File size: 100,135 Bytes
2ffb90d |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 3246 3247 3248 3249 3250 3251 3252 3253 3254 3255 3256 3257 3258 3259 3260 3261 3262 3263 3264 3265 3266 3267 3268 3269 3270 3271 3272 3273 3274 3275 3276 3277 3278 3279 3280 3281 3282 3283 3284 3285 3286 3287 3288 3289 3290 3291 3292 3293 3294 3295 3296 3297 3298 3299 3300 3301 3302 3303 3304 3305 3306 3307 3308 3309 3310 3311 3312 3313 3314 3315 3316 3317 3318 3319 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3330 3331 3332 3333 3334 3335 3336 3337 3338 3339 3340 3341 3342 3343 3344 3345 3346 3347 3348 3349 3350 3351 3352 3353 3354 3355 3356 3357 3358 3359 3360 3361 3362 3363 3364 3365 3366 3367 3368 3369 3370 3371 3372 3373 3374 3375 3376 3377 3378 3379 3380 3381 3382 3383 3384 3385 3386 3387 3388 3389 3390 3391 3392 3393 3394 3395 3396 3397 3398 3399 3400 3401 3402 3403 3404 3405 3406 3407 3408 3409 3410 3411 3412 3413 3414 3415 3416 3417 3418 3419 3420 3421 3422 3423 3424 3425 3426 3427 3428 3429 3430 3431 3432 3433 3434 3435 3436 3437 3438 3439 3440 3441 3442 3443 3444 3445 3446 3447 3448 3449 3450 3451 3452 3453 3454 3455 3456 3457 3458 3459 3460 3461 3462 3463 3464 3465 3466 3467 3468 3469 3470 3471 3472 3473 3474 3475 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497 3498 3499 3500 3501 3502 3503 3504 3505 3506 3507 3508 3509 3510 3511 3512 3513 3514 3515 3516 3517 3518 3519 3520 3521 3522 3523 3524 3525 3526 3527 3528 3529 3530 3531 3532 3533 3534 3535 3536 3537 3538 3539 3540 3541 3542 3543 3544 3545 3546 3547 3548 3549 3550 3551 3552 3553 3554 3555 3556 3557 3558 3559 3560 3561 3562 3563 3564 3565 3566 3567 3568 3569 3570 3571 3572 3573 3574 3575 3576 3577 3578 3579 3580 3581 3582 3583 3584 3585 3586 3587 3588 3589 3590 3591 3592 3593 3594 3595 3596 3597 3598 3599 3600 3601 3602 3603 3604 3605 3606 3607 3608 3609 3610 3611 3612 3613 3614 3615 3616 3617 3618 3619 3620 3621 3622 3623 3624 3625 3626 3627 3628 3629 3630 3631 3632 3633 3634 3635 3636 3637 3638 3639 3640 3641 3642 3643 3644 3645 3646 3647 3648 3649 3650 3651 3652 3653 3654 3655 3656 3657 3658 3659 3660 3661 3662 3663 3664 3665 3666 3667 3668 3669 3670 3671 3672 3673 3674 3675 3676 3677 3678 3679 3680 3681 3682 3683 3684 3685 3686 3687 3688 3689 3690 3691 3692 3693 3694 3695 3696 3697 3698 3699 3700 3701 3702 3703 3704 3705 3706 3707 3708 3709 3710 3711 3712 3713 3714 3715 3716 3717 3718 3719 3720 3721 3722 3723 3724 3725 3726 3727 3728 3729 3730 3731 3732 3733 3734 3735 3736 3737 3738 3739 3740 3741 3742 3743 3744 3745 3746 3747 3748 3749 3750 3751 3752 3753 3754 3755 3756 3757 3758 3759 3760 3761 3762 3763 3764 3765 3766 3767 3768 3769 3770 3771 3772 3773 3774 3775 3776 3777 3778 3779 3780 3781 3782 3783 3784 3785 3786 3787 3788 3789 3790 3791 3792 3793 3794 3795 3796 3797 3798 3799 3800 3801 3802 3803 3804 3805 3806 3807 3808 3809 3810 3811 3812 3813 3814 3815 3816 3817 3818 3819 3820 3821 3822 3823 3824 3825 3826 3827 3828 3829 3830 3831 3832 3833 3834 3835 3836 3837 3838 3839 3840 3841 3842 3843 3844 3845 3846 3847 3848 3849 3850 3851 3852 3853 3854 3855 3856 3857 3858 3859 3860 3861 3862 3863 3864 3865 3866 3867 3868 3869 3870 3871 3872 3873 3874 3875 3876 3877 3878 3879 3880 3881 3882 3883 3884 3885 3886 3887 3888 3889 3890 3891 3892 3893 3894 3895 3896 3897 3898 3899 3900 3901 3902 3903 3904 3905 3906 3907 3908 3909 3910 3911 3912 3913 3914 3915 3916 3917 3918 3919 3920 3921 3922 3923 3924 3925 3926 3927 3928 3929 3930 3931 3932 3933 3934 3935 3936 3937 3938 3939 3940 3941 3942 3943 3944 3945 3946 3947 3948 3949 3950 3951 3952 3953 3954 3955 3956 3957 3958 3959 3960 3961 3962 3963 3964 3965 3966 3967 3968 3969 3970 3971 3972 3973 3974 3975 3976 3977 3978 3979 3980 3981 3982 3983 3984 3985 3986 3987 3988 3989 3990 3991 3992 3993 3994 3995 3996 3997 3998 3999 4000 4001 4002 4003 4004 4005 4006 4007 4008 4009 4010 4011 4012 4013 4014 4015 4016 4017 4018 4019 4020 4021 4022 4023 4024 4025 4026 4027 4028 4029 4030 4031 4032 4033 4034 4035 4036 4037 4038 4039 4040 4041 4042 4043 4044 4045 4046 4047 4048 4049 4050 4051 4052 4053 4054 4055 4056 4057 4058 4059 4060 4061 4062 4063 4064 4065 4066 4067 4068 4069 4070 4071 4072 4073 4074 4075 4076 4077 4078 4079 4080 4081 4082 4083 4084 4085 4086 4087 4088 4089 4090 4091 4092 4093 4094 4095 4096 4097 4098 4099 4100 4101 4102 4103 4104 4105 4106 4107 4108 4109 4110 4111 4112 4113 4114 4115 4116 4117 4118 4119 4120 4121 4122 4123 4124 4125 4126 4127 4128 4129 4130 4131 4132 4133 4134 4135 4136 4137 4138 4139 4140 4141 4142 4143 4144 4145 4146 4147 4148 4149 4150 4151 4152 4153 4154 4155 4156 4157 4158 4159 4160 4161 4162 4163 4164 4165 4166 4167 4168 4169 4170 4171 4172 4173 4174 4175 4176 4177 4178 4179 4180 4181 4182 4183 4184 4185 4186 4187 4188 4189 4190 4191 4192 4193 4194 4195 4196 4197 4198 4199 4200 4201 4202 4203 4204 4205 4206 4207 4208 4209 4210 4211 4212 4213 4214 4215 4216 4217 4218 4219 4220 4221 4222 4223 4224 4225 4226 4227 4228 4229 4230 4231 4232 4233 4234 4235 4236 4237 4238 4239 4240 4241 4242 4243 4244 4245 4246 4247 4248 4249 4250 4251 4252 4253 4254 4255 4256 4257 4258 4259 4260 4261 4262 4263 4264 4265 4266 4267 4268 4269 4270 4271 4272 4273 4274 4275 4276 4277 4278 4279 4280 4281 4282 4283 4284 4285 4286 4287 4288 4289 4290 4291 4292 4293 4294 4295 4296 4297 4298 4299 4300 4301 4302 4303 4304 4305 4306 4307 4308 4309 4310 4311 4312 4313 4314 4315 4316 4317 4318 4319 4320 4321 4322 4323 4324 4325 4326 4327 4328 4329 4330 4331 4332 4333 4334 4335 4336 4337 4338 4339 4340 4341 4342 4343 4344 4345 4346 4347 4348 4349 4350 4351 4352 4353 4354 4355 4356 4357 4358 4359 4360 4361 4362 4363 4364 4365 4366 4367 4368 4369 4370 4371 4372 4373 4374 4375 4376 4377 4378 4379 4380 4381 4382 4383 4384 4385 4386 4387 4388 4389 4390 4391 4392 4393 4394 4395 4396 4397 4398 4399 4400 4401 4402 4403 4404 4405 4406 4407 4408 4409 4410 4411 4412 4413 4414 4415 4416 4417 4418 4419 4420 4421 4422 4423 4424 4425 4426 4427 4428 4429 4430 4431 4432 4433 4434 4435 4436 4437 4438 4439 4440 4441 4442 4443 4444 4445 4446 4447 4448 4449 4450 4451 4452 4453 4454 4455 4456 4457 4458 4459 4460 4461 4462 4463 4464 4465 4466 4467 4468 4469 4470 4471 4472 4473 4474 4475 4476 4477 4478 4479 4480 4481 4482 4483 4484 4485 4486 4487 4488 4489 4490 4491 4492 4493 4494 4495 4496 4497 4498 4499 4500 4501 4502 4503 4504 4505 4506 4507 4508 4509 4510 4511 4512 4513 4514 4515 4516 4517 4518 4519 4520 4521 4522 4523 4524 4525 4526 4527 4528 4529 4530 4531 4532 4533 4534 4535 4536 4537 4538 4539 4540 4541 4542 4543 4544 4545 4546 4547 4548 4549 4550 4551 4552 4553 4554 4555 4556 4557 4558 4559 4560 4561 4562 4563 4564 4565 4566 4567 4568 4569 4570 4571 4572 4573 4574 4575 4576 4577 4578 4579 4580 4581 4582 4583 4584 4585 4586 4587 4588 4589 4590 4591 4592 |
WEBVTT
00:00:03.879 --> 00:00:07.480
cool um so this time I'm going to talk
00:00:05.480 --> 00:00:08.880
about word representation and text
00:00:07.480 --> 00:00:11.480
classifiers these are kind of the
00:00:08.880 --> 00:00:14.080
foundations that you need to know uh in
00:00:11.480 --> 00:00:15.640
order to move on to the more complex
00:00:14.080 --> 00:00:17.920
things that we'll be talking in future
00:00:15.640 --> 00:00:19.640
classes uh but actually the in
00:00:17.920 --> 00:00:22.760
particular the word representation part
00:00:19.640 --> 00:00:25.439
is pretty important it's a major uh
00:00:22.760 --> 00:00:31.800
thing that we need to do for all NLP
00:00:25.439 --> 00:00:34.239
models so uh let's go into it
00:00:31.800 --> 00:00:38.200
so last class I talked about the bag of
00:00:34.239 --> 00:00:40.239
words model um and just to review this
00:00:38.200 --> 00:00:43.920
was a model where basically we take each
00:00:40.239 --> 00:00:45.520
word we represent it as a one hot Vector
00:00:43.920 --> 00:00:48.760
uh like
00:00:45.520 --> 00:00:51.120
this and we add all of these vectors
00:00:48.760 --> 00:00:53.160
together we multiply the resulting
00:00:51.120 --> 00:00:55.160
frequency vector by some weights and we
00:00:53.160 --> 00:00:57.239
get a score out of this and we can use
00:00:55.160 --> 00:00:58.559
this score for binary classification or
00:00:57.239 --> 00:01:00.239
if we want to do multiclass
00:00:58.559 --> 00:01:02.519
classification we get you know multiple
00:01:00.239 --> 00:01:05.720
scores for each
00:01:02.519 --> 00:01:08.040
class and the features F were just based
00:01:05.720 --> 00:01:08.920
on our word identities and the weights
00:01:08.040 --> 00:01:12.159
were
00:01:08.920 --> 00:01:14.680
learned and um if we look at what's
00:01:12.159 --> 00:01:17.520
missing in bag of words
00:01:14.680 --> 00:01:19.600
models um we talked about handling of
00:01:17.520 --> 00:01:23.280
conjugated or compound
00:01:19.600 --> 00:01:25.439
words we talked about handling of word
00:01:23.280 --> 00:01:27.880
similarity and we talked about handling
00:01:25.439 --> 00:01:30.240
of combination features and handling of
00:01:27.880 --> 00:01:33.280
sentence structure and so all of these
00:01:30.240 --> 00:01:35.000
are are tricky problems uh we saw that
00:01:33.280 --> 00:01:37.000
you know creating a rule-based system to
00:01:35.000 --> 00:01:39.000
solve these problems is non-trivial and
00:01:37.000 --> 00:01:41.399
at the very least would take a lot of
00:01:39.000 --> 00:01:44.079
time and so now I want to talk about
00:01:41.399 --> 00:01:47.119
some solutions to the problems in this
00:01:44.079 --> 00:01:49.280
class so the first the solution to the
00:01:47.119 --> 00:01:52.240
first problem or a solution to the first
00:01:49.280 --> 00:01:54.880
problem is uh subword or character based
00:01:52.240 --> 00:01:57.520
models and that's what I'll talk about
00:01:54.880 --> 00:02:00.719
first handling of word similarity this
00:01:57.520 --> 00:02:02.960
can be handled uh using Word edings
00:02:00.719 --> 00:02:05.079
and the word embeddings uh will be
00:02:02.960 --> 00:02:07.159
another thing we'll talk about this time
00:02:05.079 --> 00:02:08.879
handling of combination features uh we
00:02:07.159 --> 00:02:11.039
can handle through neural networks which
00:02:08.879 --> 00:02:14.040
we'll also talk about this time and then
00:02:11.039 --> 00:02:15.560
handling of sentence structure uh the
00:02:14.040 --> 00:02:17.720
kind of standard way of handling this
00:02:15.560 --> 00:02:20.120
now is through sequence-based models and
00:02:17.720 --> 00:02:24.879
that will be uh starting in a few
00:02:20.120 --> 00:02:28.080
classes so uh let's jump into
00:02:24.879 --> 00:02:30.000
it so subword models uh as I mentioned
00:02:28.080 --> 00:02:31.840
this is a really really important part
00:02:30.000 --> 00:02:33.360
all of the models that we're building
00:02:31.840 --> 00:02:35.480
nowadays including you know
00:02:33.360 --> 00:02:38.239
state-of-the-art language models and and
00:02:35.480 --> 00:02:42.200
things like this and the basic idea
00:02:38.239 --> 00:02:44.720
behind this is that we want to split uh
00:02:42.200 --> 00:02:48.040
in particular split less common words up
00:02:44.720 --> 00:02:50.200
into multiple subboard tokens so to give
00:02:48.040 --> 00:02:52.200
an example of this uh if we have
00:02:50.200 --> 00:02:55.040
something like the companies are
00:02:52.200 --> 00:02:57.000
expanding uh it might split companies
00:02:55.040 --> 00:03:02.120
into compan
00:02:57.000 --> 00:03:05.000
e and expand in like this and there are
00:03:02.120 --> 00:03:08.480
a few benefits of this uh the first
00:03:05.000 --> 00:03:10.760
benefit is that this allows you to
00:03:08.480 --> 00:03:13.360
parameters between word varieties or
00:03:10.760 --> 00:03:15.200
compound words and the other one is to
00:03:13.360 --> 00:03:17.400
reduce parameter size and save compute
00:03:15.200 --> 00:03:19.720
and meming and both of these are kind of
00:03:17.400 --> 00:03:23.239
like equally important things that we
00:03:19.720 --> 00:03:25.519
need to be uh we need to be considering
00:03:23.239 --> 00:03:26.440
so does anyone know how many words there
00:03:25.519 --> 00:03:28.680
are in
00:03:26.440 --> 00:03:31.680
English any
00:03:28.680 --> 00:03:31.680
ideas
00:03:36.799 --> 00:03:43.400
yeah two
00:03:38.599 --> 00:03:45.560
million pretty good um any other
00:03:43.400 --> 00:03:47.159
ideas
00:03:45.560 --> 00:03:50.360
yeah
00:03:47.159 --> 00:03:53.599
60,000 some models use 60,000 I I think
00:03:50.360 --> 00:03:56.200
60,000 is probably these subword models
00:03:53.599 --> 00:03:58.079
uh when you're talking about this so
00:03:56.200 --> 00:03:59.319
they can use sub models to take the 2
00:03:58.079 --> 00:04:03.480
million which I think is a reasonable
00:03:59.319 --> 00:04:07.400
guess to 6 60,000 any other
00:04:03.480 --> 00:04:08.840
ideas 700,000 okay pretty good um so
00:04:07.400 --> 00:04:11.799
this was a per question it doesn't
00:04:08.840 --> 00:04:14.760
really have a good answer um but two 200
00:04:11.799 --> 00:04:17.479
million's probably pretty good six uh
00:04:14.760 --> 00:04:19.160
700,000 is pretty good the reason why
00:04:17.479 --> 00:04:21.360
this is a trick question is because are
00:04:19.160 --> 00:04:24.440
company and companies different
00:04:21.360 --> 00:04:26.840
words uh maybe maybe not right because
00:04:24.440 --> 00:04:30.120
if we know the word company we can you
00:04:26.840 --> 00:04:32.520
know guess what the word companies means
00:04:30.120 --> 00:04:35.720
um what about automobile is that a
00:04:32.520 --> 00:04:37.400
different word well maybe if we know
00:04:35.720 --> 00:04:39.400
Auto and mobile we can kind of guess
00:04:37.400 --> 00:04:41.160
what automobile means but not really so
00:04:39.400 --> 00:04:43.479
maybe that's a different word there's
00:04:41.160 --> 00:04:45.960
all kinds of Shades of Gray there and
00:04:43.479 --> 00:04:48.120
also we have really frequent words that
00:04:45.960 --> 00:04:50.360
everybody can probably acknowledge our
00:04:48.120 --> 00:04:52.320
words like
00:04:50.360 --> 00:04:55.639
the and
00:04:52.320 --> 00:04:58.520
a and um maybe
00:04:55.639 --> 00:05:00.680
car and then we have words down here
00:04:58.520 --> 00:05:02.320
which are like Miss spellings or
00:05:00.680 --> 00:05:04.160
something like that misspellings of
00:05:02.320 --> 00:05:06.520
actual correct words or
00:05:04.160 --> 00:05:09.199
slay uh or other things like that and
00:05:06.520 --> 00:05:12.520
then it's questionable whether those are
00:05:09.199 --> 00:05:17.199
actual words or not so um there's a
00:05:12.520 --> 00:05:19.520
famous uh law called Zip's
00:05:17.199 --> 00:05:21.280
law um which probably a lot of people
00:05:19.520 --> 00:05:23.360
have heard of it's also the source of
00:05:21.280 --> 00:05:26.919
your zip
00:05:23.360 --> 00:05:30.160
file um which is using Zip's law to
00:05:26.919 --> 00:05:32.400
compress uh compress output by making
00:05:30.160 --> 00:05:34.880
the uh more frequent words have shorter
00:05:32.400 --> 00:05:37.520
bite strings and less frequent words
00:05:34.880 --> 00:05:38.800
have uh you know less frequent bite
00:05:37.520 --> 00:05:43.120
strings but basically like we're going
00:05:38.800 --> 00:05:45.120
to have an infinite number of words or
00:05:43.120 --> 00:05:46.360
at least strings that are separated by
00:05:45.120 --> 00:05:49.280
white space so we need to handle this
00:05:46.360 --> 00:05:53.199
somehow and that's what subword units
00:05:49.280 --> 00:05:54.560
do so um 60,000 was a good guess for the
00:05:53.199 --> 00:05:57.160
number of subword units you might use in
00:05:54.560 --> 00:06:00.759
a model and so uh by using subw units we
00:05:57.160 --> 00:06:04.840
can limit to about that much
00:06:00.759 --> 00:06:08.160
so there's a couple of common uh ways to
00:06:04.840 --> 00:06:10.440
create these subword units and basically
00:06:08.160 --> 00:06:14.560
all of them rely on the fact that you
00:06:10.440 --> 00:06:16.039
want more common strings to become
00:06:14.560 --> 00:06:19.599
subword
00:06:16.039 --> 00:06:22.199
units um or actually sorry I realize
00:06:19.599 --> 00:06:24.280
maybe before doing that I could explain
00:06:22.199 --> 00:06:26.360
an alternative to creating subword units
00:06:24.280 --> 00:06:29.639
so the alternative to creating subword
00:06:26.360 --> 00:06:33.560
units is to treat every character or
00:06:29.639 --> 00:06:36.919
maybe every bite in a string as a single
00:06:33.560 --> 00:06:38.560
thing that you encode in forent so in
00:06:36.919 --> 00:06:42.520
other words instead of trying to model
00:06:38.560 --> 00:06:47.919
the companies are expanding we Model T h
00:06:42.520 --> 00:06:50.199
e space c o m uh etc etc can anyone
00:06:47.919 --> 00:06:53.199
think of any downsides of
00:06:50.199 --> 00:06:53.199
this
00:06:57.039 --> 00:07:01.879
yeah yeah the set of these will be very
00:07:00.080 --> 00:07:05.000
will be very small but that's not
00:07:01.879 --> 00:07:05.000
necessarily a problem
00:07:08.560 --> 00:07:15.599
right yeah um and any other
00:07:12.599 --> 00:07:15.599
ideas
00:07:19.520 --> 00:07:24.360
yeah yeah the resulting sequences will
00:07:22.080 --> 00:07:25.520
be very long um and when you say
00:07:24.360 --> 00:07:27.160
difficult to use it could be difficult
00:07:25.520 --> 00:07:29.560
to use for a couple of reasons there's
00:07:27.160 --> 00:07:31.840
mainly two reasons actually any any IDE
00:07:29.560 --> 00:07:31.840
about
00:07:33.479 --> 00:07:37.800
this any
00:07:46.280 --> 00:07:50.599
yeah yeah that's a little bit of a
00:07:49.000 --> 00:07:52.319
separate problem than the character
00:07:50.599 --> 00:07:53.919
based model so let me get back to that
00:07:52.319 --> 00:07:56.400
but uh let let's finish the discussion
00:07:53.919 --> 00:07:58.360
of the character based models so if it's
00:07:56.400 --> 00:08:00.120
really if it's really long maybe a
00:07:58.360 --> 00:08:01.879
simple thing like uh let's say you have
00:08:00.120 --> 00:08:06.560
a big neural network and it's processing
00:08:01.879 --> 00:08:06.560
a really long sequence any ideas what
00:08:06.919 --> 00:08:10.879
happens basically you run out of memory
00:08:09.280 --> 00:08:13.440
or it takes a really long time right so
00:08:10.879 --> 00:08:16.840
you have computational problems another
00:08:13.440 --> 00:08:18.479
reason why is um think of what a bag of
00:08:16.840 --> 00:08:21.400
words model would look like if it was a
00:08:18.479 --> 00:08:21.400
bag of characters
00:08:21.800 --> 00:08:25.919
model it wouldn't be very informative
00:08:24.199 --> 00:08:27.599
about whether like a sentence is
00:08:25.919 --> 00:08:30.919
positive sentiment or negative sentiment
00:08:27.599 --> 00:08:32.959
right because instead of having uh go o
00:08:30.919 --> 00:08:35.039
you would have uh instead of having good
00:08:32.959 --> 00:08:36.360
you would have go o and that doesn't
00:08:35.039 --> 00:08:38.560
really directly tell you whether it's
00:08:36.360 --> 00:08:41.719
positive sentiment or not so those are
00:08:38.560 --> 00:08:43.680
basically the two problems um compute
00:08:41.719 --> 00:08:45.320
and lack of expressiveness in the
00:08:43.680 --> 00:08:50.720
underlying representations so you need
00:08:45.320 --> 00:08:52.080
to handle both of those yes so if we uh
00:08:50.720 --> 00:08:54.480
move from
00:08:52.080 --> 00:08:56.440
character better expressiveness and we
00:08:54.480 --> 00:08:58.920
assume that if we just get the bigger
00:08:56.440 --> 00:09:00.120
and bigger paragraphs we'll get even
00:08:58.920 --> 00:09:02.760
better
00:09:00.120 --> 00:09:05.120
yeah so a very good question I'll repeat
00:09:02.760 --> 00:09:06.560
it um and actually this also goes back
00:09:05.120 --> 00:09:08.040
to the other question you asked about
00:09:06.560 --> 00:09:09.519
words that look the same but are
00:09:08.040 --> 00:09:12.160
pronounced differently or have different
00:09:09.519 --> 00:09:14.360
meanings and so like let's say we just
00:09:12.160 --> 00:09:15.920
remembered this whole sentence right the
00:09:14.360 --> 00:09:18.279
companies are
00:09:15.920 --> 00:09:21.600
expanding um and that was like a single
00:09:18.279 --> 00:09:22.680
embedding and we somehow embedded it the
00:09:21.600 --> 00:09:25.720
problem would be we're never going to
00:09:22.680 --> 00:09:27.120
see that sentence again um or if we go
00:09:25.720 --> 00:09:29.480
to longer sentences we're never going to
00:09:27.120 --> 00:09:31.839
see the longer sentences again so it
00:09:29.480 --> 00:09:34.320
becomes too sparse so there's kind of a
00:09:31.839 --> 00:09:37.240
sweet spot between
00:09:34.320 --> 00:09:40.279
like long enough to be expressive and
00:09:37.240 --> 00:09:42.480
short enough to occur many times so that
00:09:40.279 --> 00:09:43.959
you can learn appropriately and that's
00:09:42.480 --> 00:09:47.120
kind of what subword models are aiming
00:09:43.959 --> 00:09:48.360
for and if you get longer subwords then
00:09:47.120 --> 00:09:50.200
you'll get things that are more
00:09:48.360 --> 00:09:52.959
expressive but more sparse in shorter
00:09:50.200 --> 00:09:55.440
subwords you'll get things that are like
00:09:52.959 --> 00:09:57.279
uh less expressive but less spice so you
00:09:55.440 --> 00:09:59.120
need to balance between them and then
00:09:57.279 --> 00:10:00.600
once we get into sequence modeling they
00:09:59.120 --> 00:10:02.600
start being able to model like which
00:10:00.600 --> 00:10:04.120
words are next to each other uh which
00:10:02.600 --> 00:10:06.040
tokens are next to each other and stuff
00:10:04.120 --> 00:10:07.800
like that so even if they are less
00:10:06.040 --> 00:10:11.279
expressive the combination between them
00:10:07.800 --> 00:10:12.600
can be expressive so um yeah that's kind
00:10:11.279 --> 00:10:13.440
of a preview of what we're going to be
00:10:12.600 --> 00:10:17.320
doing
00:10:13.440 --> 00:10:19.279
next okay so um let's assume that we
00:10:17.320 --> 00:10:21.320
want to have some subwords that are
00:10:19.279 --> 00:10:23.000
longer than characters but shorter than
00:10:21.320 --> 00:10:26.240
tokens how do we make these in a
00:10:23.000 --> 00:10:28.680
consistent way there's two major ways of
00:10:26.240 --> 00:10:31.480
doing this uh the first one is bite pair
00:10:28.680 --> 00:10:32.839
encoding and this is uh very very simple
00:10:31.480 --> 00:10:35.839
in fact it's so
00:10:32.839 --> 00:10:35.839
simple
00:10:36.600 --> 00:10:40.839
that we can implement
00:10:41.839 --> 00:10:47.240
it in this notebook here which you can
00:10:44.600 --> 00:10:51.720
click through to on the
00:10:47.240 --> 00:10:55.440
slides and it's uh
00:10:51.720 --> 00:10:58.040
about 10 lines of code um and so
00:10:55.440 --> 00:11:01.040
basically what B pair encoding
00:10:58.040 --> 00:11:01.040
does
00:11:04.600 --> 00:11:09.560
is that you start out with um all of the
00:11:07.000 --> 00:11:14.360
vocabulary that you want to process
00:11:09.560 --> 00:11:17.560
where each vocabulary item is split into
00:11:14.360 --> 00:11:21.240
uh the characters and an end of word
00:11:17.560 --> 00:11:23.360
symbol and you have a corresponding
00:11:21.240 --> 00:11:27.519
frequency of
00:11:23.360 --> 00:11:31.120
this you then uh get statistics about
00:11:27.519 --> 00:11:33.279
the most common pairs of tokens that
00:11:31.120 --> 00:11:34.880
occur next to each other and so here the
00:11:33.279 --> 00:11:38.240
most common pairs of tokens that occur
00:11:34.880 --> 00:11:41.920
next to each other are e s because it
00:11:38.240 --> 00:11:46.560
occurs nine times because it occurs in
00:11:41.920 --> 00:11:48.279
newest and wildest also s and t w
00:11:46.560 --> 00:11:51.440
because those occur there too and then
00:11:48.279 --> 00:11:53.519
you have we and other things like that
00:11:51.440 --> 00:11:56.000
so out of all the most frequent ones you
00:11:53.519 --> 00:11:59.920
just merge them together and that gives
00:11:56.000 --> 00:12:02.720
you uh new s new
00:11:59.920 --> 00:12:05.200
EST and wide
00:12:02.720 --> 00:12:09.360
EST and then you do the same thing this
00:12:05.200 --> 00:12:12.519
time now you get EST so now you get this
00:12:09.360 --> 00:12:14.279
uh suffix EST and that looks pretty
00:12:12.519 --> 00:12:16.399
reasonable for English right you know
00:12:14.279 --> 00:12:19.040
EST is a common suffix that we use it
00:12:16.399 --> 00:12:22.399
seems like it should be a single token
00:12:19.040 --> 00:12:25.880
and um so you just do this over and over
00:12:22.399 --> 00:12:29.279
again if you want a vocabulary of 60,000
00:12:25.880 --> 00:12:31.120
for example you would do um 60,000 minus
00:12:29.279 --> 00:12:33.079
number of characters merge operations
00:12:31.120 --> 00:12:37.160
and eventually you would get a B of
00:12:33.079 --> 00:12:41.920
60,000 um and yeah very very simple
00:12:37.160 --> 00:12:41.920
method to do this um any questions about
00:12:43.160 --> 00:12:46.160
that
00:12:57.839 --> 00:13:00.839
yeah
00:13:15.600 --> 00:13:20.959
yeah so uh just to repeat the the
00:13:18.040 --> 00:13:23.560
comment uh this seems like a greedy
00:13:20.959 --> 00:13:25.320
version of Huffman encoding which is a
00:13:23.560 --> 00:13:28.839
you know similar to what you're using in
00:13:25.320 --> 00:13:32.000
your zip file a way to shorten things by
00:13:28.839 --> 00:13:36.560
getting longer uh more frequent things
00:13:32.000 --> 00:13:39.120
being inced as a single token um I think
00:13:36.560 --> 00:13:40.760
B pair encoding did originally start
00:13:39.120 --> 00:13:43.720
like that that's part of the reason why
00:13:40.760 --> 00:13:45.760
the encoding uh thing is here I think it
00:13:43.720 --> 00:13:47.360
originally started there I haven't read
00:13:45.760 --> 00:13:49.360
really deeply into this but I can talk
00:13:47.360 --> 00:13:53.240
more about how the next one corresponds
00:13:49.360 --> 00:13:54.440
to information Theory and Tuesday I'm
00:13:53.240 --> 00:13:55.720
going to talk even more about how
00:13:54.440 --> 00:13:57.720
language models correspond to
00:13:55.720 --> 00:14:00.040
information theories so we can uh we can
00:13:57.720 --> 00:14:04.519
discuss maybe in more detail
00:14:00.040 --> 00:14:07.639
to um so the the alternative option is
00:14:04.519 --> 00:14:10.000
to use unigram models and unigram models
00:14:07.639 --> 00:14:12.240
are the simplest type of language model
00:14:10.000 --> 00:14:15.079
I'm going to talk more in detail about
00:14:12.240 --> 00:14:18.279
them next time but basically uh the way
00:14:15.079 --> 00:14:20.759
it works is you create a model that
00:14:18.279 --> 00:14:23.600
generates all word uh words in the
00:14:20.759 --> 00:14:26.199
sequence independently sorry I thought I
00:14:23.600 --> 00:14:26.199
had a
00:14:26.320 --> 00:14:31.800
um I thought I had an equation but
00:14:28.800 --> 00:14:31.800
basically the
00:14:32.240 --> 00:14:35.759
equation looks
00:14:38.079 --> 00:14:41.079
like
00:14:47.720 --> 00:14:52.120
this so you say the probability of the
00:14:50.360 --> 00:14:53.440
sequence is the product of the
00:14:52.120 --> 00:14:54.279
probabilities of each of the words in
00:14:53.440 --> 00:14:55.959
the
00:14:54.279 --> 00:15:00.079
sequence
00:14:55.959 --> 00:15:04.079
and uh then you try to pick a vocabulary
00:15:00.079 --> 00:15:06.839
that maximizes the probability of the
00:15:04.079 --> 00:15:09.320
Corpus given a fixed vocabulary size so
00:15:06.839 --> 00:15:10.320
you try to say okay you get a vocabulary
00:15:09.320 --> 00:15:14.440
size of
00:15:10.320 --> 00:15:16.920
60,000 how do you um how do you pick the
00:15:14.440 --> 00:15:19.680
best 60,000 vocabulary to maximize the
00:15:16.920 --> 00:15:22.440
probability of the the Corpus and that
00:15:19.680 --> 00:15:25.959
will result in something very similar uh
00:15:22.440 --> 00:15:27.920
it will also try to give longer uh
00:15:25.959 --> 00:15:29.880
vocabulary uh sorry more common
00:15:27.920 --> 00:15:32.240
vocabulary long sequences because that
00:15:29.880 --> 00:15:35.560
allows you to to maximize this
00:15:32.240 --> 00:15:36.959
objective um the optimization for this
00:15:35.560 --> 00:15:40.040
is performed using something called the
00:15:36.959 --> 00:15:44.440
EM algorithm where basically you uh
00:15:40.040 --> 00:15:48.560
predict the uh the probability of each
00:15:44.440 --> 00:15:51.600
token showing up and uh then select the
00:15:48.560 --> 00:15:53.279
most common tokens and then trim off the
00:15:51.600 --> 00:15:54.759
ones that are less common and then just
00:15:53.279 --> 00:15:58.120
do this over and over again until you
00:15:54.759 --> 00:15:59.839
drop down to the 60,000 token lat so the
00:15:58.120 --> 00:16:02.040
details for this are not important for
00:15:59.839 --> 00:16:04.160
most people in this class uh because
00:16:02.040 --> 00:16:07.480
you're going to just be using a toolkit
00:16:04.160 --> 00:16:08.880
that implements this for you um but if
00:16:07.480 --> 00:16:10.759
you're interested in this I'm happy to
00:16:08.880 --> 00:16:14.199
talk to you about it
00:16:10.759 --> 00:16:14.199
yeah is there
00:16:14.680 --> 00:16:18.959
problem Oh in unigram models there's a
00:16:17.199 --> 00:16:20.959
huge problem with assuming Independence
00:16:18.959 --> 00:16:22.720
in language models because then you
00:16:20.959 --> 00:16:25.120
could rearrange the order of words in
00:16:22.720 --> 00:16:26.600
sentences um that that's something we're
00:16:25.120 --> 00:16:27.519
going to talk about in language model
00:16:26.600 --> 00:16:30.560
next
00:16:27.519 --> 00:16:32.839
time but the the good thing about this
00:16:30.560 --> 00:16:34.519
is the EM algorithm requires dynamic
00:16:32.839 --> 00:16:36.079
programming in this case and you can't
00:16:34.519 --> 00:16:37.800
easily do dynamic programming if you
00:16:36.079 --> 00:16:40.160
don't make that
00:16:37.800 --> 00:16:41.880
assumptions um and then finally after
00:16:40.160 --> 00:16:43.560
you've picked your vocabulary and you've
00:16:41.880 --> 00:16:45.720
assigned a probability to each word in
00:16:43.560 --> 00:16:47.800
the vocabulary you then find a
00:16:45.720 --> 00:16:49.639
segmentation of the input that maximizes
00:16:47.800 --> 00:16:52.600
the unigram
00:16:49.639 --> 00:16:54.880
probabilities um so this is basically
00:16:52.600 --> 00:16:56.519
the idea of what's going on here um I'm
00:16:54.880 --> 00:16:58.120
not going to go into a lot of detail
00:16:56.519 --> 00:17:00.560
about this because most people are just
00:16:58.120 --> 00:17:02.279
going to be users of this algorithm so
00:17:00.560 --> 00:17:06.240
it's not super super
00:17:02.279 --> 00:17:09.400
important um the one important thing
00:17:06.240 --> 00:17:11.240
about this is that there's a library
00:17:09.400 --> 00:17:15.520
called sentence piece that's used very
00:17:11.240 --> 00:17:19.199
widely in order to build these um in
00:17:15.520 --> 00:17:22.000
order to build these subword units and
00:17:19.199 --> 00:17:23.720
uh basically what you do is you run the
00:17:22.000 --> 00:17:27.600
sentence piece
00:17:23.720 --> 00:17:30.200
train uh model or sorry uh program and
00:17:27.600 --> 00:17:32.640
that gives you uh you select your vocab
00:17:30.200 --> 00:17:34.240
size uh this also this character
00:17:32.640 --> 00:17:36.120
coverage is basically how well do you
00:17:34.240 --> 00:17:39.760
need to cover all of the characters in
00:17:36.120 --> 00:17:41.840
your vocabulary or in your input text um
00:17:39.760 --> 00:17:45.240
what model type do you use and then you
00:17:41.840 --> 00:17:48.640
run this uh sentence piece en code file
00:17:45.240 --> 00:17:51.039
uh to uh encode the output and split the
00:17:48.640 --> 00:17:54.799
output and there's also python bindings
00:17:51.039 --> 00:17:56.240
available for this and by the one thing
00:17:54.799 --> 00:17:57.919
that you should know is by default it
00:17:56.240 --> 00:18:00.600
uses the unigram model but it also
00:17:57.919 --> 00:18:01.960
supports EP in my experience it doesn't
00:18:00.600 --> 00:18:05.159
make a huge difference about which one
00:18:01.960 --> 00:18:07.640
you use the bigger thing is how um how
00:18:05.159 --> 00:18:10.159
big is your vocabulary size and if your
00:18:07.640 --> 00:18:11.880
vocabulary size is smaller then things
00:18:10.159 --> 00:18:13.760
will be more efficient but less
00:18:11.880 --> 00:18:17.480
expressive if your vocabulary size is
00:18:13.760 --> 00:18:21.280
bigger things will be um will
00:18:17.480 --> 00:18:23.240
be more expressive but less efficient
00:18:21.280 --> 00:18:25.360
and A good rule of thumb is like
00:18:23.240 --> 00:18:26.960
something like 60,000 to 80,000 is
00:18:25.360 --> 00:18:29.120
pretty reasonable if you're only doing
00:18:26.960 --> 00:18:31.320
English if you're spreading out to
00:18:29.120 --> 00:18:32.600
things that do other languages um which
00:18:31.320 --> 00:18:35.960
I'll talk about in a second then you
00:18:32.600 --> 00:18:38.720
need a much bigger B regular
00:18:35.960 --> 00:18:40.559
say so there's two considerations here
00:18:38.720 --> 00:18:42.440
two important considerations when using
00:18:40.559 --> 00:18:46.320
these models uh the first is
00:18:42.440 --> 00:18:48.760
multilinguality as I said so when you're
00:18:46.320 --> 00:18:50.760
using um subword
00:18:48.760 --> 00:18:54.710
models they're hard to use
00:18:50.760 --> 00:18:55.840
multilingually because as I said before
00:18:54.710 --> 00:18:59.799
[Music]
00:18:55.840 --> 00:19:03.799
they give longer strings to more
00:18:59.799 --> 00:19:06.520
frequent strings basically so then
00:19:03.799 --> 00:19:09.559
imagine what happens if 50% of your
00:19:06.520 --> 00:19:11.919
Corpus is English another 30% of your
00:19:09.559 --> 00:19:15.400
Corpus is
00:19:11.919 --> 00:19:17.200
other languages written in Latin script
00:19:15.400 --> 00:19:21.720
10% is
00:19:17.200 --> 00:19:25.480
Chinese uh 5% is cerlic script languages
00:19:21.720 --> 00:19:27.240
four 4% is 3% is Japanese and then you
00:19:25.480 --> 00:19:31.080
have like
00:19:27.240 --> 00:19:33.320
0.01% written in like burmes or
00:19:31.080 --> 00:19:35.520
something like that suddenly burmes just
00:19:33.320 --> 00:19:37.400
gets chunked up really really tiny
00:19:35.520 --> 00:19:38.360
really long sequences and it doesn't
00:19:37.400 --> 00:19:45.559
work as
00:19:38.360 --> 00:19:45.559
well um so one way that people fix this
00:19:45.919 --> 00:19:50.520
um and actually there's a really nice uh
00:19:48.760 --> 00:19:52.600
blog post about this called exploring
00:19:50.520 --> 00:19:53.760
B's vocabulary which I referenced here
00:19:52.600 --> 00:19:58.039
if you're interested in learning more
00:19:53.760 --> 00:20:02.960
about that um but one way that people
00:19:58.039 --> 00:20:05.240
were around this is if your
00:20:02.960 --> 00:20:07.960
actual uh data
00:20:05.240 --> 00:20:11.559
distribution looks like this like
00:20:07.960 --> 00:20:11.559
English uh
00:20:17.039 --> 00:20:23.159
Ty we actually sorry I took out the
00:20:19.280 --> 00:20:23.159
Indian languages in my example
00:20:24.960 --> 00:20:30.159
apologies
00:20:27.159 --> 00:20:30.159
so
00:20:30.400 --> 00:20:35.919
um what you do is you essentially create
00:20:33.640 --> 00:20:40.000
a different distribution that like
00:20:35.919 --> 00:20:43.559
downweights English a little bit and up
00:20:40.000 --> 00:20:47.000
weights up weights all of the other
00:20:43.559 --> 00:20:49.480
languages um so that you get more of
00:20:47.000 --> 00:20:53.159
other languages when creating so this is
00:20:49.480 --> 00:20:53.159
a common work around that you can do for
00:20:54.200 --> 00:20:59.960
this um the
00:20:56.799 --> 00:21:03.000
second problem with these is
00:20:59.960 --> 00:21:08.000
arbitrariness so as you saw in my
00:21:03.000 --> 00:21:11.240
example with bpe e s s and t and of
00:21:08.000 --> 00:21:13.520
board symbol all have the same probabil
00:21:11.240 --> 00:21:16.960
or have the same frequency right so if
00:21:13.520 --> 00:21:21.520
we get to that point do we segment es or
00:21:16.960 --> 00:21:25.039
do we seg uh EST or do we segment e
00:21:21.520 --> 00:21:26.559
s and so this is also a problem and it
00:21:25.039 --> 00:21:29.000
actually can affect your results
00:21:26.559 --> 00:21:30.480
especially if you like don't have a
00:21:29.000 --> 00:21:31.760
really strong vocabulary for the
00:21:30.480 --> 00:21:33.279
language you're working in or you're
00:21:31.760 --> 00:21:37.200
working in a new
00:21:33.279 --> 00:21:40.159
domain and so there's a few workarounds
00:21:37.200 --> 00:21:41.520
for this uh one workaround for this is
00:21:40.159 --> 00:21:44.000
uh called subword
00:21:41.520 --> 00:21:46.279
regularization and the way it works is
00:21:44.000 --> 00:21:49.400
instead
00:21:46.279 --> 00:21:51.640
of just having a single segmentation and
00:21:49.400 --> 00:21:54.679
getting the kind of
00:21:51.640 --> 00:21:56.200
maximally probable segmentation or the
00:21:54.679 --> 00:21:58.480
one the greedy one that you get out of
00:21:56.200 --> 00:22:01.360
BP instead you sample different
00:21:58.480 --> 00:22:03.000
segmentations in training time and use
00:22:01.360 --> 00:22:05.720
the different segmentations and that
00:22:03.000 --> 00:22:09.200
makes your model more robust to this
00:22:05.720 --> 00:22:10.840
kind of variation and that's also
00:22:09.200 --> 00:22:15.679
actually the reason why sentence piece
00:22:10.840 --> 00:22:17.919
was released was through this um subword
00:22:15.679 --> 00:22:19.559
regularization paper so that's also
00:22:17.919 --> 00:22:22.720
implemented in sentence piece if that's
00:22:19.559 --> 00:22:22.720
something you're interested in
00:22:24.919 --> 00:22:32.520
trying cool um are there any questions
00:22:28.480 --> 00:22:32.520
or discussions about this
00:22:53.279 --> 00:22:56.279
yeah
00:22:56.960 --> 00:22:59.960
already
00:23:06.799 --> 00:23:11.080
yeah so this is a good question um just
00:23:08.960 --> 00:23:12.760
to repeat the question it was like let's
00:23:11.080 --> 00:23:16.080
say we have a big
00:23:12.760 --> 00:23:19.640
multilingual um subword
00:23:16.080 --> 00:23:23.440
model and we want to add a new language
00:23:19.640 --> 00:23:26.240
in some way uh how can we reuse the
00:23:23.440 --> 00:23:28.880
existing model but add a new
00:23:26.240 --> 00:23:31.080
language it's a good question if you're
00:23:28.880 --> 00:23:33.679
only using it for subord
00:23:31.080 --> 00:23:36.320
segmentation um one one nice thing about
00:23:33.679 --> 00:23:36.320
the unigram
00:23:36.400 --> 00:23:41.799
model here is this is kind of a
00:23:38.880 --> 00:23:43.679
probabilistic model so it's very easy to
00:23:41.799 --> 00:23:46.360
do the kind of standard things that we
00:23:43.679 --> 00:23:48.240
do with probabilistic models which is
00:23:46.360 --> 00:23:50.559
like let's say we had an
00:23:48.240 --> 00:23:53.919
old uh an
00:23:50.559 --> 00:23:56.880
old vocabulary for
00:23:53.919 --> 00:23:59.880
this um we could just
00:23:56.880 --> 00:23:59.880
interpolate
00:24:07.159 --> 00:24:12.320
um we could interpolate like this and
00:24:09.559 --> 00:24:13.840
just you know uh combine the
00:24:12.320 --> 00:24:17.080
probabilities of the two and then use
00:24:13.840 --> 00:24:19.520
that combine probability in order to
00:24:17.080 --> 00:24:21.320
segment the new language um things like
00:24:19.520 --> 00:24:24.159
this have been uh done before but I
00:24:21.320 --> 00:24:26.159
don't remember the exact preferences uh
00:24:24.159 --> 00:24:30.440
for them but that that's what I would do
00:24:26.159 --> 00:24:31.960
here another interesting thing is um
00:24:30.440 --> 00:24:35.399
this might be getting a little ahead of
00:24:31.960 --> 00:24:35.399
myself but there's
00:24:48.559 --> 00:24:58.279
a there's a paper that talks about um
00:24:55.360 --> 00:25:00.159
how you can take things that or trained
00:24:58.279 --> 00:25:03.360
with another
00:25:00.159 --> 00:25:05.480
vocabulary and basically the idea is um
00:25:03.360 --> 00:25:09.320
you pre-train on whatever languages you
00:25:05.480 --> 00:25:10.679
have and then uh you learn embeddings in
00:25:09.320 --> 00:25:11.880
the new language you freeze the body of
00:25:10.679 --> 00:25:14.360
the model and learn embeddings in the
00:25:11.880 --> 00:25:15.880
new language so that's another uh method
00:25:14.360 --> 00:25:19.080
that's used it's called on the cross
00:25:15.880 --> 00:25:19.080
lingual printability
00:25:21.840 --> 00:25:26.159
representations and I'll probably talk
00:25:23.840 --> 00:25:28.480
about that in the last class of this uh
00:25:26.159 --> 00:25:30.720
thing so you can remember that
00:25:28.480 --> 00:25:33.720
then cool any other
00:25:30.720 --> 00:25:33.720
questions
00:25:38.480 --> 00:25:42.640
yeah is bag of words a first step to
00:25:41.039 --> 00:25:46.640
process your data if you want to do
00:25:42.640 --> 00:25:49.919
Generation Um do you mean like
00:25:46.640 --> 00:25:52.440
uh a word based model or a subword based
00:25:49.919 --> 00:25:52.440
model
00:25:56.679 --> 00:26:00.480
or like is
00:26:02.360 --> 00:26:08.000
this so the subword segmentation is the
00:26:05.919 --> 00:26:10.640
first step of creating just about any
00:26:08.000 --> 00:26:13.080
model nowadays like every model every
00:26:10.640 --> 00:26:16.600
model uses this and they usually use
00:26:13.080 --> 00:26:21.520
this either to segment characters or
00:26:16.600 --> 00:26:23.559
byes um characters are like Unicode code
00:26:21.520 --> 00:26:25.799
points so they actually correspond to an
00:26:23.559 --> 00:26:28.279
actual visual character and then bites
00:26:25.799 --> 00:26:31.120
are many unicode characters are like
00:26:28.279 --> 00:26:35.000
three by like a Chinese character is
00:26:31.120 --> 00:26:37.159
three byes if I remember correctly so um
00:26:35.000 --> 00:26:38.640
the bbased segmentation is nice because
00:26:37.159 --> 00:26:41.240
you don't even need to worry about unic
00:26:38.640 --> 00:26:43.880
code you can just do the like you can
00:26:41.240 --> 00:26:45.640
just segment the pile like literally as
00:26:43.880 --> 00:26:49.440
is and so a lot of people do it that way
00:26:45.640 --> 00:26:53.279
too uh llama as far as I know is
00:26:49.440 --> 00:26:55.720
bites I believe GPT is also bites um but
00:26:53.279 --> 00:26:58.799
pre previous to like three or four years
00:26:55.720 --> 00:27:02.799
ago people used SCS I
00:26:58.799 --> 00:27:05.000
cool um okay so this is really really
00:27:02.799 --> 00:27:05.919
important it's not like super complex
00:27:05.000 --> 00:27:09.760
and
00:27:05.919 --> 00:27:13.039
practically uh you will just maybe maybe
00:27:09.760 --> 00:27:15.840
train or maybe just use a tokenizer um
00:27:13.039 --> 00:27:18.559
but uh that that's an important thing to
00:27:15.840 --> 00:27:20.760
me cool uh next I'd like to move on to
00:27:18.559 --> 00:27:24.399
continuous word eddings
00:27:20.760 --> 00:27:26.720
so the basic idea is that previously we
00:27:24.399 --> 00:27:28.240
represented words with a sparse Vector
00:27:26.720 --> 00:27:30.120
uh with a single one
00:27:28.240 --> 00:27:31.960
also known as one poot Vector so it
00:27:30.120 --> 00:27:35.720
looked a little bit like
00:27:31.960 --> 00:27:37.640
this and instead what continuous word
00:27:35.720 --> 00:27:39.640
embeddings do is they look up a dense
00:27:37.640 --> 00:27:42.320
vector and so you get a dense
00:27:39.640 --> 00:27:45.760
representation where the entire Vector
00:27:42.320 --> 00:27:45.760
has continuous values in
00:27:46.000 --> 00:27:51.919
it and I talked about a bag of words
00:27:49.200 --> 00:27:54.320
model but we could also create a
00:27:51.919 --> 00:27:58.360
continuous bag of words model and the
00:27:54.320 --> 00:28:01.159
way this works is you look up the
00:27:58.360 --> 00:28:03.720
values of each Vector the embeddings of
00:28:01.159 --> 00:28:06.320
each Vector this gives you an embedding
00:28:03.720 --> 00:28:08.440
Vector for the entire sequence and then
00:28:06.320 --> 00:28:15.120
you multiply this by a weight
00:28:08.440 --> 00:28:17.559
Matrix uh where the so this is column so
00:28:15.120 --> 00:28:19.960
the rows of the weight Matrix uh
00:28:17.559 --> 00:28:22.919
correspond to to the size of this
00:28:19.960 --> 00:28:24.760
continuous embedding and The Columns of
00:28:22.919 --> 00:28:28.320
the weight Matrix would correspond to
00:28:24.760 --> 00:28:30.919
the uh overall um
00:28:28.320 --> 00:28:32.559
to the overall uh number of labels that
00:28:30.919 --> 00:28:36.919
you would have here and then that would
00:28:32.559 --> 00:28:40.120
give you sces and so this uh basically
00:28:36.919 --> 00:28:41.679
what this is saying is each Vector now
00:28:40.120 --> 00:28:43.440
instead of having a single thing that
00:28:41.679 --> 00:28:46.799
represents which vocabulary item you're
00:28:43.440 --> 00:28:48.679
looking at uh you would kind of hope
00:28:46.799 --> 00:28:52.120
that you would get vectors where words
00:28:48.679 --> 00:28:54.919
that are similar uh by some mention of
00:28:52.120 --> 00:28:57.760
by some concept of similar like syntatic
00:28:54.919 --> 00:28:59.679
uh syntax semantics whether they're in
00:28:57.760 --> 00:29:03.120
the same language or not are close in
00:28:59.679 --> 00:29:06.679
the vector space and each Vector element
00:29:03.120 --> 00:29:09.399
is a feature uh so for example each
00:29:06.679 --> 00:29:11.519
Vector element corresponds to is this an
00:29:09.399 --> 00:29:14.960
animate object or is this a positive
00:29:11.519 --> 00:29:17.399
word or other Vector other things like
00:29:14.960 --> 00:29:19.399
that so just to give an example here
00:29:17.399 --> 00:29:21.760
this is totally made up I just made it
00:29:19.399 --> 00:29:24.360
in keynote so it's not natural Vector
00:29:21.760 --> 00:29:26.279
space but to Ill illustrate the concept
00:29:24.360 --> 00:29:27.960
I showed here what if we had a
00:29:26.279 --> 00:29:30.240
two-dimensional vector
00:29:27.960 --> 00:29:33.399
space where the two-dimensional Vector
00:29:30.240 --> 00:29:36.240
space the xais here is corresponding to
00:29:33.399 --> 00:29:38.679
whether it's animate or not and the the
00:29:36.240 --> 00:29:41.480
Y AIS here is corresponding to whether
00:29:38.679 --> 00:29:44.080
it's like positive sentiment or not and
00:29:41.480 --> 00:29:46.399
so this is kind of like our ideal uh
00:29:44.080 --> 00:29:49.799
goal
00:29:46.399 --> 00:29:52.279
here um so why would we want to do this
00:29:49.799 --> 00:29:52.279
yeah sorry
00:29:56.320 --> 00:30:03.399
guys what do the like in the one it's
00:30:00.919 --> 00:30:06.399
one
00:30:03.399 --> 00:30:06.399
yep
00:30:07.200 --> 00:30:12.519
like so what would the four entries do
00:30:09.880 --> 00:30:14.799
here the four entries here are learned
00:30:12.519 --> 00:30:17.039
so they are um they're learned just
00:30:14.799 --> 00:30:18.519
together with the model um and I'm going
00:30:17.039 --> 00:30:22.120
to talk about exactly how we learn them
00:30:18.519 --> 00:30:24.000
soon but the the final goal is that
00:30:22.120 --> 00:30:25.399
after learning has happened they look
00:30:24.000 --> 00:30:26.799
they have these two properties like
00:30:25.399 --> 00:30:28.600
similar words are close together in the
00:30:26.799 --> 00:30:30.080
vectorace
00:30:28.600 --> 00:30:32.640
and
00:30:30.080 --> 00:30:35.679
um that's like number one that's the
00:30:32.640 --> 00:30:37.600
most important and then number two is
00:30:35.679 --> 00:30:39.279
ideally these uh features would have
00:30:37.600 --> 00:30:41.200
some meaning uh maybe human
00:30:39.279 --> 00:30:44.720
interpretable meaning maybe not human
00:30:41.200 --> 00:30:47.880
interpretable meaning but
00:30:44.720 --> 00:30:50.880
yeah so um one thing that I should
00:30:47.880 --> 00:30:53.159
mention is I I showed a contrast between
00:30:50.880 --> 00:30:55.159
the bag of words uh the one hot
00:30:53.159 --> 00:30:57.000
representations here and the dense
00:30:55.159 --> 00:31:00.880
representations here and I used this
00:30:57.000 --> 00:31:03.880
look look up operation for both of them
00:31:00.880 --> 00:31:07.399
and this this lookup
00:31:03.880 --> 00:31:09.559
operation actually um can be viewed as
00:31:07.399 --> 00:31:11.799
grabbing a single Vector from a big
00:31:09.559 --> 00:31:14.919
Matrix of word
00:31:11.799 --> 00:31:17.760
embeddings and
00:31:14.919 --> 00:31:19.760
so the way it can work is like we have
00:31:17.760 --> 00:31:22.919
this big vector and then we look up word
00:31:19.760 --> 00:31:25.919
number two in a zero index Matrix and it
00:31:22.919 --> 00:31:27.799
would just grab this out of that Matrix
00:31:25.919 --> 00:31:29.880
and that's practically what most like
00:31:27.799 --> 00:31:32.240
deep learning libraries or or whatever
00:31:29.880 --> 00:31:35.840
Library you use are going to be
00:31:32.240 --> 00:31:38.000
doing but another uh way you can view it
00:31:35.840 --> 00:31:40.880
is you can view it as multiplying by a
00:31:38.000 --> 00:31:43.880
one hot vector and so you have this
00:31:40.880 --> 00:31:48.679
Vector uh exactly the same Matrix uh but
00:31:43.880 --> 00:31:50.799
you just multiply by a vector uh 0 1 z z
00:31:48.679 --> 00:31:55.720
and that gives you exactly the same
00:31:50.799 --> 00:31:58.200
things um so the Practical imple
00:31:55.720 --> 00:31:59.720
implementations of this uh uh tend to be
00:31:58.200 --> 00:32:01.279
the first one because the first one's a
00:31:59.720 --> 00:32:04.679
lot faster to implement you don't need
00:32:01.279 --> 00:32:06.760
to multiply like this big thing by a
00:32:04.679 --> 00:32:11.000
huge Vector but there
00:32:06.760 --> 00:32:13.880
are advantages of knowing the second one
00:32:11.000 --> 00:32:15.519
uh just to give an example what if you
00:32:13.880 --> 00:32:19.600
for whatever reason you came up with
00:32:15.519 --> 00:32:21.440
like an a crazy model that predicts a
00:32:19.600 --> 00:32:24.120
probability distribution over words
00:32:21.440 --> 00:32:25.720
instead of just words maybe it's a
00:32:24.120 --> 00:32:27.679
language model that has an idea of what
00:32:25.720 --> 00:32:30.200
the next word is going to look like
00:32:27.679 --> 00:32:32.159
and maybe your um maybe your model
00:32:30.200 --> 00:32:35.279
thinks the next word has a 50%
00:32:32.159 --> 00:32:36.600
probability of being capped 30%
00:32:35.279 --> 00:32:42.279
probability of being
00:32:36.600 --> 00:32:44.960
dog and uh 2% probability uh sorry uh
00:32:42.279 --> 00:32:47.200
20% probability being
00:32:44.960 --> 00:32:50.000
bir you can take this vector and
00:32:47.200 --> 00:32:51.480
multiply it by The Matrix and get like a
00:32:50.000 --> 00:32:53.639
word embedding that's kind of a mix of
00:32:51.480 --> 00:32:55.639
all of those word which might be
00:32:53.639 --> 00:32:57.960
interesting and let you do creative
00:32:55.639 --> 00:33:02.120
things so um knowing that these two
00:32:57.960 --> 00:33:05.360
things are the same are the same is kind
00:33:02.120 --> 00:33:05.360
of useful for that kind of
00:33:05.919 --> 00:33:11.480
thing um any any questions about this
00:33:09.120 --> 00:33:13.919
I'm G to talk about how we train next so
00:33:11.480 --> 00:33:18.159
maybe maybe I can goow into
00:33:13.919 --> 00:33:23.159
that okay cool so how do we get the
00:33:18.159 --> 00:33:25.840
vectors uh like the question uh so up
00:33:23.159 --> 00:33:27.519
until now we trained a bag of words
00:33:25.840 --> 00:33:29.080
model and the way we trained a bag of
00:33:27.519 --> 00:33:31.159
words model was using the structured
00:33:29.080 --> 00:33:35.440
perceptron algorithm where if the model
00:33:31.159 --> 00:33:39.639
got the answer wrong we would either
00:33:35.440 --> 00:33:42.799
increment or decrement the embeddings
00:33:39.639 --> 00:33:45.080
based on whether uh whether the label
00:33:42.799 --> 00:33:46.559
was positive or negative right so I
00:33:45.080 --> 00:33:48.919
showed an example of this very simple
00:33:46.559 --> 00:33:51.039
algorithm you don't even uh need to
00:33:48.919 --> 00:33:52.480
write any like numpy or anything like
00:33:51.039 --> 00:33:55.919
that to implement that
00:33:52.480 --> 00:33:59.559
algorithm uh so here here it is so we
00:33:55.919 --> 00:34:02.320
have like 4X why in uh data we extract
00:33:59.559 --> 00:34:04.639
the features we run the classifier uh we
00:34:02.320 --> 00:34:07.440
have the predicted why and then we
00:34:04.639 --> 00:34:09.480
increment or decrement
00:34:07.440 --> 00:34:12.679
features but how do we train more
00:34:09.480 --> 00:34:15.599
complex models so I think most people
00:34:12.679 --> 00:34:17.079
here have taken a uh machine learning
00:34:15.599 --> 00:34:19.159
class of some kind so this will be
00:34:17.079 --> 00:34:21.079
reviewed for a lot of people uh but
00:34:19.159 --> 00:34:22.280
basically we do this uh by doing
00:34:21.079 --> 00:34:24.839
gradient
00:34:22.280 --> 00:34:27.240
descent and in order to do so we write
00:34:24.839 --> 00:34:29.919
down a loss function calculate the
00:34:27.240 --> 00:34:30.919
derivatives of the L function with
00:34:29.919 --> 00:34:35.079
respect to the
00:34:30.919 --> 00:34:37.320
parameters and move uh the parameters in
00:34:35.079 --> 00:34:40.839
the direction that reduces the loss
00:34:37.320 --> 00:34:42.720
mtion and so specifically for this bag
00:34:40.839 --> 00:34:45.560
of words or continuous bag of words
00:34:42.720 --> 00:34:48.240
model um we want this loss of function
00:34:45.560 --> 00:34:50.839
to be a loss function that gets lower as
00:34:48.240 --> 00:34:52.240
the model gets better and I'm going to
00:34:50.839 --> 00:34:54.000
give two examples from binary
00:34:52.240 --> 00:34:57.400
classification both of these are used in
00:34:54.000 --> 00:34:58.839
NLP models uh reasonably frequently
00:34:57.400 --> 00:35:01.440
uh there's a bunch of other loss
00:34:58.839 --> 00:35:02.800
functions but these are kind of the two
00:35:01.440 --> 00:35:05.480
major
00:35:02.800 --> 00:35:08.160
ones so the first one um which is
00:35:05.480 --> 00:35:10.160
actually less frequent is the hinge loss
00:35:08.160 --> 00:35:13.400
and then the second one is taking a
00:35:10.160 --> 00:35:15.800
sigmoid and then doing negative log
00:35:13.400 --> 00:35:19.760
likelyhood so the hinge loss basically
00:35:15.800 --> 00:35:22.760
what we do is we uh take the max of the
00:35:19.760 --> 00:35:26.119
label times the score that is output by
00:35:22.760 --> 00:35:29.200
the model and zero and what this looks
00:35:26.119 --> 00:35:33.480
like is we have a hinged loss uh where
00:35:29.200 --> 00:35:36.880
if Y is equal to one the loss if Y is
00:35:33.480 --> 00:35:39.520
greater than zero is zero so as long as
00:35:36.880 --> 00:35:42.680
we get basically as long as we get the
00:35:39.520 --> 00:35:45.079
answer right there's no loss um as the
00:35:42.680 --> 00:35:47.400
answer gets more wrong the loss gets
00:35:45.079 --> 00:35:49.880
worse like this and then similarly if
00:35:47.400 --> 00:35:53.160
the label is negative if we get a
00:35:49.880 --> 00:35:54.839
negative score uh then we get zero loss
00:35:53.160 --> 00:35:55.800
and the loss increases if we have a
00:35:54.839 --> 00:35:58.800
positive
00:35:55.800 --> 00:36:00.800
score so the sigmoid plus negative log
00:35:58.800 --> 00:36:05.440
likelihood the way this works is you
00:36:00.800 --> 00:36:07.400
multiply y * the score here and um then
00:36:05.440 --> 00:36:09.960
we have the sigmoid function which is
00:36:07.400 --> 00:36:14.079
just kind of a nice function that looks
00:36:09.960 --> 00:36:15.440
like this with zero and one centered
00:36:14.079 --> 00:36:19.480
around
00:36:15.440 --> 00:36:21.240
zero and then we take the negative log
00:36:19.480 --> 00:36:22.319
of this sigmoid function or the negative
00:36:21.240 --> 00:36:27.160
log
00:36:22.319 --> 00:36:28.520
likelihood and that gives us a uh L that
00:36:27.160 --> 00:36:30.440
looks a little bit like this so
00:36:28.520 --> 00:36:32.640
basically you can see that these look
00:36:30.440 --> 00:36:36.040
very similar right the difference being
00:36:32.640 --> 00:36:37.760
that the hinge loss is uh sharp and we
00:36:36.040 --> 00:36:41.119
get exactly a zero loss if we get the
00:36:37.760 --> 00:36:44.319
answer right and the sigmoid is smooth
00:36:41.119 --> 00:36:48.440
uh and we never get a zero
00:36:44.319 --> 00:36:50.680
loss um so does anyone have an idea of
00:36:48.440 --> 00:36:53.119
the benefits and disadvantages of
00:36:50.680 --> 00:36:55.680
these I kind of flashed one on the
00:36:53.119 --> 00:36:57.599
screen already
00:36:55.680 --> 00:36:59.400
but
00:36:57.599 --> 00:37:01.359
so I flash that on the screen so I'll
00:36:59.400 --> 00:37:03.680
give this one and then I can have a quiz
00:37:01.359 --> 00:37:06.319
about the sign but the the hinge glass
00:37:03.680 --> 00:37:07.720
is more closely linked to accuracy and
00:37:06.319 --> 00:37:10.400
the reason why it's more closely linked
00:37:07.720 --> 00:37:13.640
to accuracy is because basically we will
00:37:10.400 --> 00:37:16.079
get a zero loss if the model gets the
00:37:13.640 --> 00:37:18.319
answer right so when the model gets all
00:37:16.079 --> 00:37:20.240
of the answers right we will just stop
00:37:18.319 --> 00:37:22.760
updating our model whatsoever because we
00:37:20.240 --> 00:37:25.440
never we don't have any loss whatsoever
00:37:22.760 --> 00:37:27.720
and the gradient of the loss is zero um
00:37:25.440 --> 00:37:29.960
what about the sigmoid uh a negative log
00:37:27.720 --> 00:37:33.160
likelihood uh there there's kind of two
00:37:29.960 --> 00:37:36.160
major advantages of this anyone want to
00:37:33.160 --> 00:37:36.160
review their machine learning
00:37:38.240 --> 00:37:41.800
test sorry what was
00:37:43.800 --> 00:37:49.960
that for for R uh yeah maybe there's a
00:37:48.200 --> 00:37:51.319
more direct I think I know what you're
00:37:49.960 --> 00:37:54.560
saying but maybe there's a more direct
00:37:51.319 --> 00:37:54.560
way to say that um
00:37:54.839 --> 00:38:00.760
yeah yeah so the gradient is nonzero
00:37:57.560 --> 00:38:04.240
everywhere and uh the gradient also kind
00:38:00.760 --> 00:38:05.839
of increases as your score gets worse so
00:38:04.240 --> 00:38:08.440
those are that's one advantage it makes
00:38:05.839 --> 00:38:11.240
it easier to optimize models um another
00:38:08.440 --> 00:38:13.839
one linked to the ROC score but maybe we
00:38:11.240 --> 00:38:13.839
could say it more
00:38:16.119 --> 00:38:19.400
directly any
00:38:20.040 --> 00:38:26.920
ideas okay um basically the sigmoid can
00:38:23.240 --> 00:38:30.160
be interpreted as a probability so um if
00:38:26.920 --> 00:38:32.839
the the sigmoid is between Zer and one
00:38:30.160 --> 00:38:34.640
uh and because it's between zero and one
00:38:32.839 --> 00:38:36.720
we can say the sigmoid is a
00:38:34.640 --> 00:38:38.640
probability um and that can be useful
00:38:36.720 --> 00:38:40.119
for various things like if we want a
00:38:38.640 --> 00:38:41.960
downstream model or if we want a
00:38:40.119 --> 00:38:45.480
confidence prediction out of the model
00:38:41.960 --> 00:38:48.200
so those are two uh advantages of using
00:38:45.480 --> 00:38:49.920
a s plus negative log likelihood there's
00:38:48.200 --> 00:38:53.160
no probabilistic interpretation to
00:38:49.920 --> 00:38:56.560
something transing theas
00:38:53.160 --> 00:38:59.200
basically cool um so the next thing that
00:38:56.560 --> 00:39:01.240
that we do is we calculate derivatives
00:38:59.200 --> 00:39:04.040
and we calculate the derivative of the
00:39:01.240 --> 00:39:05.920
parameter given the loss function um to
00:39:04.040 --> 00:39:09.839
give an example of the bag of words
00:39:05.920 --> 00:39:13.480
model and the hinge loss um the hinge
00:39:09.839 --> 00:39:16.480
loss as I said is the max of the score
00:39:13.480 --> 00:39:19.359
and times y in the bag of words model
00:39:16.480 --> 00:39:22.640
the score was the frequency of that
00:39:19.359 --> 00:39:25.880
vocabulary item in the input multiplied
00:39:22.640 --> 00:39:27.680
by the weight here and so if we this is
00:39:25.880 --> 00:39:29.520
a simple a function that I can just do
00:39:27.680 --> 00:39:34.440
the derivative by hand and if I do the
00:39:29.520 --> 00:39:36.920
deriva by hand what comes out is if y *
00:39:34.440 --> 00:39:39.319
this value is greater than zero so in
00:39:36.920 --> 00:39:44.640
other words if this Max uh picks this
00:39:39.319 --> 00:39:48.319
instead of this then the derivative is y
00:39:44.640 --> 00:39:52.359
* stre and otherwise uh it
00:39:48.319 --> 00:39:52.359
is in the opposite
00:39:55.400 --> 00:40:00.160
direction
00:39:56.920 --> 00:40:02.839
then uh optimizing gradients uh we do
00:40:00.160 --> 00:40:06.200
standard uh in standard stochastic
00:40:02.839 --> 00:40:07.839
gradient descent uh which is the most
00:40:06.200 --> 00:40:10.920
standard optimization algorithm for
00:40:07.839 --> 00:40:14.440
these models uh we basically have a
00:40:10.920 --> 00:40:17.440
gradient over uh you take the gradient
00:40:14.440 --> 00:40:20.040
over the parameter of the loss function
00:40:17.440 --> 00:40:22.480
and we call it GT so here um sorry I
00:40:20.040 --> 00:40:25.599
switched my terminology between W and
00:40:22.480 --> 00:40:28.280
Theta so this could be W uh the previous
00:40:25.599 --> 00:40:31.000
value of w
00:40:28.280 --> 00:40:35.440
um and this is the gradient of the loss
00:40:31.000 --> 00:40:37.040
and then uh we take the previous value
00:40:35.440 --> 00:40:39.680
and then we subtract out the learning
00:40:37.040 --> 00:40:39.680
rate times the
00:40:40.680 --> 00:40:45.720
gradient and uh there are many many
00:40:43.200 --> 00:40:47.280
other optimization options uh I'll cover
00:40:45.720 --> 00:40:50.960
the more frequent one called Adam at the
00:40:47.280 --> 00:40:54.319
end of this uh this lecture but um this
00:40:50.960 --> 00:40:57.160
is the basic way of optimizing the
00:40:54.319 --> 00:41:00.599
model so
00:40:57.160 --> 00:41:03.359
then my question now is what is this
00:41:00.599 --> 00:41:07.000
algorithm with respect
00:41:03.359 --> 00:41:10.119
to this is an algorithm that is
00:41:07.000 --> 00:41:12.280
taking that has a loss function it's
00:41:10.119 --> 00:41:14.079
calculating derivatives and it's
00:41:12.280 --> 00:41:17.240
optimizing gradients using stochastic
00:41:14.079 --> 00:41:18.839
gradient descent so does anyone have a
00:41:17.240 --> 00:41:20.960
guess about what the loss function is
00:41:18.839 --> 00:41:23.520
here and maybe what is the learning rate
00:41:20.960 --> 00:41:23.520
of stas
00:41:24.319 --> 00:41:29.480
gradient I kind of gave you a hint about
00:41:26.599 --> 00:41:29.480
the L one
00:41:31.640 --> 00:41:37.839
actually and just to recap what this is
00:41:34.440 --> 00:41:41.440
doing here it's um if predicted Y is
00:41:37.839 --> 00:41:44.560
equal to Y then it is moving the uh the
00:41:41.440 --> 00:41:48.240
future weights in the direction of Y
00:41:44.560 --> 00:41:48.240
times the frequency
00:41:52.599 --> 00:41:56.960
Vector
00:41:55.240 --> 00:41:59.079
yeah
00:41:56.960 --> 00:42:01.640
yeah exactly so the loss function is
00:41:59.079 --> 00:42:05.800
hinge loss and the learning rate is one
00:42:01.640 --> 00:42:07.880
um and just to show how that you know
00:42:05.800 --> 00:42:12.359
corresponds we have this if statement
00:42:07.880 --> 00:42:12.359
here and we have the increment of the
00:42:12.960 --> 00:42:20.240
features and this is what the um what
00:42:16.920 --> 00:42:21.599
the L sorry the derivative looked like
00:42:20.240 --> 00:42:24.240
so we have
00:42:21.599 --> 00:42:26.920
if this is moving in the right direction
00:42:24.240 --> 00:42:29.520
for the label uh then we increment
00:42:26.920 --> 00:42:31.599
otherwise we do nothing so
00:42:29.520 --> 00:42:33.559
basically you can see that even this
00:42:31.599 --> 00:42:35.200
really simple algorithm that I you know
00:42:33.559 --> 00:42:37.480
implemented with a few lines of python
00:42:35.200 --> 00:42:38.839
is essentially equivalent to this uh
00:42:37.480 --> 00:42:40.760
stochastic gradient descent that we
00:42:38.839 --> 00:42:44.559
doing
00:42:40.760 --> 00:42:46.359
models so the good news about this is
00:42:44.559 --> 00:42:48.359
you know this this is really simple but
00:42:46.359 --> 00:42:50.599
it only really works forit like a bag of
00:42:48.359 --> 00:42:55.400
words model or a simple feature based
00:42:50.599 --> 00:42:57.200
model uh but it opens up a lot of uh new
00:42:55.400 --> 00:43:00.440
possibilities for how we can optimize
00:42:57.200 --> 00:43:01.599
models and in particular I mentioned uh
00:43:00.440 --> 00:43:04.839
that there was a problem with
00:43:01.599 --> 00:43:08.200
combination features last class like
00:43:04.839 --> 00:43:11.200
don't hate and don't love are not just
00:43:08.200 --> 00:43:12.760
you know hate plus don't and love plus
00:43:11.200 --> 00:43:14.119
don't it's actually the combination of
00:43:12.760 --> 00:43:17.680
the two is really
00:43:14.119 --> 00:43:20.160
important and so um yeah just to give an
00:43:17.680 --> 00:43:23.440
example we have don't love is maybe bad
00:43:20.160 --> 00:43:26.960
uh nothing I don't love is very
00:43:23.440 --> 00:43:30.960
good and so in order
00:43:26.960 --> 00:43:34.040
to solve this problem we turn to neural
00:43:30.960 --> 00:43:37.160
networks and the way we do this is we
00:43:34.040 --> 00:43:39.119
have a lookup of dense embeddings sorry
00:43:37.160 --> 00:43:41.839
I actually I just realized my coloring
00:43:39.119 --> 00:43:44.119
is off I was using red to indicate dense
00:43:41.839 --> 00:43:46.480
embeddings so this should be maybe red
00:43:44.119 --> 00:43:49.319
instead of blue but um we take these
00:43:46.480 --> 00:43:51.200
stents embeddings and then we create
00:43:49.319 --> 00:43:53.720
some complicated function to extract
00:43:51.200 --> 00:43:55.079
combination features um and then use
00:43:53.720 --> 00:43:57.359
those to calculate
00:43:55.079 --> 00:44:02.200
scores
00:43:57.359 --> 00:44:04.480
um and so we calculate these combination
00:44:02.200 --> 00:44:08.240
features and what we want to do is we
00:44:04.480 --> 00:44:12.880
want to extract vectors from the input
00:44:08.240 --> 00:44:12.880
where each Vector has features
00:44:15.839 --> 00:44:21.040
um sorry this is in the wrong order so
00:44:18.240 --> 00:44:22.559
I'll I'll get back to this um so this
00:44:21.040 --> 00:44:25.319
this was talking about the The
00:44:22.559 --> 00:44:27.200
Continuous bag of words features so the
00:44:25.319 --> 00:44:30.960
problem with the continuous bag of words
00:44:27.200 --> 00:44:30.960
features was we were extracting
00:44:31.359 --> 00:44:36.359
features
00:44:33.079 --> 00:44:36.359
um like
00:44:36.839 --> 00:44:41.400
this but then we were directly using the
00:44:39.760 --> 00:44:43.359
the feature the dense features that we
00:44:41.400 --> 00:44:45.559
extracted to make predictions without
00:44:43.359 --> 00:44:48.839
actually allowing for any interactions
00:44:45.559 --> 00:44:51.839
between the features um and
00:44:48.839 --> 00:44:55.160
so uh neural networks the way we fix
00:44:51.839 --> 00:44:57.079
this is we first extract these features
00:44:55.160 --> 00:44:59.440
uh we take these these features of each
00:44:57.079 --> 00:45:04.000
word embedding and then we run them
00:44:59.440 --> 00:45:07.240
through uh kind of linear transforms in
00:45:04.000 --> 00:45:09.880
nonlinear uh like linear multiplications
00:45:07.240 --> 00:45:10.880
and then nonlinear transforms to extract
00:45:09.880 --> 00:45:13.920
additional
00:45:10.880 --> 00:45:15.839
features and uh finally run this through
00:45:13.920 --> 00:45:18.640
several layers and then use the
00:45:15.839 --> 00:45:21.119
resulting features to make our
00:45:18.640 --> 00:45:23.200
predictions and when we do this this
00:45:21.119 --> 00:45:25.319
allows us to do more uh interesting
00:45:23.200 --> 00:45:28.319
things so like for example we could
00:45:25.319 --> 00:45:30.000
learn feature combination a node in the
00:45:28.319 --> 00:45:32.599
second layer might be feature one and
00:45:30.000 --> 00:45:35.240
feature five are active so that could be
00:45:32.599 --> 00:45:38.680
like feature one corresponds to negative
00:45:35.240 --> 00:45:43.640
sentiment words like hate
00:45:38.680 --> 00:45:45.839
despise um and other things like that so
00:45:43.640 --> 00:45:50.079
for hate and despise feature one would
00:45:45.839 --> 00:45:53.119
have a high value like 8.0 and then
00:45:50.079 --> 00:45:55.480
7.2 and then we also have negation words
00:45:53.119 --> 00:45:57.040
like don't or not or something like that
00:45:55.480 --> 00:46:00.040
and those would
00:45:57.040 --> 00:46:00.040
have
00:46:03.720 --> 00:46:08.640
don't would have a high value for like 2
00:46:11.880 --> 00:46:15.839
five and so these would be the word
00:46:14.200 --> 00:46:18.040
embeddings where each word embedding
00:46:15.839 --> 00:46:20.599
corresponded to you know features of the
00:46:18.040 --> 00:46:23.480
words and
00:46:20.599 --> 00:46:25.480
then um after that we would extract
00:46:23.480 --> 00:46:29.319
feature combinations in this second
00:46:25.480 --> 00:46:32.079
layer that say oh we see at least one
00:46:29.319 --> 00:46:33.760
word where the first feature is active
00:46:32.079 --> 00:46:36.359
and we see at least one word where the
00:46:33.760 --> 00:46:37.920
fifth feature is active so now that
00:46:36.359 --> 00:46:40.640
allows us to capture the fact that we
00:46:37.920 --> 00:46:42.319
saw like don't hate or don't despise or
00:46:40.640 --> 00:46:44.559
not hate or not despise or something
00:46:42.319 --> 00:46:44.559
like
00:46:45.079 --> 00:46:51.760
that so this is the way uh kind of this
00:46:49.680 --> 00:46:54.839
is a deep uh continuous bag of words
00:46:51.760 --> 00:46:56.839
model um this actually was proposed in
00:46:54.839 --> 00:46:58.119
205 15 I don't think I have the
00:46:56.839 --> 00:47:02.599
reference on the slide but I think it's
00:46:58.119 --> 00:47:05.040
in the notes um on the website and
00:47:02.599 --> 00:47:07.200
actually at that point in time they
00:47:05.040 --> 00:47:09.200
demon there were several interesting
00:47:07.200 --> 00:47:11.960
results that showed that even this like
00:47:09.200 --> 00:47:13.960
really simple model did really well uh
00:47:11.960 --> 00:47:16.319
at text classification and other simple
00:47:13.960 --> 00:47:18.640
tasks like that because it was able to
00:47:16.319 --> 00:47:21.720
you know share features of the words and
00:47:18.640 --> 00:47:23.800
then extract combinations to the
00:47:21.720 --> 00:47:28.200
features
00:47:23.800 --> 00:47:29.760
so um in order order to learn these we
00:47:28.200 --> 00:47:30.920
need to start turning to neural networks
00:47:29.760 --> 00:47:34.400
and the reason why we need to start
00:47:30.920 --> 00:47:38.040
turning to neural networks is
00:47:34.400 --> 00:47:41.920
because while I can calculate the loss
00:47:38.040 --> 00:47:43.280
function of the while I can calculate
00:47:41.920 --> 00:47:44.839
the loss function of the hinged loss for
00:47:43.280 --> 00:47:47.720
a bag of words model by hand I
00:47:44.839 --> 00:47:49.359
definitely don't I probably could but
00:47:47.720 --> 00:47:51.240
don't want to do it for a model that
00:47:49.359 --> 00:47:53.200
starts become as complicated as this
00:47:51.240 --> 00:47:57.440
with multiple Matrix multiplications
00:47:53.200 --> 00:48:00.520
Andes and stuff like that so the way we
00:47:57.440 --> 00:48:05.000
do this just a very brief uh coverage of
00:48:00.520 --> 00:48:06.200
this uh for because um I think probably
00:48:05.000 --> 00:48:08.400
a lot of people have dealt with neural
00:48:06.200 --> 00:48:10.200
networks before um the original
00:48:08.400 --> 00:48:12.880
motivation was that we had neurons in
00:48:10.200 --> 00:48:16.160
the brain uh where
00:48:12.880 --> 00:48:18.839
the each of the neuron synapses took in
00:48:16.160 --> 00:48:21.480
an electrical signal and once they got
00:48:18.839 --> 00:48:24.079
enough electrical signal they would fire
00:48:21.480 --> 00:48:25.960
um but now the current conception of
00:48:24.079 --> 00:48:28.160
neural networks or deep learning models
00:48:25.960 --> 00:48:30.440
is basically computation
00:48:28.160 --> 00:48:32.400
graphs and the way a computation graph
00:48:30.440 --> 00:48:34.760
Works um and I'm especially going to
00:48:32.400 --> 00:48:36.240
talk about the way it works in natural
00:48:34.760 --> 00:48:38.119
language processing which might be a
00:48:36.240 --> 00:48:42.319
contrast to the way it works in computer
00:48:38.119 --> 00:48:43.960
vision is um we have an expression uh
00:48:42.319 --> 00:48:46.480
that looks like this and maybe maybe
00:48:43.960 --> 00:48:47.640
it's the expression X corresponding to
00:48:46.480 --> 00:48:51.880
uh a
00:48:47.640 --> 00:48:53.400
scal um and each node corresponds to
00:48:51.880 --> 00:48:55.599
something like a tensor a matrix a
00:48:53.400 --> 00:48:57.599
vector a scalar so scaler is uh kind
00:48:55.599 --> 00:49:00.480
kind of Zero Dimensional it's a single
00:48:57.599 --> 00:49:01.720
value one dimensional two dimensional or
00:49:00.480 --> 00:49:04.200
arbitrary
00:49:01.720 --> 00:49:06.040
dimensional um and then we also have
00:49:04.200 --> 00:49:08.000
nodes that correspond to the result of
00:49:06.040 --> 00:49:11.480
function applications so if we have X be
00:49:08.000 --> 00:49:14.079
a vector uh we take the vector transpose
00:49:11.480 --> 00:49:18.160
and so each Edge represents a function
00:49:14.079 --> 00:49:20.559
argument and also a data
00:49:18.160 --> 00:49:23.960
dependency and a node with an incoming
00:49:20.559 --> 00:49:27.000
Edge is a function of that Edge's tail
00:49:23.960 --> 00:49:29.040
node and importantly each node knows how
00:49:27.000 --> 00:49:30.640
to compute its value and the value of
00:49:29.040 --> 00:49:32.640
its derivative with respect to each
00:49:30.640 --> 00:49:34.440
argument times the derivative of an
00:49:32.640 --> 00:49:37.920
arbitrary
00:49:34.440 --> 00:49:41.000
input and functions could be basically
00:49:37.920 --> 00:49:45.400
arbitrary functions it can be unary Nary
00:49:41.000 --> 00:49:49.440
unary binary Nary often unary or binary
00:49:45.400 --> 00:49:52.400
and computation graphs are directed in
00:49:49.440 --> 00:49:57.040
cyclic and um one important thing to
00:49:52.400 --> 00:50:00.640
note is that you can um have multiple
00:49:57.040 --> 00:50:02.559
ways of expressing the same function so
00:50:00.640 --> 00:50:04.839
this is actually really important as you
00:50:02.559 --> 00:50:06.920
start implementing things and the reason
00:50:04.839 --> 00:50:09.359
why is the left graph and the right
00:50:06.920 --> 00:50:12.960
graph both express the same thing the
00:50:09.359 --> 00:50:18.640
left graph expresses X
00:50:12.960 --> 00:50:22.559
transpose time A Time X where is whereas
00:50:18.640 --> 00:50:27.160
this one has x a and then it puts it
00:50:22.559 --> 00:50:28.760
into a node that is X transpose a x
00:50:27.160 --> 00:50:30.319
and so these Express exactly the same
00:50:28.760 --> 00:50:32.319
thing but the graph on the left is
00:50:30.319 --> 00:50:33.760
larger and the reason why this is
00:50:32.319 --> 00:50:38.920
important is for practical
00:50:33.760 --> 00:50:40.359
implementation of neural networks um you
00:50:38.920 --> 00:50:43.200
the larger graphs are going to take more
00:50:40.359 --> 00:50:46.799
memory and going to be slower usually
00:50:43.200 --> 00:50:48.200
and so often um in a neural network we
00:50:46.799 --> 00:50:49.559
look at like pipe part which we're going
00:50:48.200 --> 00:50:52.160
to look at in a
00:50:49.559 --> 00:50:55.520
second
00:50:52.160 --> 00:50:57.920
um you will have something you will be
00:50:55.520 --> 00:50:57.920
able to
00:50:58.680 --> 00:51:01.680
do
00:51:03.079 --> 00:51:07.880
this or you'll be able to do
00:51:18.760 --> 00:51:22.880
like
00:51:20.359 --> 00:51:24.839
this so these are two different options
00:51:22.880 --> 00:51:26.920
this one is using more operations and
00:51:24.839 --> 00:51:29.559
this one is using using less operations
00:51:26.920 --> 00:51:31.000
and this is going to be faster because
00:51:29.559 --> 00:51:33.119
basically the implementation within
00:51:31.000 --> 00:51:34.799
Pythor will have been optimized for you
00:51:33.119 --> 00:51:36.799
it will only require one graph node
00:51:34.799 --> 00:51:37.880
instead of multiple graph nodes and
00:51:36.799 --> 00:51:39.799
that's even more important when you
00:51:37.880 --> 00:51:41.040
start talking about like attention or
00:51:39.799 --> 00:51:43.920
something like that which we're going to
00:51:41.040 --> 00:51:46.079
be covering very soon um attention is a
00:51:43.920 --> 00:51:47.359
very multi-head attention or something
00:51:46.079 --> 00:51:49.839
like that is a very complicated
00:51:47.359 --> 00:51:52.079
operation so you want to make sure that
00:51:49.839 --> 00:51:54.359
you're using the operators that are
00:51:52.079 --> 00:51:57.359
available to you to make this more
00:51:54.359 --> 00:51:57.359
efficient
00:51:57.440 --> 00:52:00.760
um and then finally we could like add
00:51:59.280 --> 00:52:01.920
all of these together at the end we
00:52:00.760 --> 00:52:04.000
could add a
00:52:01.920 --> 00:52:05.880
constant um and then we get this
00:52:04.000 --> 00:52:09.520
expression here which gives us kind of a
00:52:05.880 --> 00:52:09.520
polinomial polom
00:52:09.680 --> 00:52:15.760
expression um also another thing to note
00:52:13.480 --> 00:52:17.599
is within a neural network computation
00:52:15.760 --> 00:52:21.920
graph variable names are just labelings
00:52:17.599 --> 00:52:25.359
of nodes and so if you're using a a
00:52:21.920 --> 00:52:27.680
computation graph like this you might
00:52:25.359 --> 00:52:29.240
only be declaring one variable here but
00:52:27.680 --> 00:52:30.839
actually there's a whole bunch of stuff
00:52:29.240 --> 00:52:32.359
going on behind the scenes and all of
00:52:30.839 --> 00:52:34.240
that will take memory and computation
00:52:32.359 --> 00:52:35.440
time and stuff like that so it's
00:52:34.240 --> 00:52:37.119
important to be aware of that if you
00:52:35.440 --> 00:52:40.400
want to make your implementations more
00:52:37.119 --> 00:52:40.400
efficient than other other
00:52:41.119 --> 00:52:46.680
things so we have several algorithms
00:52:44.480 --> 00:52:49.079
that go into implementing neural nuts um
00:52:46.680 --> 00:52:50.760
the first one is graph construction uh
00:52:49.079 --> 00:52:53.480
the second one is forward
00:52:50.760 --> 00:52:54.839
propagation uh and graph construction is
00:52:53.480 --> 00:52:56.359
basically constructing the graph
00:52:54.839 --> 00:52:58.680
declaring ing all the variables stuff
00:52:56.359 --> 00:53:01.520
like this the second one is forward
00:52:58.680 --> 00:53:03.880
propagation and um the way you do this
00:53:01.520 --> 00:53:06.480
is in topological order uh you compute
00:53:03.880 --> 00:53:08.280
the value of a node given its inputs and
00:53:06.480 --> 00:53:11.000
so basically you start out with all of
00:53:08.280 --> 00:53:12.680
the nodes that you give is input and
00:53:11.000 --> 00:53:16.040
then you find any node in the graph
00:53:12.680 --> 00:53:17.799
where all of its uh all of its tail
00:53:16.040 --> 00:53:20.280
nodes or all of its children have been
00:53:17.799 --> 00:53:22.119
calculated so in this case that would be
00:53:20.280 --> 00:53:24.640
these two nodes and then in arbitrary
00:53:22.119 --> 00:53:27.000
order or even in parallel you calculate
00:53:24.640 --> 00:53:28.280
the value of all of the satisfied nodes
00:53:27.000 --> 00:53:31.799
until you get to the
00:53:28.280 --> 00:53:34.280
end and then uh the remaining algorithms
00:53:31.799 --> 00:53:36.200
are back propagation and parameter
00:53:34.280 --> 00:53:38.240
update I already talked about parameter
00:53:36.200 --> 00:53:40.799
update uh using stochastic gradient
00:53:38.240 --> 00:53:42.760
descent but for back propagation we then
00:53:40.799 --> 00:53:45.400
process examples in Reverse topological
00:53:42.760 --> 00:53:47.640
order uh calculate derivatives of
00:53:45.400 --> 00:53:50.400
parameters with respect to final
00:53:47.640 --> 00:53:52.319
value and so we start out with the very
00:53:50.400 --> 00:53:54.200
final value usually this is your loss
00:53:52.319 --> 00:53:56.200
function and then you just step
00:53:54.200 --> 00:54:00.440
backwards in top ological order to
00:53:56.200 --> 00:54:04.160
calculate the derivatives of all these
00:54:00.440 --> 00:54:05.920
so um this is pretty simple I think a
00:54:04.160 --> 00:54:08.040
lot of people may have seen this already
00:54:05.920 --> 00:54:09.920
but keeping this in mind as you're
00:54:08.040 --> 00:54:12.480
implementing NLP models especially
00:54:09.920 --> 00:54:14.240
models that are really memory intensive
00:54:12.480 --> 00:54:16.559
or things like that is pretty important
00:54:14.240 --> 00:54:19.040
because if you accidentally like for
00:54:16.559 --> 00:54:21.799
example calculate the same thing twice
00:54:19.040 --> 00:54:23.559
or accidentally create a graph that is
00:54:21.799 --> 00:54:25.720
manipulating very large tensors and
00:54:23.559 --> 00:54:27.319
creating very large intermediate States
00:54:25.720 --> 00:54:29.720
that can kill your memory and and cause
00:54:27.319 --> 00:54:31.839
big problems so it's an important thing
00:54:29.720 --> 00:54:31.839
to
00:54:34.359 --> 00:54:38.880
be um cool any any questions about
00:54:39.040 --> 00:54:44.440
this okay if not I will go on to the
00:54:41.680 --> 00:54:45.680
next one so neural network Frameworks
00:54:44.440 --> 00:54:48.920
there's several neural network
00:54:45.680 --> 00:54:52.880
Frameworks but in NLP nowadays I really
00:54:48.920 --> 00:54:55.079
only see two and mostly only see one um
00:54:52.880 --> 00:54:57.960
so that one that almost everybody us
00:54:55.079 --> 00:55:01.240
uses is pie torch um and I would
00:54:57.960 --> 00:55:04.559
recommend using it unless you uh you
00:55:01.240 --> 00:55:07.480
know if you're a fan of like rust or you
00:55:04.559 --> 00:55:09.200
know esoteric uh not esoteric but like
00:55:07.480 --> 00:55:11.960
unusual programming languages and you
00:55:09.200 --> 00:55:14.720
like Beauty and things like this another
00:55:11.960 --> 00:55:15.799
option might be Jacks uh so I'll explain
00:55:14.720 --> 00:55:18.440
a little bit about the difference
00:55:15.799 --> 00:55:19.960
between them uh and you can pick
00:55:18.440 --> 00:55:23.559
accordingly
00:55:19.960 --> 00:55:25.359
um first uh both of these Frameworks uh
00:55:23.559 --> 00:55:26.839
are developed by big companies and they
00:55:25.359 --> 00:55:28.520
have a lot of engineering support behind
00:55:26.839 --> 00:55:29.720
them that's kind of an important thing
00:55:28.520 --> 00:55:31.280
to think about when you're deciding
00:55:29.720 --> 00:55:32.599
which framework to use because you know
00:55:31.280 --> 00:55:36.000
it'll be well
00:55:32.599 --> 00:55:38.039
supported um pytorch is definitely most
00:55:36.000 --> 00:55:40.400
widely used in NLP especially NLP
00:55:38.039 --> 00:55:44.240
research um and it's used in some NLP
00:55:40.400 --> 00:55:47.359
project J is used in some NLP
00:55:44.240 --> 00:55:49.960
projects um pytorch favors Dynamic
00:55:47.359 --> 00:55:53.760
execution so what dynamic execution
00:55:49.960 --> 00:55:55.880
means is um you basically create a
00:55:53.760 --> 00:55:59.760
computation graph and and then execute
00:55:55.880 --> 00:56:02.760
it uh every time you process an input uh
00:55:59.760 --> 00:56:04.680
in contrast there's also you define the
00:56:02.760 --> 00:56:07.200
computation graph first and then execute
00:56:04.680 --> 00:56:09.280
it over and over again so in other words
00:56:07.200 --> 00:56:10.680
the graph construction step only happens
00:56:09.280 --> 00:56:13.119
once kind of at the beginning of
00:56:10.680 --> 00:56:16.799
computation and then you compile it
00:56:13.119 --> 00:56:20.039
afterwards and it's actually pytorch
00:56:16.799 --> 00:56:23.359
supports kind of defining and compiling
00:56:20.039 --> 00:56:27.480
and Jax supports more Dynamic things but
00:56:23.359 --> 00:56:30.160
the way they were designed is uh is kind
00:56:27.480 --> 00:56:32.960
of favoring Dynamic execution or
00:56:30.160 --> 00:56:37.079
favoring definition in population
00:56:32.960 --> 00:56:39.200
and the difference between these two is
00:56:37.079 --> 00:56:41.760
this one gives you more flexibility this
00:56:39.200 --> 00:56:45.440
one gives you better optimization in wor
00:56:41.760 --> 00:56:49.760
speed if you want to if you want to do
00:56:45.440 --> 00:56:52.400
that um another thing about Jax is um
00:56:49.760 --> 00:56:55.200
it's kind of very close to numpy in a
00:56:52.400 --> 00:56:57.440
way like it uses a very num something
00:56:55.200 --> 00:56:59.960
that's kind of close to numpy it's very
00:56:57.440 --> 00:57:02.359
heavily based on tensors and so because
00:56:59.960 --> 00:57:04.640
of this you can kind of easily do some
00:57:02.359 --> 00:57:06.640
interesting things like okay I want to
00:57:04.640 --> 00:57:11.319
take this tensor and I want to split it
00:57:06.640 --> 00:57:14.000
over two gpus um and this is good if
00:57:11.319 --> 00:57:17.119
you're training like a very large model
00:57:14.000 --> 00:57:20.920
and you want to put kind
00:57:17.119 --> 00:57:20.920
of this part of the
00:57:22.119 --> 00:57:26.520
model uh you want to put this part of
00:57:24.119 --> 00:57:30.079
the model on GP 1 this on gpu2 this on
00:57:26.520 --> 00:57:31.599
GPU 3 this on GPU it's slightly simpler
00:57:30.079 --> 00:57:34.400
conceptually to do in Jacks but it's
00:57:31.599 --> 00:57:37.160
also possible to do in
00:57:34.400 --> 00:57:39.119
p and pytorch by far has the most
00:57:37.160 --> 00:57:41.640
vibrant ecosystem so like as I said
00:57:39.119 --> 00:57:44.200
pytorch is a good default choice but you
00:57:41.640 --> 00:57:47.480
can consider using Jack if you uh if you
00:57:44.200 --> 00:57:47.480
like new
00:57:48.079 --> 00:57:55.480
things cool um yeah actually I already
00:57:51.599 --> 00:57:58.079
talked about that so in the interest of
00:57:55.480 --> 00:58:02.119
time I may not go into these very deeply
00:57:58.079 --> 00:58:05.799
but it's important to note that we have
00:58:02.119 --> 00:58:05.799
examples of all of
00:58:06.920 --> 00:58:12.520
the models that I talked about in the
00:58:09.359 --> 00:58:16.720
class today these are created for
00:58:12.520 --> 00:58:17.520
Simplicity not for Speed or efficiency
00:58:16.720 --> 00:58:20.480
of
00:58:17.520 --> 00:58:24.920
implementation um so these are kind of
00:58:20.480 --> 00:58:27.760
torch P torch based uh examples uh where
00:58:24.920 --> 00:58:31.599
you can create the bag of words
00:58:27.760 --> 00:58:36.440
Model A continuous bag of words
00:58:31.599 --> 00:58:39.640
model um and
00:58:36.440 --> 00:58:41.640
a deep continuous bag of wordss
00:58:39.640 --> 00:58:44.359
model
00:58:41.640 --> 00:58:46.039
and all of these I believe are
00:58:44.359 --> 00:58:48.760
implemented in
00:58:46.039 --> 00:58:51.960
model.py and the most important thing is
00:58:48.760 --> 00:58:54.960
where you define the forward pass and
00:58:51.960 --> 00:58:57.319
maybe I can just give a a simple example
00:58:54.960 --> 00:58:58.200
this but here this is where you do the
00:58:57.319 --> 00:59:01.839
word
00:58:58.200 --> 00:59:04.400
embedding this is where you sum up all
00:59:01.839 --> 00:59:08.119
of the embeddings and add a
00:59:04.400 --> 00:59:10.200
bias um and then this is uh where you
00:59:08.119 --> 00:59:13.960
return the the
00:59:10.200 --> 00:59:13.960
score and then oh
00:59:14.799 --> 00:59:19.119
sorry the continuous bag of words model
00:59:17.520 --> 00:59:22.160
sums up some
00:59:19.119 --> 00:59:23.640
embeddings uh or gets the embeddings
00:59:22.160 --> 00:59:25.799
sums up some
00:59:23.640 --> 00:59:28.079
embeddings
00:59:25.799 --> 00:59:30.599
uh gets the score here and then runs it
00:59:28.079 --> 00:59:33.200
through a linear or changes the view
00:59:30.599 --> 00:59:35.119
runs it through a linear layer and then
00:59:33.200 --> 00:59:38.319
the Deep continuous bag of words model
00:59:35.119 --> 00:59:41.160
also adds a few layers of uh like linear
00:59:38.319 --> 00:59:43.119
transformations in Dage so you should be
00:59:41.160 --> 00:59:44.640
able to see that these correspond pretty
00:59:43.119 --> 00:59:47.440
closely to the things that I had on the
00:59:44.640 --> 00:59:49.280
slides so um hopefully that's a good
00:59:47.440 --> 00:59:51.839
start if you're not very familiar with
00:59:49.280 --> 00:59:51.839
implementing
00:59:53.119 --> 00:59:58.440
model oh and yes the recitation uh will
00:59:56.599 --> 00:59:59.799
be about playing around with sentence
00:59:58.440 --> 01:00:01.200
piece and playing around with these so
00:59:59.799 --> 01:00:02.839
if you have any look at them have any
01:00:01.200 --> 01:00:05.000
questions you're welcome to show up
01:00:02.839 --> 01:00:09.880
where I walk
01:00:05.000 --> 01:00:09.880
through cool um any any questions about
01:00:12.839 --> 01:00:19.720
these okay so a few more final important
01:00:16.720 --> 01:00:21.720
Concepts um another concept that you
01:00:19.720 --> 01:00:25.440
should definitely be aware of is the
01:00:21.720 --> 01:00:27.280
atom Optimizer uh so there's lots of uh
01:00:25.440 --> 01:00:30.559
optimizers that you could be using but
01:00:27.280 --> 01:00:32.200
almost all research in NLP uses some uh
01:00:30.559 --> 01:00:38.440
variety of the atom
01:00:32.200 --> 01:00:40.839
Optimizer and the U the way this works
01:00:38.440 --> 01:00:42.559
is it
01:00:40.839 --> 01:00:45.640
optimizes
01:00:42.559 --> 01:00:48.480
the um it optimizes model considering
01:00:45.640 --> 01:00:49.359
the rolling average of the gradient and
01:00:48.480 --> 01:00:53.160
uh
01:00:49.359 --> 01:00:55.920
momentum and the way it works is here we
01:00:53.160 --> 01:00:58.839
have a gradient here we have
01:00:55.920 --> 01:01:04.000
momentum and what you can see is
01:00:58.839 --> 01:01:06.680
happening here is we add a little bit of
01:01:04.000 --> 01:01:09.200
the gradient in uh how much you add in
01:01:06.680 --> 01:01:12.720
is with respect to the size of this beta
01:01:09.200 --> 01:01:16.000
1 parameter and you add it into uh the
01:01:12.720 --> 01:01:18.640
momentum term so this momentum term like
01:01:16.000 --> 01:01:20.440
gradually increases and decreases so in
01:01:18.640 --> 01:01:23.440
contrast to standard gradient percent
01:01:20.440 --> 01:01:25.839
which could be
01:01:23.440 --> 01:01:28.440
updating
01:01:25.839 --> 01:01:31.440
uh each parameter kind of like very
01:01:28.440 --> 01:01:33.359
differently on each time step this will
01:01:31.440 --> 01:01:35.680
make the momentum kind of transition
01:01:33.359 --> 01:01:37.240
more smoothly by taking the rolling
01:01:35.680 --> 01:01:39.880
average of the
01:01:37.240 --> 01:01:43.400
gradient and then the the second thing
01:01:39.880 --> 01:01:47.640
is um by taking the momentum this is the
01:01:43.400 --> 01:01:51.000
rolling average of the I guess gradient
01:01:47.640 --> 01:01:54.440
uh variance sorry I this should be
01:01:51.000 --> 01:01:58.079
variance and the reason why you need
01:01:54.440 --> 01:02:01.319
need to keep track of the variance is
01:01:58.079 --> 01:02:03.319
some uh some parameters will have very
01:02:01.319 --> 01:02:06.559
large variance in their gradients and
01:02:03.319 --> 01:02:11.480
might fluctuate very uh strongly and
01:02:06.559 --> 01:02:13.039
others might have a smaller uh chain
01:02:11.480 --> 01:02:15.240
variant in their gradients and not
01:02:13.039 --> 01:02:18.240
fluctuate very much but we want to make
01:02:15.240 --> 01:02:20.200
sure that we update the ones we still
01:02:18.240 --> 01:02:22.240
update the ones that have a very small
01:02:20.200 --> 01:02:25.760
uh change of their variance and the
01:02:22.240 --> 01:02:27.440
reason why is kind of let's say you have
01:02:25.760 --> 01:02:30.440
a
01:02:27.440 --> 01:02:30.440
multi-layer
01:02:32.480 --> 01:02:38.720
network
01:02:34.480 --> 01:02:41.240
um or actually sorry a better
01:02:38.720 --> 01:02:44.319
um a better example is like let's say we
01:02:41.240 --> 01:02:47.559
have a big word embedding Matrix and
01:02:44.319 --> 01:02:53.359
over here we have like really frequent
01:02:47.559 --> 01:02:56.279
words and then over here we have uh
01:02:53.359 --> 01:02:59.319
gradi
01:02:56.279 --> 01:03:00.880
no we have like less frequent words we
01:02:59.319 --> 01:03:02.799
want to make sure that all of these get
01:03:00.880 --> 01:03:06.160
updated appropriately all of these get
01:03:02.799 --> 01:03:08.640
like enough updates and so over here
01:03:06.160 --> 01:03:10.760
this one will have lots of updates and
01:03:08.640 --> 01:03:13.680
so uh kind of
01:03:10.760 --> 01:03:16.599
the amount that we
01:03:13.680 --> 01:03:20.039
update or the the amount that we update
01:03:16.599 --> 01:03:21.799
the uh this will be relatively large
01:03:20.039 --> 01:03:23.119
whereas over here this will not have
01:03:21.799 --> 01:03:24.880
very many updates we'll have lots of
01:03:23.119 --> 01:03:26.480
zero updates also
01:03:24.880 --> 01:03:29.160
and so the amount that we update this
01:03:26.480 --> 01:03:32.520
will be relatively small and so this
01:03:29.160 --> 01:03:36.119
kind of squared to gradient here will uh
01:03:32.520 --> 01:03:38.400
be smaller for the values over here and
01:03:36.119 --> 01:03:41.359
what that allows us to do is it allows
01:03:38.400 --> 01:03:44.200
us to maybe I can just go to the bottom
01:03:41.359 --> 01:03:46.039
we end up uh dividing by the square root
01:03:44.200 --> 01:03:47.599
of this and because we divide by the
01:03:46.039 --> 01:03:51.000
square root of this if this is really
01:03:47.599 --> 01:03:55.680
large like 50 and 70 and then this over
01:03:51.000 --> 01:03:59.480
here is like one 0.5
01:03:55.680 --> 01:04:01.920
uh or something we will be upgrading the
01:03:59.480 --> 01:04:03.920
ones that have like less Square
01:04:01.920 --> 01:04:06.880
gradients so it will it allows you to
01:04:03.920 --> 01:04:08.760
upweight the less common gradients more
01:04:06.880 --> 01:04:10.440
frequently and then there's also some
01:04:08.760 --> 01:04:13.400
terms for correcting bias early in
01:04:10.440 --> 01:04:16.440
training because these momentum in uh in
01:04:13.400 --> 01:04:19.559
variance or momentum in squared gradient
01:04:16.440 --> 01:04:23.119
terms are not going to be like well
01:04:19.559 --> 01:04:24.839
calibrated yet so it prevents them from
01:04:23.119 --> 01:04:28.880
going very three wire beginning of
01:04:24.839 --> 01:04:30.839
training so this is uh the details of
01:04:28.880 --> 01:04:33.640
this again are not like super super
01:04:30.839 --> 01:04:37.359
important um another thing that I didn't
01:04:33.640 --> 01:04:40.200
write on the slides is uh now in
01:04:37.359 --> 01:04:43.920
Transformers it's also super common to
01:04:40.200 --> 01:04:47.400
have an overall learning rate schle so
01:04:43.920 --> 01:04:50.520
even um Even Adam has this uh Ada
01:04:47.400 --> 01:04:53.440
learning rate parameter here and we what
01:04:50.520 --> 01:04:55.240
we often do is we adjust this so we
01:04:53.440 --> 01:04:57.839
start at low
01:04:55.240 --> 01:04:59.640
we raise it up and then we have a Decay
01:04:57.839 --> 01:05:03.039
uh at the end and exactly how much you
01:04:59.640 --> 01:05:04.440
do this kind of depends on um you know
01:05:03.039 --> 01:05:06.160
how big your model is how much data
01:05:04.440 --> 01:05:09.160
you're tring on eventually and the
01:05:06.160 --> 01:05:12.440
reason why we do this is transformers
01:05:09.160 --> 01:05:13.839
are unfortunately super sensitive to
01:05:12.440 --> 01:05:15.359
having a high learning rate right at the
01:05:13.839 --> 01:05:16.559
very beginning so if you update them
01:05:15.359 --> 01:05:17.920
with a high learning rate right at the
01:05:16.559 --> 01:05:22.920
very beginning they go haywire and you
01:05:17.920 --> 01:05:24.400
get a really weird model um and but you
01:05:22.920 --> 01:05:26.760
want to raise it eventually so your
01:05:24.400 --> 01:05:28.920
model is learning appropriately and then
01:05:26.760 --> 01:05:30.400
in all stochastic gradient descent no
01:05:28.920 --> 01:05:31.680
matter whether you're using atom or
01:05:30.400 --> 01:05:33.400
anything else it's a good idea to
01:05:31.680 --> 01:05:36.200
gradually decrease the learning rate at
01:05:33.400 --> 01:05:38.119
the end to prevent the model from
01:05:36.200 --> 01:05:40.480
continuing to fluctuate and getting it
01:05:38.119 --> 01:05:42.760
to a stable point that gives you good
01:05:40.480 --> 01:05:45.559
accuracy over a large part of data so
01:05:42.760 --> 01:05:47.480
this is often included like if you look
01:05:45.559 --> 01:05:51.000
at any standard Transformer training
01:05:47.480 --> 01:05:53.079
recipe it will have that this so that's
01:05:51.000 --> 01:05:54.799
kind of the the go-to
01:05:53.079 --> 01:05:58.960
optimizer
01:05:54.799 --> 01:06:01.039
um are there any questions or
01:05:58.960 --> 01:06:02.599
discussion there's also tricky things
01:06:01.039 --> 01:06:04.000
like cyclic learning rates where you
01:06:02.599 --> 01:06:06.599
decrease the learning rate increase it
01:06:04.000 --> 01:06:08.559
and stuff like that but I won't go into
01:06:06.599 --> 01:06:11.000
that and don't actually use it that
01:06:08.559 --> 01:06:12.760
much second thing is visualization of
01:06:11.000 --> 01:06:15.400
embeddings so normally when we have word
01:06:12.760 --> 01:06:19.760
embeddings usually they're kind of large
01:06:15.400 --> 01:06:21.559
um and they can be like 512 or 1024
01:06:19.760 --> 01:06:25.079
dimensions
01:06:21.559 --> 01:06:28.720
and so one thing that we can do is we
01:06:25.079 --> 01:06:31.079
can down weight them or sorry down uh
01:06:28.720 --> 01:06:34.400
like reduce the dimensions or perform
01:06:31.079 --> 01:06:35.880
dimensionality reduction and put them in
01:06:34.400 --> 01:06:37.680
like two or three dimensions which are
01:06:35.880 --> 01:06:40.200
easy for humans to
01:06:37.680 --> 01:06:42.000
visualize this is an example using
01:06:40.200 --> 01:06:44.839
principal component analysis which is a
01:06:42.000 --> 01:06:48.279
linear Dimension reduction technique and
01:06:44.839 --> 01:06:50.680
this is uh an example from 10 years ago
01:06:48.279 --> 01:06:52.359
now uh one of the first major word
01:06:50.680 --> 01:06:55.240
embedding papers where they demonstrated
01:06:52.359 --> 01:06:57.720
that if you do this sort of linear
01:06:55.240 --> 01:06:59.440
Dimension reduction uh you get actually
01:06:57.720 --> 01:07:01.279
some interesting things where you can
01:06:59.440 --> 01:07:03.240
draw a vector that's almost the same
01:07:01.279 --> 01:07:06.400
direction between like countries and
01:07:03.240 --> 01:07:09.319
their uh countries and their capitals
01:07:06.400 --> 01:07:13.720
for example so this is a good thing to
01:07:09.319 --> 01:07:16.559
do but actually PCA uh doesn't give
01:07:13.720 --> 01:07:20.760
you in some cases PCA doesn't give you
01:07:16.559 --> 01:07:22.920
super great uh visualizations sorry yeah
01:07:20.760 --> 01:07:25.920
well for like if it's
01:07:22.920 --> 01:07:25.920
like
01:07:29.880 --> 01:07:35.039
um for things like this I think you
01:07:33.119 --> 01:07:37.359
probably would still see vectors in the
01:07:35.039 --> 01:07:38.760
same direction but I don't think it like
01:07:37.359 --> 01:07:40.920
there's a reason why I'm introducing
01:07:38.760 --> 01:07:44.279
nonlinear projections next because the
01:07:40.920 --> 01:07:46.799
more standard way to do this is uh
01:07:44.279 --> 01:07:50.640
nonlinear projections in in particular a
01:07:46.799 --> 01:07:54.880
method called tisne and the way um they
01:07:50.640 --> 01:07:56.880
do this is they try to group
01:07:54.880 --> 01:07:59.000
things that are close together in high
01:07:56.880 --> 01:08:01.240
dimensional space so that they're also
01:07:59.000 --> 01:08:04.440
close together in low dimensional space
01:08:01.240 --> 01:08:08.520
but they remove the Restriction that
01:08:04.440 --> 01:08:10.799
this is uh that this is linear so this
01:08:08.520 --> 01:08:15.480
is an example of just grouping together
01:08:10.799 --> 01:08:18.040
some digits uh from the memus data
01:08:15.480 --> 01:08:20.279
set or sorry reducing the dimension of
01:08:18.040 --> 01:08:23.640
digits from the mest data
01:08:20.279 --> 01:08:25.640
set according to PCA and you can see it
01:08:23.640 --> 01:08:28.000
gives these kind of blobs that overlap
01:08:25.640 --> 01:08:29.799
with each other and stuff like this but
01:08:28.000 --> 01:08:31.679
if you do it with tney this is
01:08:29.799 --> 01:08:34.799
completely unsupervised actually it's
01:08:31.679 --> 01:08:37.080
not training any model for labeling the
01:08:34.799 --> 01:08:39.239
labels are just used to draw the colors
01:08:37.080 --> 01:08:42.520
and you can see that it gets pretty
01:08:39.239 --> 01:08:44.520
coherent um clusters that correspond to
01:08:42.520 --> 01:08:48.120
like what the actual digits
01:08:44.520 --> 01:08:50.120
are um however uh one problem with
01:08:48.120 --> 01:08:53.159
titney I I still think it's better than
01:08:50.120 --> 01:08:55.000
PCA for a large number of uh
01:08:53.159 --> 01:08:59.199
applications
01:08:55.000 --> 01:09:01.040
but settings of tisy matter and tisy has
01:08:59.199 --> 01:09:02.920
a few settings kind of the most
01:09:01.040 --> 01:09:04.120
important ones are the overall
01:09:02.920 --> 01:09:06.560
perplexity
01:09:04.120 --> 01:09:09.040
hyperparameter and uh the number of
01:09:06.560 --> 01:09:12.319
steps that you perform and there's a
01:09:09.040 --> 01:09:14.920
nice example uh of a paper or kind of
01:09:12.319 --> 01:09:16.359
like online post uh that demonstrates
01:09:14.920 --> 01:09:18.560
how if you change these parameters you
01:09:16.359 --> 01:09:22.279
can get very different things so if this
01:09:18.560 --> 01:09:24.080
is the original data you run tisy and it
01:09:22.279 --> 01:09:26.640
gives you very different things based on
01:09:24.080 --> 01:09:29.279
the hyper parameters that you change um
01:09:26.640 --> 01:09:32.880
and here's another example uh you have
01:09:29.279 --> 01:09:36.960
two linear uh things like this and so
01:09:32.880 --> 01:09:40.839
PCA no matter how you ran PCA you would
01:09:36.960 --> 01:09:44.080
still get a linear output from this so
01:09:40.839 --> 01:09:45.960
normally uh you know it might change the
01:09:44.080 --> 01:09:49.239
order it might squash it a little bit or
01:09:45.960 --> 01:09:51.239
something like this but um if you run
01:09:49.239 --> 01:09:53.400
tisy it gives you crazy things it even
01:09:51.239 --> 01:09:56.040
gives you like DNA and other stuff like
01:09:53.400 --> 01:09:58.040
that so so um you do need to be a little
01:09:56.040 --> 01:10:00.600
bit careful that uh this is not
01:09:58.040 --> 01:10:02.320
necessarily going to tell you nice
01:10:00.600 --> 01:10:04.400
linear correlations like this so like
01:10:02.320 --> 01:10:06.159
let's say this correlation existed if
01:10:04.400 --> 01:10:09.199
you use tisy it might not necessarily
01:10:06.159 --> 01:10:09.199
come out to
01:10:09.320 --> 01:10:14.880
TIY
01:10:11.800 --> 01:10:16.920
cool yep uh that that's my final thing
01:10:14.880 --> 01:10:18.520
actually I talked said sequence models
01:10:16.920 --> 01:10:19.679
in the next class but it's in the class
01:10:18.520 --> 01:10:21.440
after this I'm going to be talking about
01:10:19.679 --> 01:10:24.199
language
01:10:21.440 --> 01:10:27.159
modeling uh cool any any questions
01:10:24.199 --> 01:10:27.159
or
|