHref":5373},[383,5411,5413],{"dataMmlNode":1576,"transform":5412,"dataMjxTexclass":1577},"translate(509.9,1150) scale(0.707)",[383,5414,5415],{"dataMmlNode":393},[395,5416],{"dataC":1795,"xLinkHref":5378},[383,5418,5420],{"dataMmlNode":401,"transform":5419},"translate(6444.2,0)",[395,5421],{"dataC":405,"xLinkHref":5422},"#MJX-56-TEX-N-28",[383,5424,5426,5432],{"dataMmlNode":887,"transform":5425},"translate(6833.2,0)",[383,5427,5428],{"dataMmlNode":393},[395,5429],{"dataC":5430,"xLinkHref":5431},"1D44C","#MJX-56-TEX-I-1D44C",[383,5433,5435],{"dataMmlNode":393,"transform":5434},"translate(614,-150) scale(0.707)",[395,5436],{"dataC":1788,"xLinkHref":5399},[383,5438,5440],{"dataMmlNode":401,"transform":5439},"translate(7963.4,0)",[395,5441],{"dataC":600,"xLinkHref":5442},"#MJX-56-TEX-N-2212",[383,5444,5446,5462],{"dataMmlNode":887,"transform":5445},"translate(8963.6,0)",[383,5447,5448],{"dataMmlNode":1576,"dataMjxTexclass":1577},[383,5449,5451,5455],{"dataMmlNode":5450},"mover",[383,5452,5453],{"dataMmlNode":393},[395,5454],{"dataC":5430,"xLinkHref":5431},[383,5456,5458],{"dataMmlNode":401,"transform":5457},"translate(427,257) translate(-250 0)",[395,5459],{"dataC":5460,"xLinkHref":5461},"5E","#MJX-56-TEX-N-5E",[383,5463,5464],{"dataMmlNode":393,"transform":5434},[395,5465],{"dataC":1788,"xLinkHref":5399},[383,5467,5469,5474],{"dataMmlNode":2828,"transform":5468},"translate(9871.6,0)",[383,5470,5471],{"dataMmlNode":401},[395,5472],{"dataC":419,"xLinkHref":5473},"#MJX-56-TEX-N-29",[383,5475,5476],{"dataMmlNode":492,"transform":2836},[395,5477],{"dataC":969,"xLinkHref":5478},"#MJX-56-TEX-N-32",[2066,5480,5482,5485],{"className":5481},[2069,2070],[2072,5483,5484],{},"Understanding the formula",[2076,5486,5488,5491,5544,5599,5685],{"className":5487},[2079],[16,5489,5490],{},"This formula is really just an ultimate scoreboard for AI.",[16,5492,5493,345,5496,5543],{},[28,5494,5495],{},"Mean:",[347,5497,5499],{"className":5498,"jax":351},[350],[353,5500,5505,5517],{"style":5501,"xmlns":356,"width":5502,"height":5503,"role":94,"focusable":359,"viewBox":5504,"xmlnsXLink":361},"vertical-align: -0.798ex;","4.722ex","2.755ex","0 -864.9 2086.9 1217.7",[363,5506,5507,5510,5513],{},[366,5508],{"id":5509,"d":454},"MJX-57-TEX-N-31",[366,5511],{"id":5512,"d":1695},"MJX-57-TEX-I-1D45B",[366,5514],{"id":5515,"d":5516},"MJX-57-TEX-SO-2211","M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z",[383,5518,5519],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,5520,5521,5537],{"dataMmlNode":390},[383,5522,5523,5529,5534],{"dataMmlNode":2714},[383,5524,5526],{"dataMmlNode":492,"transform":5525},"translate(255.4,394) scale(0.707)",[395,5527],{"dataC":496,"xLinkHref":5528},"#MJX-57-TEX-N-31",[383,5530,5531],{"dataMmlNode":393,"transform":2876},[395,5532],{"dataC":1795,"xLinkHref":5533},"#MJX-57-TEX-I-1D45B",[2728,5535],{"width":5536,"height":2731,"x":2732,"y":2733},624.3,[383,5538,5540],{"dataMmlNode":401,"transform":5539},"translate(1030.9,0)",[395,5541],{"dataC":5390,"xLinkHref":5542},"#MJX-57-TEX-SO-2211"," (Add them up and divide by n)",[16,5545,5546,345,5549],{},[28,5547,5548],{},"Squared:",[347,5550,5552],{"className":5551,"jax":351},[350],[353,5553,5557,5571],{"style":355,"xmlns":356,"width":5554,"height":5555,"role":94,"focusable":359,"viewBox":5556,"xmlnsXLink":361},"5.399ex","2.452ex","0 -833.9 2386.6 1083.9",[363,5558,5559,5562,5565,5568],{},[366,5560],{"id":5561,"d":373},"MJX-58-TEX-N-28",[366,5563],{"id":5564,"d":3426},"MJX-58-TEX-N-2026",[366,5566],{"id":5567,"d":381},"MJX-58-TEX-N-29",[366,5569],{"id":5570,"d":827},"MJX-58-TEX-N-32",[383,5572,5573],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,5574,5575,5580,5585],{"dataMmlNode":390},[383,5576,5577],{"dataMmlNode":401},[395,5578],{"dataC":405,"xLinkHref":5579},"#MJX-58-TEX-N-28",[383,5581,5582],{"dataMmlNode":401,"transform":3258},[395,5583],{"dataC":3533,"xLinkHref":5584},"#MJX-58-TEX-N-2026",[383,5586,5588,5593],{"dataMmlNode":2828,"transform":5587},"translate(1561,0)",[383,5589,5590],{"dataMmlNode":401},[395,5591],{"dataC":419,"xLinkHref":5592},"#MJX-58-TEX-N-29",[383,5594,5596],{"dataMmlNode":492,"transform":5595},"translate(422,363) scale(0.707)",[395,5597],{"dataC":969,"xLinkHref":5598},"#MJX-58-TEX-N-32",[16,5600,5601,345,5604],{},[28,5602,5603],{},"Error:",[347,5605,5607],{"className":5606,"jax":351},[350],[353,5608,5612,5632],{"style":355,"xmlns":356,"width":5609,"height":5610,"role":94,"focusable":359,"viewBox":5611,"xmlnsXLink":361},"8.634ex","2.943ex","0 -1051 3816.3 1301",[363,5613,5614,5617,5620,5623,5626,5629],{},[366,5615],{"id":5616,"d":373},"MJX-59-TEX-N-28",[366,5618],{"id":5619,"d":5321},"MJX-59-TEX-I-1D44C",[366,5621],{"id":5622,"d":1691},"MJX-59-TEX-I-1D456",[366,5624],{"id":5625,"d":560},"MJX-59-TEX-N-2212",[366,5627],{"id":5628,"d":5328},"MJX-59-TEX-N-5E",[366,5630],{"id":5631,"d":381},"MJX-59-TEX-N-29",[383,5633,5634],{"stroke":385,"fill":385,"stroke-width":386,"transform":387},[383,5635,5636,5641,5653,5659,5679],{"dataMmlNode":390},[383,5637,5638],{"dataMmlNode":401},[395,5639],{"dataC":405,"xLinkHref":5640},"#MJX-59-TEX-N-28",[383,5642,5643,5648],{"dataMmlNode":887,"transform":3258},[383,5644,5645],{"dataMmlNode":393},[395,5646],{"dataC":5430,"xLinkHref":5647},"#MJX-59-TEX-I-1D44C",[383,5649,5650],{"dataMmlNode":393,"transform":5434},[395,5651],{"dataC":1788,"xLinkHref":5652},"#MJX-59-TEX-I-1D456",[383,5654,5656],{"dataMmlNode":401,"transform":5655},"translate(1519.2,0)",[395,5657],{"dataC":600,"xLinkHref":5658},"#MJX-59-TEX-N-2212",[383,5660,5662,5675],{"dataMmlNode":887,"transform":5661},"translate(2519.4,0)",[383,5663,5664],{"dataMmlNode":1576,"dataMjxTexclass":1577},[383,5665,5666,5670],{"dataMmlNode":5450},[383,5667,5668],{"dataMmlNode":393},[395,5669],{"dataC":5430,"xLinkHref":5647},[383,5671,5672],{"dataMmlNode":401,"transform":5457},[395,5673],{"dataC":5460,"xLinkHref":5674},"#MJX-59-TEX-N-5E",[383,5676,5677],{"dataMmlNode":393,"transform":5434},[395,5678],{"dataC":1788,"xLinkHref":5652},[383,5680,5682],{"dataMmlNode":401,"transform":5681},"translate(3427.3,0)",[395,5683],{"dataC":419,"xLinkHref":5684},"#MJX-59-TEX-N-29",[16,5686,5687],{},"It adds up all the errors, and find the average error rate so that you can compare it between models.",[11,5689,5691],{"id":5690},"training-data-where-does-it-come-from","Training Data: Where Does It Come From?",[16,5693,5694],{},"The source and nature of training data matters a lot. A few scenarios:",[36,5696,5697,5703,5709,5715],{},[39,5698,5699,5702],{},[28,5700,5701],{},"Random examples"," provided by the environment (most common in practice)",[39,5704,5705,5708],{},[28,5706,5707],{},"Teacher-selected examples"," chosen to be maximally informative (like \"near-miss\" examples)",[39,5710,5711,5714],{},[28,5712,5713],{},"Active learning"," where the model queries an oracle \u002F human for labels on examples it's unsure about",[39,5716,5717,5720],{},[28,5718,5719],{},"Self-directed experimentation"," where the learner designs its own experiments",[16,5722,5723,5724,5727,5728,5731,5732,5735],{},"A key assumption in most ML is that training and test data are ",[28,5725,5726],{},"independently and identically distributed (IID)"," — drawn from the same underlying distribution. When this assumption breaks down, you need techniques like ",[28,5729,5730],{},"transfer learning"," (different distributions) or ",[28,5733,5734],{},"collective classification"," (non-independent examples).",[2066,5737,5739,5742],{"className":5738},[2069,2070],[2072,5740,5741],{},"What is IID? (Independently and Identically Distributed)",[2076,5743,5745,5748,5753,5756,5770,5775,5778,5796,5802,5804,5808,5813,5816,5822,5837,5840,5842,5846,5851,5854,5857,5868,5883],{"className":5744},[2079],[16,5746,5747],{},"IID is a mathematical assumption that ML models make about the world. It assumes your training data and your real-world test data are perfectly consistent. Let's split it into its two halves:",[16,5749,5750],{},[28,5751,5752],{},"1. \"Independently\"",[16,5754,5755],{},"This means that one piece of data has absolutely no connection to the next piece of data. Drawing one doesn't change the probability of the next.",[36,5757,5758,5764],{},[39,5759,5760,5763],{},[28,5761,5762],{},"IID (Independent):"," Rolling a die. Rolling a 6 doesn't change the odds of rolling a 6 on the next turn. Diagnosing patients in a clinic; Patient A having a cold doesn't magically make Patient B have a broken leg.",[39,5765,5766,5769],{},[28,5767,5768],{},"NOT Independent:"," Predicting the weather. If it is raining on Tuesday, it is highly likely to be raining on Wednesday. The data points are linked in time.",[16,5771,5772],{},[28,5773,5774],{},"2. \"Identically Distributed\"",[16,5776,5777],{},"This means all your data is pulled from the exact same \"world,\" under the exact same rules, conditions, and demographics.",[36,5779,5780,5790],{},[39,5781,5782,5785,5786,5789],{},[28,5783,5784],{},"IID (Identical):"," Training an AI to grade math tests from a specific school, and testing it on different math tests from that ",[20,5787,5788],{},"same"," school.",[39,5791,5792,5795],{},[28,5793,5794],{},"NOT Identical:"," Training a self-driving car entirely on the sunny, wide streets of Phoenix, Arizona (Training Data), and then dropping it into a blizzard in the narrow streets of Boston (Test Data). The \"distribution\" of the data—the weather, the roads, the driver behavior—has completely changed.",[16,5797,5798,5799],{},"When an AI model is trained, it only learns the exact rules of its training data. ",[28,5800,5801],{},"If the real world is not IID to the training data, the AI will confidently make terrible predictions.",[4551,5803],{},[4859,5805,5807],{"id":5806},"what-is-transfer-learning","What is Transfer Learning?",[16,5809,5810],{},[20,5811,5812],{},"(The fix for when data is NOT Identically Distributed)",[16,5814,5815],{},"Let's say the \"Identically Distributed\" assumption breaks. You want to build a medical AI to detect a very rare disease in X-rays. Because the disease is rare, you only have 100 training images. That isn't enough to train a neural network from scratch.",[16,5817,5818,5821],{},[28,5819,5820],{},"Transfer Learning"," is the process of taking a model trained on a massive, different dataset, and \"transferring\" its foundational knowledge to your new problem.",[302,5823,5824,5827,5830],{},[39,5825,5826],{},"You take a model that Google already trained on 10 million random internet images (cats, dogs, cars, trees). This model already knows how to detect edges, shapes, textures, and shadows.",[39,5828,5829],{},"You take that pre-trained model and do a little bit of extra training using your 100 rare X-rays.",[39,5831,5832,5833,5836],{},"The model ",[20,5834,5835],{},"transfers"," its general knowledge of shapes and textures to the specific task of reading X-rays.",[16,5838,5839],{},"It saves massive amounts of time and data when your target environment doesn't match a massive, easily available training environment.",[4551,5841],{},[4859,5843,5845],{"id":5844},"what-is-collective-classification","What is Collective Classification?",[16,5847,5848],{},[20,5849,5850],{},"(The fix for when data is NOT Independent)",[16,5852,5853],{},"Let's say the \"Independent\" assumption breaks. Your data points are heavily connected to one another, usually in a network or a graph.",[16,5855,5856],{},"Imagine you are trying to catch bot accounts on a social media platform. If you look at an account strictly in isolation (its bio, its profile picture, its post frequency), you might not be able to tell if it's a bot.",[16,5858,5859,5860,5863,5864,5867],{},"However, in a social network, users aren't independent. ",[28,5861,5862],{},"Collective Classification"," is a technique that looks at the ",[20,5865,5866],{},"relationships"," between data points.",[36,5869,5870,5873,5876],{},[39,5871,5872],{},"If Account A follows 500 known bots.",[39,5874,5875],{},"If Account A is followed by 500 known bots.",[39,5877,5878,5879,5882],{},"Collective Classification uses the known labels of the ",[20,5880,5881],{},"neighbors"," to classify the target. It concludes Account A is almost certainly a bot, too!",[16,5884,5885,5888],{},[28,5886,5887],{},"To sum up your notes:"," IID is the \"perfect laboratory condition\" for an AI. Transfer Learning and Collective Classification are the rescue tools you use when those perfect conditions shatter in the real world.",[11,5890,5892],{"id":5891},"how-we-represent-target-functions","How We Represent Target Functions",[16,5894,5895],{},"Different representations offer different trade-offs between expressiveness and learnability:",[16,5897,5898,5901],{},[28,5899,5900],{},"Numerical functions"," — linear regression, neural networks, support vector machines. These are great at capturing smooth, continuous patterns.",[16,5903,5904,5907],{},[28,5905,5906],{},"Symbolic functions"," — decision trees, logical rules. These produce human-interpretable models.",[16,5909,5910,5913],{},[28,5911,5912],{},"Instance-based functions"," — nearest-neighbor, case-based reasoning. These make predictions by comparing new examples to stored training examples.",[16,5915,5916,5919],{},[28,5917,5918],{},"Probabilistic graphical models"," — Naïve Bayes, Bayesian networks, Hidden Markov Models. These explicitly model uncertainty and dependencies between variables.",[16,5921,5922],{},"The more expressive a representation, the more complex functions it can capture — but it also needs more data to learn accurately. This is a fundamental trade-off in ML.",[11,5924,5926],{"id":5925},"evaluating-learning-systems","Evaluating Learning Systems",[16,5928,5929],{},"How do we know if a learning system is actually good? There are two main approaches:",[16,5931,5932,5935],{},[28,5933,5934],{},"Experimental evaluation"," — Run controlled experiments using cross-validation on benchmark datasets. Measure things like test accuracy, training time, and testing time. Use statistical tests to determine whether differences between methods are meaningful.",[16,5937,5938,5941],{},[28,5939,5940],{},"Theoretical analysis"," — Prove mathematical guarantees about algorithms, such as computational complexity, the ability to fit data, and sample complexity (how many examples are needed to learn well).",[16,5943,5944],{},"In practice, most ML work uses a combination of both.",[11,5946,5948],{"id":5947},"a-brief-history-of-machine-learning","A Brief History of Machine Learning",[16,5950,5951],{},"ML has a rich history spanning several decades:",[36,5953,5954,5960,5966,5972,5978,5984],{},[39,5955,5956,5959],{},[28,5957,5958],{},"1950s"," — Samuel's checkers player at IBM, one of the first programs to learn from experience",[39,5961,5962,5965],{},[28,5963,5964],{},"1960s"," — The Perceptron (an early neural network), and Minsky & Papert's proof of its limitations",[39,5967,5968,5971],{},[28,5969,5970],{},"1970s"," — Symbolic approaches take center stage: decision trees (ID3), expert systems, and scientific discovery programs",[39,5973,5974,5977],{},[28,5975,5976],{},"1980s"," — Neural networks make a comeback with backpropagation; PAC learning theory provides mathematical foundations",[39,5979,5980,5983],{},[28,5981,5982],{},"1990s"," — Data mining, reinforcement learning, ensemble methods (bagging, boosting), and Bayesian approaches",[39,5985,5986,5989],{},[28,5987,5988],{},"2000s"," — Support vector machines, kernel methods, transfer learning, and ML applications in security, robotics, and personalization\nAnd of course, from the 2010s onward, deep learning has transformed the field — but that's a story for later weeks!",[11,5991,5993],{"id":5992},"key-takeaways","Key Takeaways",[302,5995,5996,6002,6008,6014,6020],{},[39,5997,5998,6001],{},[28,5999,6000],{},"Machine learning is about learning from experience"," — using data to approximate functions, rather than coding rules by hand.",[39,6003,6004,6007],{},[28,6005,6006],{},"Every ML problem can be framed as T, P, E"," — the task, the performance metric, and the experience.",[39,6009,6010,6013],{},[28,6011,6012],{},"Designing an ML system involves four choices",": training experience, target function, representation, and learning algorithm.",[39,6015,6016,6019],{},[28,6017,6018],{},"There's always a trade-off"," between model expressiveness and the amount of data needed.",[39,6021,6022,6025],{},[28,6023,6024],{},"Evaluation matters"," — a model is only as good as its performance on unseen data.",[6027,6028,6029],"style",{},"\nmjx-container[jax=\"SVG\"] {\n  direction: ltr;\n}\n\nmjx-container[jax=\"SVG\"] > svg {\n  overflow: visible;\n  min-height: 1px;\n  min-width: 1px;\n}\n\nmjx-container[jax=\"SVG\"] > svg a {\n  fill: blue;\n  stroke: blue;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"] {\n  display: block;\n  text-align: center;\n  margin: 1em 0;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"][width=\"full\"] {\n  display: 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