[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"summary-63e2ecb9ef81ee97-how-adam-s-variance-normalization-fixes-sgd-s-freq-summary":3,"summaries-facets-categories":109,"summary-related-63e2ecb9ef81ee97-how-adam-s-variance-normalization-fixes-sgd-s-freq-summary":3988},{"id":4,"title":5,"ai":6,"body":13,"categories":69,"created_at":71,"date_modified":71,"description":63,"extension":72,"faq":71,"featured":73,"kicker_label":71,"meta":74,"navigation":90,"path":91,"published_at":92,"question":71,"scraped_at":93,"seo":94,"sitemap":95,"source_id":96,"source_name":97,"source_type":98,"source_url":99,"stem":100,"tags":101,"thumbnail_url":71,"tldr":106,"tweet":71,"unknown_tags":107,"__hash__":108},"summaries\u002Fsummaries\u002F63e2ecb9ef81ee97-how-adam-s-variance-normalization-fixes-sgd-s-freq-summary.md","How Adam's Variance Normalization Fixes SGD's Frequency Bias",{"provider":7,"model":8,"input_tokens":9,"output_tokens":10,"processing_time_ms":11,"cost_usd":12},"openrouter","google\u002Fgemini-3.1-flash-lite",10587,561,3073,0.00348825,{"type":14,"value":15,"toc":62},"minimark",[16,21,25,29,32,55,59],[17,18,20],"h2",{"id":19},"the-frequency-bias-problem-in-sgd","The Frequency Bias Problem in SGD",[22,23,24],"p",{},"Modern language models rely on training data with highly uneven token distributions. In standard Stochastic Gradient Descent (SGD), every parameter is updated using a fixed learning rate. This creates a significant optimization bottleneck: common tokens receive frequent gradient signals and converge quickly, while rare tokens—which may appear in only 0.1% of batches—receive insufficient updates. Consequently, parameters associated with rare tokens often remain near their random initialization, leading to poor model performance on underrepresented data.",[17,26,28],{"id":27},"how-adam-normalizes-learning-dynamics","How Adam Normalizes Learning Dynamics",[22,30,31],{},"Adam addresses this imbalance through adaptive optimization, specifically via variance normalization. Unlike SGD, Adam maintains a running estimate of the squared gradients (variance) for each parameter independently.",[33,34,35,43,49],"ul",{},[36,37,38,42],"li",{},[39,40,41],"strong",{},"Variance Tracking:"," Adam tracks the historical magnitude of gradients for every parameter.",[36,44,45,48],{},[39,46,47],{},"Adaptive Scaling:"," Before applying an update, Adam divides the learning rate by the square root of the accumulated variance estimate.",[36,50,51,54],{},[39,52,53],{},"Automatic Amplification:"," For rare tokens, the variance estimate remains very small because updates are infrequent. This causes the effective learning rate to be automatically amplified. In a controlled experiment, rare tokens received an effective learning rate over 40 times higher than common tokens, allowing them to converge to the target weight (1.0) despite receiving sparse signals.",[17,56,58],{"id":57},"experimental-evidence","Experimental Evidence",[22,60,61],{},"In a comparative study using a six-token vocabulary with frequencies spanning four orders of magnitude, SGD failed to move rare token weights beyond 0.15–0.53, while Adam successfully pushed all weights toward the target of 1.0. The results demonstrate that Adam acts as an \"automatic equalizer,\" requiring no manual tuning to compensate for frequency imbalance; the variance normalization term derives the necessary scaling directly from the gradient history.",{"title":63,"searchDepth":64,"depth":64,"links":65},"",2,[66,67,68],{"id":19,"depth":64,"text":20},{"id":27,"depth":64,"text":28},{"id":57,"depth":64,"text":58},[70],"AI & LLMs",null,"md",false,{"content_references":75,"triage":84},[76,81],{"type":77,"title":78,"url":79,"context":80},"tool","NumPy","https:\u002F\u002Fnumpy.org\u002F","mentioned",{"type":77,"title":82,"url":83,"context":80},"Matplotlib","https:\u002F\u002Fmatplotlib.org\u002F",{"relevance":85,"novelty":86,"quality":86,"actionability":87,"composite":88,"reasoning":89},5,4,3,4.15,"Category: AI & LLMs. The article provides a deep dive into how Adam's optimization technique addresses a specific problem in training language models, which is highly relevant for AI developers. It presents new insights into variance normalization and its impact on rare token optimization, making it actionable for those looking to improve model performance.",true,"\u002Fsummaries\u002F63e2ecb9ef81ee97-how-adam-s-variance-normalization-fixes-sgd-s-freq-summary","2026-05-18 20:18:55","2026-05-18 23:00:19",{"title":5,"description":63},{"loc":91},"63e2ecb9ef81ee97","MarkTechPost","article","https:\u002F\u002Fwww.marktechpost.com\u002F2026\u002F05\u002F18\u002Fstochastic-gradient-descent-sgds-frequency-bias-and-how-adam-fixes-it\u002F","summaries\u002F63e2ecb9ef81ee97-how-adam-s-variance-normalization-fixes-sgd-s-freq-summary",[102,103,104,105],"llm","machine-learning","python","optimization","Standard SGD fails to optimize rare tokens because they receive infrequent gradient updates. Adam solves this by using variance normalization to automatically amplify the effective learning rate for rare parameters.",[105],"_i3B42aRvOxuhgIJqWBCZrpm6JMn6VhobP9Wj9JNeok",[110,113,116,118,121,124,126,128,130,132,134,136,139,141,143,145,147,149,151,153,155,157,159,161,163,166,169,171,173,176,178,180,183,185,187,189,191,193,195,197,199,201,203,205,208,210,212,214,216,218,220,222,224,226,228,230,232,234,236,238,240,242,244,246,248,250,252,254,256,258,260,262,264,266,268,270,272,274,276,278,280,282,284,286,288,290,292,294,296,298,300,302,304,306,308,310,312,314,316,318,320,322,324,326,328,330,332,334,336,338,340,342,344,346,348,350,352,354,356,358,360,362,364,366,368,370,372,374,376,378,380,382,384,386,388,390,392,394,396,398,400,402,404,406,408,410,412,414,416,418,420,422,424,426,428,430,432,434,436,438,440,442,444,446,448,450,452,454,456,458,460,462,464,466,468,470,472,474,476,478,480,482,484,486,488,490,492,494,496,498,500,502,504,506,508,510,512,514,516,518,520,522,524,526,528,530,532,534,536,538,540,542,544,546,548,550,552,554,556,558,560,562,564,566,568,570,572,574,576,578,580,582,584,586,588,590,592,594,596,598,600,602,604,606,608,610,612,614,616,618,620,622,624,626,628,630,632,634,636,638,640,642,644,646,648,650,652,654,656,658,660,662,664,666,668,670,672,674,676,678,680,682,684,686,688,690,692,694,696,698,700,702,704,706,708,710,712,714,716,718,720,722,724,726,728,730,732,734,736,738,740,742,744,746,748,750,752,754,756,758,760,762,764,766,768,770,772,774,776,778,780,782,784,786,788,790,792,794,796,798,800,802,804,806,808,810,812,814,816,818,820,822,824,826,828,830,832,834,836,838,840,842,844,846,848,850,852,854,856,858,860,862,864,866,868,870,872,874,876,878,880,882,884,886,888,890,892,894,896,898,900,902,904,906,908,910,912,914,916,918,920,922,924,926,928,930,932,934,936,938,940,942,944,946,948,950,952,954,956,958,960,962,964,966,968,970,972,974,976,978,980,982,984,986,988,990,992,994,996,998,1000,1002,1004,1006,1008,1010,1012,1014,1016,1018,1020,1022,1024,1026,1028,1030,1032,1034,1036,1038,1040,1042,1044,1046,1048,1050,1052,1054,1056,1058,1060,1062,1064,1066,1068,1070,1072,1074,1076,1078,1080,1082,1084,1086,1088,1090,1092,1094,1096,1098,1100,1102,1104,1106,1108,1110,1112,1114,1116,1118,1120,1122,1124,1126,1128,1130,1132,1134,1136,1138,1140,1142,1144,1146,1148,1150,1152,1154,1156,1158,1160,1162,1164,1166,1168,1170,1172,1174,1176,1178,1180,1182,1184,1186,1188,1190,1192,1194,1196,1198,1200,1202,1204,1206,1208,1210,1212,1214,1216,1218,1220,1222,1224,1226,1228,1230,1232,1234,1236,1238,1240,1242,1244,1246,1248,1250,1252,1254,1256,1258,1260,1262,1264,1266,1268,1270,1272,1274,1276,1278,1280,1282,1284,1286,1288,1290,1292,1294,1296,1298,1300,1302,1304,1306,1308,1310,1312,1314,1316,1318,1320,1322,1324,1326,1328,1330,1332,1334,1336,1338,1340,1342,1344,1346,1348,1350,1352,1354,1356,1358,1360,1362,1364,1366,1368,1370,1372,1374,1376,1378,1380,1382,1384,1386,1388,1390,1392,1394,1396,1398,1400,1402,1404,1406,1408,1410,1412,1414,1416,1418,1420,1422,1424,1426,1428,1430,1432,1434,1436,1438,1440,1442,1444,1446,1448,1450,1452,1454,1456,1458,1460,1462,1464,1466,1468,1470,1472,1474,1476,1478,1480,1482,1484,1486,1488,1490,1492,1494,1496,1498,1500,1502,1504,1506,1508,1510,1512,1514,1516,1518,1520,1522,1524,1526,1528,1530,1532,1534,1536,1538,1540,1542,1544,1546,1548,1550,1552,1554,1556,1558,1560,1562,1564,1566,1568,1570,1572,1574,1576,1578,1580,1582,1584,1586,1588,1590,1592,1594,1596,1598,1600,1602,1604,1606,1608,1610,1612,1614,1616,1618,1620,1622,1624,1626,1628,1630,1632,1634,1636,1638,1640,1642,1644,1646,1648,1650,1652,1654,1656,1658,1660,1662,1664,1666,1668,1670,1672,1674,1676,1678,1680,1682,1684,1686,1688,1690,1692,1694,1696,1698,1700,1702,1704,1706,1708,1710,1712,1714,1716,1718,1720,1722,1724,1726,1728,1730,1732,1734,1736,1738,1740,1742,1744,1746,1748,1750,1752,1754,1756,1758,1760,1762,1764,1766,1768,1770,1772,1774,1776,1778,1780,1782,1784,1786,1788,1790,1792,1794,1796,1798,1800,1802,1804,1806,1808,1810,1812,1814,1816,1818,1820,1822,1824,1826,1828,1830,1832,1834,1836,1838,1840,1842,1844,1846,1848,1850,1852,1854,1856,1858,1860,1862,1864,1866,1868,1870,1872,1874,1876,1878,1880,1882,1884,1886,1888,1890,1892,1894,1896,1898,1900,1902,1904,1906,1908,1910,1912,1914,1916,1918,1920,1922,1924,1926,1928,1930,1932,1934,1936,1938,1940,1942,1944,1946,1948,1950,1952,1954,1956,1958,1960,1962,1964,1966,1968,1970,1972,1974,1976,1978,1980,1982,1984,1986,1988,1990,1992,1994,1996,1998,2000,2002,2004,2006,2008,2010,2012,2014,2016,2018,2020,2022,2024,2026,2028,2030,2032,2034,2036,2038,2040,2042,2044,2046,2048,2050,2052,2054,2056,2058,2060,2062,2064,2066,2068,2070,2072,2074,2076,2078,2080,2082,2084,2086,2088,2090,2092,2094,2096,2098,2100,2102,2104,2106,2108,2110,2112,2114,2116,2118,2120,2122,2124,2126,2128,2130,2132,2134,2136,2138,2140,2142,2144,2146,2148,2150,2152,2154,2156,2158,2160,2162,2164,2166,2168,2170,2172,2174,2176,2178,2180,2182,2184,2186,2188,2190,2192,2194,2196,2198,2200,2202,2204,2206,2208,2210,2212,2214,2216,2218,2220,2222,2224,2226,2228,2230,2232,2234,2236,2238,2240,2242,2244,2246,2248,2250,2252,2254,2256,2258,2260,2262,2264,2266,2268,2270,2272,2274,2276,2278,2280,2282,2284,2286,2288,2290,2292,2294,2296,2298,2300,2302,2304,2306,2308,2310,2312,2314,2316,2318,2320,2322,2324,2326,2328,2330,2332,2334,2336,2338,2340,2342,2344,2346,2348,2350,2352,2354,2356,2358,2360,2362,2364,2366,2368,2370,2372,2374,2376,2378,2380,2382,2384,2386,2388,2390,2392,2394,2396,2398,2400,2402,2404,2406,2408,2410,2412,2414,2416,2418,2420,2422,2424,2426,2428,2430,2432,2434,2436,2438,2440,2442,2444,2446,2448,2450,2452,2454,2456,2458,2460,2462,2464,2466,2468,2470,2472,2474,2476,2478,2480,2482,2484,2486,2488,2490,2492,2494,2496,2498,2500,2502,2504,2506,2508,2510,2512,2514,2516,2518,2520,2522,2524,2526,2528,2530,2532,2534,2536,2538,2540,2542,2544,2546,2548,2550,2552,2554,2556,2558,2560,2562,2564,2566,2568,2570,2572,2574,2576,2578,2580,2582,2584,2586,2588,2590,2592,2594,2596,2598,2600,2602,2604,2606,2608,2610,2612,2614,2616,2618,2620,2622,2624,2626,2628,2630,2632,2634,2636,2638,2640,2642,2644,2646,2648,2650,2652,2654,2656,2658,2660,2662,2664,2666,2668,2670,2672,2674,2676,2678,2680,2682,2684,2686,2688,2690,2692,2694,2696,2698,2700,2702,2704,2706,2708,2710,2712,2714,2716,2718,2720,2722,2724,2726,2728,2730,2732,2734,2736,2738,2740,2742,2744,2746,2748,2750,2752,2754,2756,2758,2760,2762,2764,2766,2768,2770,2772,2774,2776,2778,2780,2782,2784,2786,2788,2790,2792,2794,2796,2798,2800,2802,2804,2806,2808,2810,2812,2814,2816,2818,2820,2822,2824,2826,2828,2830,2832,2834,2836,2838,2840,2842,2844,2846,2848,2850,2852,2854,2856,2858,2860,2862,2864,2866,2868,2870,2872,2874,2876,2878,2880,2882,2884,2886,2888,2890,2892,2894,2896,2898,2900,2902,2904,2906,2908,2910,2912,2914,2916,2918,2920,2922,2924,2926,2928,2930,2932,2934,2936,2938,2940,2942,2944,2946,2948,2950,2952,2954,2956,2958,2960,2962,2964,2966,2968,2970,2972,2974,2976,2978,2980,2982,2984,2986,2988,2990,2992,2994,2996,2998,3000,3002,3004,3006,3008,3010,3012,3014,3016,3018,3020,3022,3024,3026,3028,3030,3032,3034,3036,3038,3040,3042,3044,3046,3048,3050,3052,3054,3056,3058,3060,3062,3064,3066,3068,3070,3072,3074,3076,3078,3080,3082,3084,3086,3088,3090,3092,3094,3096,3098,3100,3102,3104,3106,3108,3110,3112,3114,3116,3118,3120,3122,3124,3126,3128,3130,3132,3134,3136,3138,3140,3142,3144,3146,3148,3150,3152,3154,3156,3158,3160,3162,3164,3166,3168,3170,3172,3174,3176,3178,3180,3182,3184,3186,3188,3190,3192,3194,3196,3198,3200,3202,3204,3206,3208,3210,3212,3214,3216,3218,3220,3222,3224,3226,3228,3230,3232,3234,3236,3238,3240,3242,3244,3246,3248,3250,3252,3254,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276,3278,3280,3282,3284,3286,3288,3290,3292,3294,3296,3298,3300,3302,3304,3306,3308,3310,3312,3314,3316,3318,3320,3322,3324,3326,3328,3330,3332,3334,3336,3338,3340,3342,3344,3346,3348,3350,3352,3354,3356,3358,3360,3362,3364,3366,3368,3370,3372,3374,3376,3378,3380,3382,3384,3386,3388,3390,3392,3394,3396,3398,3400,3402,3404,3406,3408,3410,3412,3414,3416,3418,3420,3422,3424,3426,3428,3430,3432,3434,3436,3438,3440,3442,3444,3446,3448,3450,3452,3454,3456,3458,3460,3462,3464,3466,3468,3470,3472,3474,3476,3478,3480,3482,3484,3486,3488,3490,3492,3494,3496,3498,3500,3502,3504,3506,3508,3510,3512,3514,3516,3518,3520,3522,3524,3526,3528,3530,3532,3534,3536,3538,3540,3542,3544,3546,3548,3550,3552,3554,3556,3558,3560,3562,3564,3566,3568,3570,3572,3574,3576,3578,3580,3582,3584,3586,3588,3590,3592,3594,3596,3598,3600,3602,3604,3606,3608,3610,3612,3614,3616,3618,3620,3622,3624,3626,3628,3630,3632,3634,3636,3638,3640,3642,3644,3646,3648,3650,3652,3654,3656,3658,3660,3662,3664,3666,3668,3670,3672,3674,3676,3678,3680,3682,3684,3686,3688,3690,3692,3694,3696,3698,3700,3702,3704,3706,3708,3710,3712,3714,3716,3718,3720,3722,3724,3726,3728,3730,3732,3734,3736,3738,3740,3742,3744,3746,3748,3750,3752,3754,3756,3758,3760,3762,3764,3766,3768,3770,3772,3774,3776,3778,3780,3782,3784,3786,3788,3790,3792,3794,3796,3798,3800,3802,3804,3806,3808,3810,3812,3814,3816,3818,3820,3822,3824,3826,3828,3830,3832,3834,3836,3838,3840,3842,3844,3846,3848,3850,3852,3854,3856,3858,3860,3862,3864,3866,3868,3870,3872,3874,3876,3878,3880,3882,3884,3886,3888,3890,3892,3894,3896,3898,3900,3902,3904,3906,3908,3910,3912,3914,3916,3918,3920,3922,3924,3926,3928,3930,3932,3934,3936,3938,3940,3942,3944,3946,3948,3950,3952,3954,3956,3958,3960,3962,3964,3966,3968,3970,3972,3974,3976,3978,3980,3982,3984,3986],{"categories":111},[112],"Developer Productivity",{"categories":114},[115],"Business & SaaS",{"categories":117},[70],{"categories":119},[120],"AI Automation",{"categories":122},[123],"Product Strategy",{"categories":125},[70],{"categories":127},[112],{"categories":129},[115],{"categories":131},[],{"categories":133},[70],{"categories":135},[],{"categories":137},[138],"AI News & Trends",{"categories":140},[120],{"categories":142},[120],{"categories":144},[138],{"categories":146},[120],{"categories":148},[120],{"categories":150},[70],{"categories":152},[70],{"categories":154},[70],{"categories":156},[138],{"categories":158},[70],{"categories":160},[70],{"categories":162},[],{"categories":164},[165],"Design & Frontend",{"categories":167},[168],"Data Science & Visualization",{"categories":170},[138],{"categories":172},[],{"categories":174},[175],"Software Engineering",{"categories":177},[70],{"categories":179},[120],{"categories":181},[182],"Marketing & Growth",{"categories":184},[165],{"categories":186},[70],{"categories":188},[120],{"categories":190},[],{"categories":192},[],{"categories":194},[165],{"categories":196},[120],{"categories":198},[112],{"categories":200},[175],{"categories":202},[165],{"categories":204},[70],{"categories":206},[207],"DevOps & Cloud",{"categories":209},[120],{"categories":211},[138],{"categories":213},[],{"categories":215},[],{"categories":217},[120],{"categories":219},[175],{"categories":221},[],{"categories":223},[115],{"categories":225},[],{"categories":227},[],{"categories":229},[120],{"categories":231},[70],{"categories":233},[120],{"categories":235},[70],{"categories":237},[70],{"categories":239},[],{"categories":241},[175],{"categories":243},[],{"categories":245},[],{"categories":247},[175],{"categories":249},[],{"categories":251},[175],{"categories":253},[70],{"categories":255},[70],{"categories":257},[182],{"categories":259},[165],{"categories":261},[165],{"categories":263},[70],{"categories":265},[120],{"categories":267},[175],{"categories":269},[70],{"categories":271},[70],{"categories":273},[120],{"categories":275},[120],{"categories":277},[168],{"categories":279},[138],{"categories":281},[120],{"categories":283},[182],{"categories":285},[120],{"categories":287},[123],{"categories":289},[175],{"categories":291},[],{"categories":293},[120],{"categories":295},[],{"categories":297},[120],{"categories":299},[175],{"categories":301},[207],{"categories":303},[165],{"categories":305},[70],{"categories":307},[],{"categories":309},[],{"categories":311},[120],{"categories":313},[],{"categories":315},[70],{"categories":317},[],{"categories":319},[112],{"categories":321},[175],{"categories":323},[115],{"categories":325},[70],{"categories":327},[138],{"categories":329},[70],{"categories":331},[],{"categories":333},[70],{"categories":335},[],{"categories":337},[175],{"categories":339},[168],{"categories":341},[],{"categories":343},[70],{"categories":345},[165],{"categories":347},[],{"categories":349},[165],{"categories":351},[120],{"categories":353},[],{"categories":355},[70],{"categories":357},[120],{"categories":359},[138],{"categories":361},[115],{"categories":363},[70],{"categories":365},[],{"categories":367},[120],{"categories":369},[70],{"categories":371},[123],{"categories":373},[],{"categories":375},[70],{"categories":377},[120],{"categories":379},[120],{"categories":381},[],{"categories":383},[168],{"categories":385},[70],{"categories":387},[],{"categories":389},[112],{"categories":391},[115],{"categories":393},[70],{"categories":395},[120],{"categories":397},[175],{"categories":399},[70],{"categories":401},[],{"categories":403},[],{"categories":405},[70],{"categories":407},[70],{"categories":409},[],{"categories":411},[165],{"categories":413},[],{"categories":415},[70],{"categories":417},[],{"categories":419},[120],{"categories":421},[70],{"categories":423},[165],{"categories":425},[],{"categories":427},[70],{"categories":429},[70],{"categories":431},[115],{"categories":433},[120],{"categories":435},[70],{"categories":437},[165],{"categories":439},[120],{"categories":441},[],{"categories":443},[],{"categories":445},[138],{"categories":447},[],{"categories":449},[70],{"categories":451},[115,182],{"categories":453},[],{"categories":455},[70],{"categories":457},[120],{"categories":459},[],{"categories":461},[],{"categories":463},[70],{"categories":465},[],{"categories":467},[70],{"categories":469},[207],{"categories":471},[],{"categories":473},[138],{"categories":475},[165],{"categories":477},[],{"categories":479},[138],{"categories":481},[138],{"categories":483},[70],{"categories":485},[182],{"categories":487},[],{"categories":489},[115],{"categories":491},[120],{"categories":493},[],{"categories":495},[70,207],{"categories":497},[70],{"categories":499},[70],{"categories":501},[70],{"categories":503},[120],{"categories":505},[70,175],{"categories":507},[168],{"categories":509},[70],{"categories":511},[182],{"categories":513},[120],{"categories":515},[120],{"categories":517},[],{"categories":519},[120],{"categories":521},[70],{"categories":523},[70,115],{"categories":525},[],{"categories":527},[165],{"categories":529},[165],{"categories":531},[],{"categories":533},[],{"categories":535},[138],{"categories":537},[],{"categories":539},[112],{"categories":541},[175],{"categories":543},[70],{"categories":545},[165],{"categories":547},[120],{"categories":549},[175],{"categories":551},[138],{"categories":553},[165],{"categories":555},[],{"categories":557},[70],{"categories":559},[70],{"categories":561},[70],{"categories":563},[70],{"categories":565},[138],{"categories":567},[112],{"categories":569},[70],{"categories":571},[120],{"categories":573},[207],{"categories":575},[165],{"categories":577},[120],{"categories":579},[],{"categories":581},[],{"categories":583},[165],{"categories":585},[138],{"categories":587},[168],{"categories":589},[],{"categories":591},[70],{"categories":593},[70],{"categories":595},[115],{"categories":597},[70],{"categories":599},[70],{"categories":601},[138],{"categories":603},[],{"categories":605},[120],{"categories":607},[175],{"categories":609},[],{"categories":611},[70],{"categories":613},[70],{"categories":615},[120],{"categories":617},[],{"categories":619},[],{"categories":621},[70],{"categories":623},[],{"categories":625},[115],{"categories":627},[120],{"categories":629},[120],{"categories":631},[],{"categories":633},[112],{"categories":635},[70],{"categories":637},[115],{"categories":639},[138],{"categories":641},[112],{"categories":643},[],{"categories":645},[],{"categories":647},[],{"categories":649},[138],{"categories":651},[138],{"categories":653},[],{"categories":655},[],{"categories":657},[115],{"categories":659},[],{"categories":661},[],{"categories":663},[112],{"categories":665},[],{"categories":667},[182],{"categories":669},[120],{"categories":671},[115],{"categories":673},[120],{"categories":675},[175],{"categories":677},[],{"categories":679},[123],{"categories":681},[165],{"categories":683},[175],{"categories":685},[70],{"categories":687},[120],{"categories":689},[115],{"categories":691},[70],{"categories":693},[],{"categories":695},[],{"categories":697},[175],{"categories":699},[168],{"categories":701},[123],{"categories":703},[120],{"categories":705},[70],{"categories":707},[],{"categories":709},[207],{"categories":711},[],{"categories":713},[120],{"categories":715},[],{"categories":717},[112],{"categories":719},[],{"categories":721},[70],{"categories":723},[70],{"categories":725},[165],{"categories":727},[182],{"categories":729},[120],{"categories":731},[],{"categories":733},[112],{"categories":735},[],{"categories":737},[138],{"categories":739},[70,207],{"categories":741},[70],{"categories":743},[138],{"categories":745},[70],{"categories":747},[115],{"categories":749},[70],{"categories":751},[],{"categories":753},[70],{"categories":755},[115],{"categories":757},[],{"categories":759},[175],{"categories":761},[165],{"categories":763},[138],{"categories":765},[168],{"categories":767},[112],{"categories":769},[70],{"categories":771},[120],{"categories":773},[175],{"categories":775},[],{"categories":777},[],{"categories":779},[123],{"categories":781},[],{"categories":783},[70],{"categories":785},[],{"categories":787},[165],{"categories":789},[175],{"categories":791},[165],{"categories":793},[70],{"categories":795},[165],{"categories":797},[],{"categories":799},[],{"categories":801},[138],{"categories":803},[120],{"categories":805},[70],{"categories":807},[70],{"categories":809},[70],{"categories":811},[115],{"categories":813},[70],{"categories":815},[],{"categories":817},[175],{"categories":819},[175],{"categories":821},[115],{"categories":823},[],{"categories":825},[70],{"categories":827},[70],{"categories":829},[115],{"categories":831},[138],{"categories":833},[182],{"categories":835},[70],{"categories":837},[120],{"categories":839},[],{"categories":841},[165],{"categories":843},[],{"categories":845},[70],{"categories":847},[70],{"categories":849},[],{"categories":851},[115],{"categories":853},[120],{"categories":855},[],{"categories":857},[207],{"categories":859},[168],{"categories":861},[175],{"categories":863},[182],{"categories":865},[70],{"categories":867},[175],{"categories":869},[120],{"categories":871},[],{"categories":873},[],{"categories":875},[120],{"categories":877},[112],{"categories":879},[120],{"categories":881},[123],{"categories":883},[115],{"categories":885},[],{"categories":887},[70],{"categories":889},[123],{"categories":891},[70],{"categories":893},[70],{"categories":895},[182],{"categories":897},[70],{"categories":899},[165],{"categories":901},[120],{"categories":903},[],{"categories":905},[],{"categories":907},[207],{"categories":909},[175],{"categories":911},[],{"categories":913},[120],{"categories":915},[70],{"categories":917},[165,70],{"categories":919},[112],{"categories":921},[],{"categories":923},[70],{"categories":925},[112],{"categories":927},[165],{"categories":929},[120],{"categories":931},[175],{"categories":933},[],{"categories":935},[70],{"categories":937},[],{"categories":939},[],{"categories":941},[70],{"categories":943},[112],{"categories":945},[],{"categories":947},[120],{"categories":949},[123],{"categories":951},[70],{"categories":953},[70],{"categories":955},[70],{"categories":957},[165],{"categories":959},[120],{"categories":961},[207],{"categories":963},[165],{"categories":965},[120],{"categories":967},[70],{"categories":969},[70],{"categories":971},[70],{"categories":973},[175],{"categories":975},[],{"categories":977},[138],{"categories":979},[],{"categories":981},[123],{"categories":983},[120],{"categories":985},[165],{"categories":987},[70],{"categories":989},[120],{"categories":991},[175],{"categories":993},[165],{"categories":995},[120],{"categories":997},[138],{"categories":999},[],{"categories":1001},[70],{"categories":1003},[165],{"categories":1005},[70],{"categories":1007},[112],{"categories":1009},[138],{"categories":1011},[70],{"categories":1013},[182],{"categories":1015},[70],{"categories":1017},[120],{"categories":1019},[70],{"categories":1021},[120],{"categories":1023},[120],{"categories":1025},[70],{"categories":1027},[120],{"categories":1029},[165],{"categories":1031},[70],{"categories":1033},[],{"categories":1035},[],{"categories":1037},[175],{"categories":1039},[],{"categories":1041},[112],{"categories":1043},[207],{"categories":1045},[70],{"categories":1047},[],{"categories":1049},[112],{"categories":1051},[115],{"categories":1053},[182],{"categories":1055},[],{"categories":1057},[115],{"categories":1059},[],{"categories":1061},[70],{"categories":1063},[],{"categories":1065},[],{"categories":1067},[],{"categories":1069},[],{"categories":1071},[70],{"categories":1073},[120],{"categories":1075},[207],{"categories":1077},[112],{"categories":1079},[175],{"categories":1081},[70],{"categories":1083},[175],{"categories":1085},[123],{"categories":1087},[70],{"categories":1089},[182],{"categories":1091},[115],{"categories":1093},[70],{"categories":1095},[70],{"categories":1097},[70],{"categories":1099},[70,112],{"categories":1101},[175],{"categories":1103},[175],{"categories":1105},[165],{"categories":1107},[70],{"categories":1109},[],{"categories":1111},[],{"categories":1113},[],{"categories":1115},[175],{"categories":1117},[168],{"categories":1119},[138],{"categories":1121},[165],{"categories":1123},[],{"categories":1125},[70],{"categories":1127},[70],{"categories":1129},[],{"categories":1131},[120],{"categories":1133},[70],{"categories":1135},[],{"categories":1137},[120],{"categories":1139},[70],{"categories":1141},[115],{"categories":1143},[],{"categories":1145},[112],{"categories":1147},[70],{"categories":1149},[112],{"categories":1151},[70],{"categories":1153},[175],{"categories":1155},[182],{"categories":1157},[120],{"categories":1159},[70,165],{"categories":1161},[138],{"categories":1163},[70],{"categories":1165},[165],{"categories":1167},[],{"categories":1169},[175],{"categories":1171},[207],{"categories":1173},[165],{"categories":1175},[120],{"categories":1177},[],{"categories":1179},[],{"categories":1181},[],{"categories":1183},[],{"categories":1185},[175],{"categories":1187},[120],{"categories":1189},[120],{"categories":1191},[207],{"categories":1193},[70],{"categories":1195},[70],{"categories":1197},[120],{"categories":1199},[70],{"categories":1201},[70],{"categories":1203},[],{"categories":1205},[165],{"categories":1207},[],{"categories":1209},[],{"categories":1211},[120],{"categories":1213},[],{"categories":1215},[],{"categories":1217},[182],{"categories":1219},[182],{"categories":1221},[120],{"categories":1223},[175],{"categories":1225},[],{"categories":1227},[70],{"categories":1229},[70],{"categories":1231},[175],{"categories":1233},[165],{"categories":1235},[165],{"categories":1237},[120],{"categories":1239},[112],{"categories":1241},[70],{"categories":1243},[165],{"categories":1245},[165],{"categories":1247},[120],{"categories":1249},[120],{"categories":1251},[70],{"categories":1253},[],{"categories":1255},[],{"categories":1257},[70],{"categories":1259},[120],{"categories":1261},[138],{"categories":1263},[175],{"categories":1265},[70],{"categories":1267},[112],{"categories":1269},[70],{"categories":1271},[],{"categories":1273},[120],{"categories":1275},[120],{"categories":1277},[],{"categories":1279},[70],{"categories":1281},[112],{"categories":1283},[70],{"categories":1285},[112],{"categories":1287},[112],{"categories":1289},[],{"categories":1291},[],{"categories":1293},[120],{"categories":1295},[138],{"categories":1297},[120],{"categories":1299},[70],{"categories":1301},[70],{"categories":1303},[138],{"categories":1305},[168],{"categories":1307},[123],{"categories":1309},[138],{"categories":1311},[165],{"categories":1313},[],{"categories":1315},[],{"categories":1317},[138],{"categories":1319},[],{"categories":1321},[],{"categories":1323},[],{"categories":1325},[],{"categories":1327},[175],{"categories":1329},[168],{"categories":1331},[],{"categories":1333},[70],{"categories":1335},[70],{"categories":1337},[168],{"categories":1339},[175],{"categories":1341},[],{"categories":1343},[],{"categories":1345},[120],{"categories":1347},[138],{"categories":1349},[138],{"categories":1351},[120],{"categories":1353},[112],{"categories":1355},[70,207],{"categories":1357},[],{"categories":1359},[165],{"categories":1361},[112],{"categories":1363},[120],{"categories":1365},[165],{"categories":1367},[],{"categories":1369},[120],{"categories":1371},[120],{"categories":1373},[70],{"categories":1375},[182],{"categories":1377},[175],{"categories":1379},[165],{"categories":1381},[],{"categories":1383},[120],{"categories":1385},[70],{"categories":1387},[120],{"categories":1389},[120],{"categories":1391},[120],{"categories":1393},[182],{"categories":1395},[70],{"categories":1397},[120],{"categories":1399},[70],{"categories":1401},[],{"categories":1403},[182],{"categories":1405},[138],{"categories":1407},[120],{"categories":1409},[],{"categories":1411},[],{"categories":1413},[70],{"categories":1415},[120],{"categories":1417},[138],{"categories":1419},[120],{"categories":1421},[120],{"categories":1423},[],{"categories":1425},[70],{"categories":1427},[],{"categories":1429},[],{"categories":1431},[120],{"categories":1433},[],{"categories":1435},[],{"categories":1437},[168],{"categories":1439},[70],{"categories":1441},[168],{"categories":1443},[138],{"categories":1445},[70],{"categories":1447},[70],{"categories":1449},[120],{"categories":1451},[70],{"categories":1453},[],{"categories":1455},[],{"categories":1457},[207],{"categories":1459},[70],{"categories":1461},[],{"categories":1463},[],{"categories":1465},[112],{"categories":1467},[],{"categories":1469},[],{"categories":1471},[70],{"categories":1473},[],{"categories":1475},[],{"categories":1477},[175],{"categories":1479},[138],{"categories":1481},[182],{"categories":1483},[115],{"categories":1485},[70],{"categories":1487},[70],{"categories":1489},[115],{"categories":1491},[],{"categories":1493},[165],{"categories":1495},[120],{"categories":1497},[115],{"categories":1499},[70],{"categories":1501},[70],{"categories":1503},[112],{"categories":1505},[],{"categories":1507},[112],{"categories":1509},[70],{"categories":1511},[182],{"categories":1513},[120],{"categories":1515},[138],{"categories":1517},[115],{"categories":1519},[70],{"categories":1521},[70],{"categories":1523},[120],{"categories":1525},[],{"categories":1527},[70],{"categories":1529},[112],{"categories":1531},[70],{"categories":1533},[70],{"categories":1535},[],{"categories":1537},[138],{"categories":1539},[70],{"categories":1541},[],{"categories":1543},[115],{"categories":1545},[115],{"categories":1547},[70],{"categories":1549},[],{"categories":1551},[],{"categories":1553},[],{"categories":1555},[70],{"categories":1557},[138],{"categories":1559},[],{"categories":1561},[207],{"categories":1563},[70],{"categories":1565},[],{"categories":1567},[70],{"categories":1569},[70],{"categories":1571},[70],{"categories":1573},[70,207],{"categories":1575},[70],{"categories":1577},[70],{"categories":1579},[165],{"categories":1581},[120],{"categories":1583},[],{"categories":1585},[120],{"categories":1587},[120],{"categories":1589},[70],{"categories":1591},[70],{"categories":1593},[70],{"categories":1595},[112],{"categories":1597},[112],{"categories":1599},[175],{"categories":1601},[165],{"categories":1603},[120],{"categories":1605},[],{"categories":1607},[70],{"categories":1609},[138],{"categories":1611},[70],{"categories":1613},[115],{"categories":1615},[],{"categories":1617},[207],{"categories":1619},[165],{"categories":1621},[165],{"categories":1623},[120],{"categories":1625},[138],{"categories":1627},[120],{"categories":1629},[70],{"categories":1631},[],{"categories":1633},[70],{"categories":1635},[],{"categories":1637},[],{"categories":1639},[70],{"categories":1641},[70],{"categories":1643},[70],{"categories":1645},[120],{"categories":1647},[70],{"categories":1649},[70],{"categories":1651},[],{"categories":1653},[168],{"categories":1655},[120],{"categories":1657},[],{"categories":1659},[],{"categories":1661},[70],{"categories":1663},[138],{"categories":1665},[],{"categories":1667},[165],{"categories":1669},[207],{"categories":1671},[138],{"categories":1673},[175],{"categories":1675},[175],{"categories":1677},[138],{"categories":1679},[138],{"categories":1681},[207],{"categories":1683},[],{"categories":1685},[138],{"categories":1687},[70],{"categories":1689},[112],{"categories":1691},[70],{"categories":1693},[138],{"categories":1695},[],{"categories":1697},[175],{"categories":1699},[168],{"categories":1701},[70],{"categories":1703},[138],{"categories":1705},[175],{"categories":1707},[120],{"categories":1709},[138],{"categories":1711},[207],{"categories":1713},[120],{"categories":1715},[70],{"categories":1717},[70],{"categories":1719},[70],{"categories":1721},[],{"categories":1723},[115],{"categories":1725},[],{"categories":1727},[],{"categories":1729},[70],{"categories":1731},[70],{"categories":1733},[70],{"categories":1735},[70],{"categories":1737},[],{"categories":1739},[168],{"categories":1741},[112],{"categories":1743},[],{"categories":1745},[70],{"categories":1747},[70],{"categories":1749},[207],{"categories":1751},[207],{"categories":1753},[],{"categories":1755},[120],{"categories":1757},[138],{"categories":1759},[138],{"categories":1761},[70],{"categories":1763},[120],{"categories":1765},[],{"categories":1767},[165],{"categories":1769},[70],{"categories":1771},[70],{"categories":1773},[],{"categories":1775},[70],{"categories":1777},[],{"categories":1779},[175],{"categories":1781},[207],{"categories":1783},[70],{"categories":1785},[175],{"categories":1787},[115],{"categories":1789},[70],{"categories":1791},[],{"categories":1793},[120],{"categories":1795},[112],{"categories":1797},[112],{"categories":1799},[],{"categories":1801},[70],{"categories":1803},[165],{"categories":1805},[120],{"categories":1807},[],{"categories":1809},[70],{"categories":1811},[70],{"categories":1813},[120],{"categories":1815},[],{"categories":1817},[120],{"categories":1819},[175],{"categories":1821},[],{"categories":1823},[70],{"categories":1825},[],{"categories":1827},[70],{"categories":1829},[],{"categories":1831},[70],{"categories":1833},[70],{"categories":1835},[],{"categories":1837},[70],{"categories":1839},[138],{"categories":1841},[70],{"categories":1843},[70],{"categories":1845},[112],{"categories":1847},[70],{"categories":1849},[138],{"categories":1851},[120],{"categories":1853},[],{"categories":1855},[70],{"categories":1857},[165],{"categories":1859},[182],{"categories":1861},[70],{"categories":1863},[],{"categories":1865},[],{"categories":1867},[],{"categories":1869},[112],{"categories":1871},[138],{"categories":1873},[120],{"categories":1875},[70],{"categories":1877},[165],{"categories":1879},[120],{"categories":1881},[],{"categories":1883},[120],{"categories":1885},[],{"categories":1887},[70],{"categories":1889},[120],{"categories":1891},[70],{"categories":1893},[],{"categories":1895},[70],{"categories":1897},[70],{"categories":1899},[138],{"categories":1901},[165],{"categories":1903},[120],{"categories":1905},[165],{"categories":1907},[115],{"categories":1909},[],{"categories":1911},[],{"categories":1913},[70],{"categories":1915},[112],{"categories":1917},[138],{"categories":1919},[],{"categories":1921},[165],{"categories":1923},[],{"categories":1925},[175],{"categories":1927},[175],{"categories":1929},[165],{"categories":1931},[],{"categories":1933},[70],{"categories":1935},[],{"categories":1937},[182],{"categories":1939},[70],{"categories":1941},[207],{"categories":1943},[175],{"categories":1945},[],{"categories":1947},[120],{"categories":1949},[70],{"categories":1951},[112],{"categories":1953},[120],{"categories":1955},[120],{"categories":1957},[70],{"categories":1959},[],{"categories":1961},[112],{"categories":1963},[70],{"categories":1965},[115],{"categories":1967},[175],{"categories":1969},[165],{"categories":1971},[],{"categories":1973},[],{"categories":1975},[],{"categories":1977},[120],{"categories":1979},[165],{"categories":1981},[138],{"categories":1983},[70],{"categories":1985},[138],{"categories":1987},[165],{"categories":1989},[],{"categories":1991},[165],{"categories":1993},[138],{"categories":1995},[115],{"categories":1997},[175],{"categories":1999},[70],{"categories":2001},[138],{"categories":2003},[182],{"categories":2005},[],{"categories":2007},[],{"categories":2009},[168],{"categories":2011},[70,175],{"categories":2013},[138],{"categories":2015},[70],{"categories":2017},[120],{"categories":2019},[70],{"categories":2021},[120],{"categories":2023},[70],{"categories":2025},[70],{"categories":2027},[],{"categories":2029},[175],{"categories":2031},[70],{"categories":2033},[168],{"categories":2035},[120],{"categories":2037},[182],{"categories":2039},[207],{"categories":2041},[],{"categories":2043},[112],{"categories":2045},[120],{"categories":2047},[120],{"categories":2049},[175],{"categories":2051},[70],{"categories":2053},[70],{"categories":2055},[],{"categories":2057},[],{"categories":2059},[],{"categories":2061},[207],{"categories":2063},[138],{"categories":2065},[70],{"categories":2067},[70],{"categories":2069},[70],{"categories":2071},[],{"categories":2073},[168],{"categories":2075},[115],{"categories":2077},[],{"categories":2079},[120],{"categories":2081},[207],{"categories":2083},[],{"categories":2085},[165],{"categories":2087},[165],{"categories":2089},[],{"categories":2091},[175],{"categories":2093},[70],{"categories":2095},[165],{"categories":2097},[70],{"categories":2099},[],{"categories":2101},[138],{"categories":2103},[70],{"categories":2105},[70],{"categories":2107},[165],{"categories":2109},[120],{"categories":2111},[138],{"categories":2113},[],{"categories":2115},[120],{"categories":2117},[165],{"categories":2119},[70],{"categories":2121},[],{"categories":2123},[70],{"categories":2125},[70],{"categories":2127},[207],{"categories":2129},[138],{"categories":2131},[168],{"categories":2133},[168],{"categories":2135},[],{"categories":2137},[],{"categories":2139},[],{"categories":2141},[120],{"categories":2143},[175],{"categories":2145},[175],{"categories":2147},[70],{"categories":2149},[],{"categories":2151},[],{"categories":2153},[70],{"categories":2155},[],{"categories":2157},[120],{"categories":2159},[70],{"categories":2161},[],{"categories":2163},[70],{"categories":2165},[115],{"categories":2167},[70],{"categories":2169},[182],{"categories":2171},[120],{"categories":2173},[70],{"categories":2175},[70],{"categories":2177},[70],{"categories":2179},[175],{"categories":2181},[],{"categories":2183},[138],{"categories":2185},[120],{"categories":2187},[],{"categories":2189},[138],{"categories":2191},[120],{"categories":2193},[120],{"categories":2195},[],{"categories":2197},[115],{"categories":2199},[120],{"categories":2201},[],{"categories":2203},[70],{"categories":2205},[112],{"categories":2207},[138],{"categories":2209},[207],{"categories":2211},[120],{"categories":2213},[120],{"categories":2215},[112],{"categories":2217},[],{"categories":2219},[70],{"categories":2221},[],{"categories":2223},[],{"categories":2225},[165],{"categories":2227},[70,115],{"categories":2229},[70],{"categories":2231},[],{"categories":2233},[112],{"categories":2235},[168],{"categories":2237},[70],{"categories":2239},[175],{"categories":2241},[70],{"categories":2243},[120],{"categories":2245},[70],{"categories":2247},[70],{"categories":2249},[138],{"categories":2251},[120],{"categories":2253},[],{"categories":2255},[],{"categories":2257},[120],{"categories":2259},[70],{"categories":2261},[207],{"categories":2263},[],{"categories":2265},[70],{"categories":2267},[120],{"categories":2269},[],{"categories":2271},[120],{"categories":2273},[70],{"categories":2275},[182],{"categories":2277},[168],{"categories":2279},[120],{"categories":2281},[70],{"categories":2283},[207],{"categories":2285},[],{"categories":2287},[70],{"categories":2289},[182],{"categories":2291},[165],{"categories":2293},[70],{"categories":2295},[70],{"categories":2297},[],{"categories":2299},[182],{"categories":2301},[138],{"categories":2303},[70],{"categories":2305},[70],{"categories":2307},[112],{"categories":2309},[],{"categories":2311},[],{"categories":2313},[165],{"categories":2315},[70],{"categories":2317},[168],{"categories":2319},[182],{"categories":2321},[182],{"categories":2323},[138],{"categories":2325},[],{"categories":2327},[],{"categories":2329},[70],{"categories":2331},[70],{"categories":2333},[70],{"categories":2335},[],{"categories":2337},[70,175],{"categories":2339},[138],{"categories":2341},[120],{"categories":2343},[175],{"categories":2345},[70],{"categories":2347},[112],{"categories":2349},[],{"categories":2351},[],{"categories":2353},[112],{"categories":2355},[175],{"categories":2357},[182],{"categories":2359},[70],{"categories":2361},[],{"categories":2363},[165,70],{"categories":2365},[207],{"categories":2367},[112],{"categories":2369},[],{"categories":2371},[115],{"categories":2373},[115],{"categories":2375},[70],{"categories":2377},[70],{"categories":2379},[175],{"categories":2381},[120],{"categories":2383},[138],{"categories":2385},[182],{"categories":2387},[165],{"categories":2389},[70],{"categories":2391},[70],{"categories":2393},[70],{"categories":2395},[112],{"categories":2397},[70],{"categories":2399},[120],{"categories":2401},[138],{"categories":2403},[],{"categories":2405},[],{"categories":2407},[168],{"categories":2409},[175],{"categories":2411},[70],{"categories":2413},[165],{"categories":2415},[70],{"categories":2417},[168],{"categories":2419},[70],{"categories":2421},[70],{"categories":2423},[70],{"categories":2425},[120],{"categories":2427},[120],{"categories":2429},[70,115],{"categories":2431},[],{"categories":2433},[165],{"categories":2435},[],{"categories":2437},[70],{"categories":2439},[138],{"categories":2441},[112],{"categories":2443},[112],{"categories":2445},[120],{"categories":2447},[70],{"categories":2449},[70],{"categories":2451},[115],{"categories":2453},[175],{"categories":2455},[182],{"categories":2457},[70],{"categories":2459},[],{"categories":2461},[138],{"categories":2463},[70],{"categories":2465},[70],{"categories":2467},[70],{"categories":2469},[70],{"categories":2471},[138],{"categories":2473},[175],{"categories":2475},[175],{"categories":2477},[70],{"categories":2479},[70],{"categories":2481},[120],{"categories":2483},[138],{"categories":2485},[70],{"categories":2487},[165],{"categories":2489},[70],{"categories":2491},[70],{"categories":2493},[207],{"categories":2495},[70],{"categories":2497},[123],{"categories":2499},[120],{"categories":2501},[70],{"categories":2503},[138],{"categories":2505},[120],{"categories":2507},[182],{"categories":2509},[70],{"categories":2511},[],{"categories":2513},[70],{"categories":2515},[],{"categories":2517},[],{"categories":2519},[],{"categories":2521},[115],{"categories":2523},[70],{"categories":2525},[120],{"categories":2527},[138],{"categories":2529},[138],{"categories":2531},[138],{"categories":2533},[138],{"categories":2535},[],{"categories":2537},[112],{"categories":2539},[120],{"categories":2541},[138],{"categories":2543},[70],{"categories":2545},[112],{"categories":2547},[120],{"categories":2549},[70],{"categories":2551},[70,120],{"categories":2553},[120],{"categories":2555},[207],{"categories":2557},[138],{"categories":2559},[138],{"categories":2561},[120],{"categories":2563},[70],{"categories":2565},[],{"categories":2567},[138],{"categories":2569},[182],{"categories":2571},[112],{"categories":2573},[70],{"categories":2575},[70],{"categories":2577},[],{"categories":2579},[175],{"categories":2581},[],{"categories":2583},[112],{"categories":2585},[120],{"categories":2587},[138],{"categories":2589},[70],{"categories":2591},[138],{"categories":2593},[112],{"categories":2595},[138],{"categories":2597},[138],{"categories":2599},[],{"categories":2601},[115],{"categories":2603},[120],{"categories":2605},[138],{"categories":2607},[138],{"categories":2609},[138],{"categories":2611},[138],{"categories":2613},[138],{"categories":2615},[138],{"categories":2617},[138],{"categories":2619},[138],{"categories":2621},[138],{"categories":2623},[138],{"categories":2625},[168],{"categories":2627},[112],{"categories":2629},[70],{"categories":2631},[70],{"categories":2633},[],{"categories":2635},[70,112],{"categories":2637},[],{"categories":2639},[120],{"categories":2641},[138],{"categories":2643},[120],{"categories":2645},[70],{"categories":2647},[70],{"categories":2649},[70],{"categories":2651},[70],{"categories":2653},[70],{"categories":2655},[120],{"categories":2657},[115],{"categories":2659},[],{"categories":2661},[165],{"categories":2663},[138],{"categories":2665},[70],{"categories":2667},[],{"categories":2669},[],{"categories":2671},[120],{"categories":2673},[165],{"categories":2675},[70],{"categories":2677},[],{"categories":2679},[70],{"categories":2681},[],{"categories":2683},[182],{"categories":2685},[70],{"categories":2687},[],{"categories":2689},[],{"categories":2691},[138],{"categories":2693},[112],{"categories":2695},[70],{"categories":2697},[115],{"categories":2699},[70],{"categories":2701},[115],{"categories":2703},[165],{"categories":2705},[],{"categories":2707},[138],{"categories":2709},[],{"categories":2711},[165],{"categories":2713},[70],{"categories":2715},[182],{"categories":2717},[],{"categories":2719},[182],{"categories":2721},[],{"categories":2723},[],{"categories":2725},[120],{"categories":2727},[],{"categories":2729},[115],{"categories":2731},[112],{"categories":2733},[165],{"categories":2735},[175],{"categories":2737},[],{"categories":2739},[],{"categories":2741},[70],{"categories":2743},[112],{"categories":2745},[182],{"categories":2747},[],{"categories":2749},[120],{"categories":2751},[120],{"categories":2753},[138],{"categories":2755},[175],{"categories":2757},[70],{"categories":2759},[120],{"categories":2761},[70],{"categories":2763},[120],{"categories":2765},[70],{"categories":2767},[123],{"categories":2769},[138],{"categories":2771},[],{"categories":2773},[182],{"categories":2775},[],{"categories":2777},[175],{"categories":2779},[120],{"categories":2781},[],{"categories":2783},[70],{"categories":2785},[120],{"categories":2787},[115],{"categories":2789},[112],{"categories":2791},[70],{"categories":2793},[165],{"categories":2795},[175],{"categories":2797},[175],{"categories":2799},[70],{"categories":2801},[168],{"categories":2803},[70],{"categories":2805},[120],{"categories":2807},[115],{"categories":2809},[165],{"categories":2811},[120],{"categories":2813},[70],{"categories":2815},[70],{"categories":2817},[120],{"categories":2819},[138],{"categories":2821},[],{"categories":2823},[112],{"categories":2825},[70],{"categories":2827},[120],{"categories":2829},[70],{"categories":2831},[70],{"categories":2833},[],{"categories":2835},[165],{"categories":2837},[115],{"categories":2839},[138],{"categories":2841},[70],{"categories":2843},[70],{"categories":2845},[165],{"categories":2847},[70],{"categories":2849},[182],{"categories":2851},[168],{"categories":2853},[70],{"categories":2855},[138],{"categories":2857},[70],{"categories":2859},[120],{"categories":2861},[207],{"categories":2863},[70],{"categories":2865},[120],{"categories":2867},[168],{"categories":2869},[],{"categories":2871},[120],{"categories":2873},[175],{"categories":2875},[165],{"categories":2877},[70],{"categories":2879},[112],{"categories":2881},[115],{"categories":2883},[175],{"categories":2885},[70],{"categories":2887},[],{"categories":2889},[120],{"categories":2891},[120],{"categories":2893},[70],{"categories":2895},[168],{"categories":2897},[],{"categories":2899},[138],{"categories":2901},[],{"categories":2903},[138],{"categories":2905},[70],{"categories":2907},[120],{"categories":2909},[120],{"categories":2911},[120],{"categories":2913},[],{"categories":2915},[138],{"categories":2917},[],{"categories":2919},[70],{"categories":2921},[70],{"categories":2923},[],{"categories":2925},[165],{"categories":2927},[120],{"categories":2929},[182],{"categories":2931},[112],{"categories":2933},[],{"categories":2935},[70],{"categories":2937},[],{"categories":2939},[112],{"categories":2941},[138],{"categories":2943},[175],{"categories":2945},[70],{"categories":2947},[70],{"categories":2949},[70],{"categories":2951},[175],{"categories":2953},[138],{"categories":2955},[165],{"categories":2957},[70],{"categories":2959},[70],{"categories":2961},[70],{"categories":2963},[138],{"categories":2965},[70],{"categories":2967},[138],{"categories":2969},[138],{"categories":2971},[120],{"categories":2973},[120],{"categories":2975},[175],{"categories":2977},[138],{"categories":2979},[120],{"categories":2981},[70],{"categories":2983},[175],{"categories":2985},[165],{"categories":2987},[],{"categories":2989},[120],{"categories":2991},[],{"categories":2993},[],{"categories":2995},[],{"categories":2997},[115],{"categories":2999},[70],{"categories":3001},[120],{"categories":3003},[112],{"categories":3005},[120],{"categories":3007},[182],{"categories":3009},[],{"categories":3011},[120],{"categories":3013},[],{"categories":3015},[112],{"categories":3017},[120],{"categories":3019},[],{"categories":3021},[120],{"categories":3023},[70],{"categories":3025},[138],{"categories":3027},[70],{"categories":3029},[120],{"categories":3031},[138],{"categories":3033},[120],{"categories":3035},[175],{"categories":3037},[165],{"categories":3039},[112],{"categories":3041},[],{"categories":3043},[120],{"categories":3045},[165],{"categories":3047},[207],{"categories":3049},[138],{"categories":3051},[70],{"categories":3053},[165],{"categories":3055},[112],{"categories":3057},[],{"categories":3059},[120],{"categories":3061},[70],{"categories":3063},[120],{"categories":3065},[70],{"categories":3067},[],{"categories":3069},[120],{"categories":3071},[123],{"categories":3073},[138],{"categories":3075},[120],{"categories":3077},[115],{"categories":3079},[],{"categories":3081},[70],{"categories":3083},[123],{"categories":3085},[70],{"categories":3087},[120],{"categories":3089},[138],{"categories":3091},[112],{"categories":3093},[207],{"categories":3095},[70],{"categories":3097},[70],{"categories":3099},[70],{"categories":3101},[138],{"categories":3103},[115],{"categories":3105},[70],{"categories":3107},[165],{"categories":3109},[138],{"categories":3111},[207],{"categories":3113},[70],{"categories":3115},[],{"categories":3117},[],{"categories":3119},[70],{"categories":3121},[207],{"categories":3123},[168],{"categories":3125},[120],{"categories":3127},[120],{"categories":3129},[138],{"categories":3131},[70],{"categories":3133},[112],{"categories":3135},[165],{"categories":3137},[120],{"categories":3139},[70],{"categories":3141},[182],{"categories":3143},[70],{"categories":3145},[120],{"categories":3147},[],{"categories":3149},[70],{"categories":3151},[70],{"categories":3153},[138],{"categories":3155},[112],{"categories":3157},[],{"categories":3159},[70],{"categories":3161},[70],{"categories":3163},[175],{"categories":3165},[165],{"categories":3167},[70,120],{"categories":3169},[182,115],{"categories":3171},[70],{"categories":3173},[],{"categories":3175},[120],{"categories":3177},[],{"categories":3179},[175],{"categories":3181},[70],{"categories":3183},[],{"categories":3185},[70],{"categories":3187},[138],{"categories":3189},[],{"categories":3191},[120],{"categories":3193},[70],{"categories":3195},[],{"categories":3197},[165],{"categories":3199},[120],{"categories":3201},[70],{"categories":3203},[112],{"categories":3205},[120],{"categories":3207},[70],{"categories":3209},[],{"categories":3211},[207],{"categories":3213},[182],{"categories":3215},[115],{"categories":3217},[115],{"categories":3219},[112],{"categories":3221},[112],{"categories":3223},[70],{"categories":3225},[120],{"categories":3227},[70],{"categories":3229},[70],{"categories":3231},[112],{"categories":3233},[70],{"categories":3235},[182],{"categories":3237},[138],{"categories":3239},[70],{"categories":3241},[120],{"categories":3243},[70],{"categories":3245},[],{"categories":3247},[175],{"categories":3249},[],{"categories":3251},[175],{"categories":3253},[120],{"categories":3255},[112],{"categories":3257},[],{"categories":3259},[207],{"categories":3261},[70],{"categories":3263},[],{"categories":3265},[138],{"categories":3267},[120],{"categories":3269},[175],{"categories":3271},[70],{"categories":3273},[120],{"categories":3275},[175],{"categories":3277},[120],{"categories":3279},[138],{"categories":3281},[112],{"categories":3283},[138],{"categories":3285},[175],{"categories":3287},[70],{"categories":3289},[165],{"categories":3291},[70],{"categories":3293},[70],{"categories":3295},[70],{"categories":3297},[70],{"categories":3299},[70],{"categories":3301},[120],{"categories":3303},[70],{"categories":3305},[120],{"categories":3307},[70],{"categories":3309},[112],{"categories":3311},[70],{"categories":3313},[120],{"categories":3315},[165],{"categories":3317},[112],{"categories":3319},[120],{"categories":3321},[165],{"categories":3323},[],{"categories":3325},[70],{"categories":3327},[70],{"categories":3329},[175],{"categories":3331},[],{"categories":3333},[120],{"categories":3335},[182],{"categories":3337},[70],{"categories":3339},[138],{"categories":3341},[182],{"categories":3343},[120],{"categories":3345},[115],{"categories":3347},[115],{"categories":3349},[70],{"categories":3351},[112],{"categories":3353},[],{"categories":3355},[120],{"categories":3357},[70],{"categories":3359},[],{"categories":3361},[112],{"categories":3363},[70],{"categories":3365},[120],{"categories":3367},[120],{"categories":3369},[],{"categories":3371},[175],{"categories":3373},[175],{"categories":3375},[182],{"categories":3377},[165],{"categories":3379},[],{"categories":3381},[70],{"categories":3383},[120],{"categories":3385},[112],{"categories":3387},[70],{"categories":3389},[175],{"categories":3391},[112],{"categories":3393},[138],{"categories":3395},[138],{"categories":3397},[],{"categories":3399},[138],{"categories":3401},[120],{"categories":3403},[165],{"categories":3405},[168],{"categories":3407},[70],{"categories":3409},[],{"categories":3411},[138],{"categories":3413},[175],{"categories":3415},[115],{"categories":3417},[70],{"categories":3419},[112],{"categories":3421},[207],{"categories":3423},[112],{"categories":3425},[],{"categories":3427},[],{"categories":3429},[138],{"categories":3431},[],{"categories":3433},[120],{"categories":3435},[120],{"categories":3437},[120],{"categories":3439},[],{"categories":3441},[70],{"categories":3443},[],{"categories":3445},[138],{"categories":3447},[112],{"categories":3449},[165],{"categories":3451},[70],{"categories":3453},[138],{"categories":3455},[138],{"categories":3457},[],{"categories":3459},[138],{"categories":3461},[112],{"categories":3463},[70],{"categories":3465},[],{"categories":3467},[120],{"categories":3469},[120],{"categories":3471},[112],{"categories":3473},[],{"categories":3475},[],{"categories":3477},[],{"categories":3479},[165],{"categories":3481},[120],{"categories":3483},[70],{"categories":3485},[],{"categories":3487},[],{"categories":3489},[],{"categories":3491},[165],{"categories":3493},[],{"categories":3495},[70],{"categories":3497},[112],{"categories":3499},[],{"categories":3501},[],{"categories":3503},[165],{"categories":3505},[70],{"categories":3507},[138],{"categories":3509},[],{"categories":3511},[182],{"categories":3513},[138],{"categories":3515},[182],{"categories":3517},[70],{"categories":3519},[],{"categories":3521},[],{"categories":3523},[120],{"categories":3525},[],{"categories":3527},[],{"categories":3529},[120],{"categories":3531},[70],{"categories":3533},[],{"categories":3535},[120],{"categories":3537},[138],{"categories":3539},[70],{"categories":3541},[182],{"categories":3543},[168],{"categories":3545},[120],{"categories":3547},[120],{"categories":3549},[],{"categories":3551},[],{"categories":3553},[],{"categories":3555},[138],{"categories":3557},[],{"categories":3559},[],{"categories":3561},[165],{"categories":3563},[112],{"categories":3565},[],{"categories":3567},[115],{"categories":3569},[182],{"categories":3571},[70],{"categories":3573},[175],{"categories":3575},[112],{"categories":3577},[168],{"categories":3579},[115],{"categories":3581},[175],{"categories":3583},[175],{"categories":3585},[],{"categories":3587},[],{"categories":3589},[120],{"categories":3591},[112],{"categories":3593},[165],{"categories":3595},[112],{"categories":3597},[120],{"categories":3599},[207],{"categories":3601},[70],{"categories":3603},[112],{"categories":3605},[120],{"categories":3607},[],{"categories":3609},[70],{"categories":3611},[138],{"categories":3613},[175],{"categories":3615},[],{"categories":3617},[165],{"categories":3619},[138],{"categories":3621},[112],{"categories":3623},[120],{"categories":3625},[70],{"categories":3627},[115],{"categories":3629},[120,207],{"categories":3631},[120],{"categories":3633},[175],{"categories":3635},[70],{"categories":3637},[70],{"categories":3639},[168],{"categories":3641},[182],{"categories":3643},[120],{"categories":3645},[],{"categories":3647},[120],{"categories":3649},[70],{"categories":3651},[115],{"categories":3653},[],{"categories":3655},[],{"categories":3657},[70],{"categories":3659},[168],{"categories":3661},[70],{"categories":3663},[],{"categories":3665},[138],{"categories":3667},[],{"categories":3669},[138],{"categories":3671},[112],{"categories":3673},[175],{"categories":3675},[70],{"categories":3677},[120],{"categories":3679},[70],{"categories":3681},[70],{"categories":3683},[182],{"categories":3685},[175],{"categories":3687},[],{"categories":3689},[138],{"categories":3691},[70],{"categories":3693},[],{"categories":3695},[70],{"categories":3697},[120],{"categories":3699},[70],{"categories":3701},[120],{"categories":3703},[70],{"categories":3705},[70],{"categories":3707},[70],{"categories":3709},[70],{"categories":3711},[115],{"categories":3713},[],{"categories":3715},[123],{"categories":3717},[138],{"categories":3719},[70],{"categories":3721},[],{"categories":3723},[175],{"categories":3725},[70],{"categories":3727},[70],{"categories":3729},[70],{"categories":3731},[120],{"categories":3733},[138],{"categories":3735},[70],{"categories":3737},[70],{"categories":3739},[70],{"categories":3741},[115],{"categories":3743},[120],{"categories":3745},[165],{"categories":3747},[],{"categories":3749},[168],{"categories":3751},[70],{"categories":3753},[],{"categories":3755},[138],{"categories":3757},[182],{"categories":3759},[],{"categories":3761},[],{"categories":3763},[138],{"categories":3765},[138],{"categories":3767},[182],{"categories":3769},[112],{"categories":3771},[120],{"categories":3773},[120],{"categories":3775},[70],{"categories":3777},[115],{"categories":3779},[],{"categories":3781},[],{"categories":3783},[138],{"categories":3785},[168],{"categories":3787},[175],{"categories":3789},[120],{"categories":3791},[165],{"categories":3793},[168],{"categories":3795},[168],{"categories":3797},[],{"categories":3799},[138],{"categories":3801},[70],{"categories":3803},[70],{"categories":3805},[175],{"categories":3807},[],{"categories":3809},[138],{"categories":3811},[138],{"categories":3813},[138],{"categories":3815},[],{"categories":3817},[120],{"categories":3819},[70],{"categories":3821},[],{"categories":3823},[112],{"categories":3825},[115],{"categories":3827},[],{"categories":3829},[70],{"categories":3831},[70],{"categories":3833},[],{"categories":3835},[175],{"categories":3837},[],{"categories":3839},[],{"categories":3841},[],{"categories":3843},[],{"categories":3845},[70],{"categories":3847},[138],{"categories":3849},[],{"categories":3851},[],{"categories":3853},[70],{"categories":3855},[70],{"categories":3857},[70],{"categories":3859},[168],{"categories":3861},[70],{"categories":3863},[168],{"categories":3865},[],{"categories":3867},[168],{"categories":3869},[168],{"categories":3871},[207],{"categories":3873},[120],{"categories":3875},[175],{"categories":3877},[],{"categories":3879},[],{"categories":3881},[168],{"categories":3883},[175],{"categories":3885},[175],{"categories":3887},[175],{"categories":3889},[],{"categories":3891},[112],{"categories":3893},[175],{"categories":3895},[175],{"categories":3897},[112],{"categories":3899},[175],{"categories":3901},[115],{"categories":3903},[175],{"categories":3905},[175],{"categories":3907},[175],{"categories":3909},[168],{"categories":3911},[138],{"categories":3913},[138],{"categories":3915},[70],{"categories":3917},[175],{"categories":3919},[168],{"categories":3921},[207],{"categories":3923},[168],{"categories":3925},[168],{"categories":3927},[168],{"categories":3929},[],{"categories":3931},[115],{"categories":3933},[],{"categories":3935},[207],{"categories":3937},[175],{"categories":3939},[175],{"categories":3941},[175],{"categories":3943},[120],{"categories":3945},[138,115],{"categories":3947},[168],{"categories":3949},[],{"categories":3951},[],{"categories":3953},[168],{"categories":3955},[],{"categories":3957},[168],{"categories":3959},[138],{"categories":3961},[120],{"categories":3963},[],{"categories":3965},[175],{"categories":3967},[70],{"categories":3969},[165],{"categories":3971},[],{"categories":3973},[70],{"categories":3975},[],{"categories":3977},[138],{"categories":3979},[112],{"categories":3981},[168],{"categories":3983},[],{"categories":3985},[175],{"categories":3987},[138],[3989,4087,4189,4272],{"id":3990,"title":3991,"ai":3992,"body":3998,"categories":4054,"created_at":71,"date_modified":71,"description":63,"extension":72,"faq":71,"featured":73,"kicker_label":71,"meta":4055,"navigation":90,"path":4075,"published_at":4076,"question":71,"scraped_at":4077,"seo":4078,"sitemap":4079,"source_id":4080,"source_name":97,"source_type":98,"source_url":4081,"stem":4082,"tags":4083,"thumbnail_url":71,"tldr":4084,"tweet":71,"unknown_tags":4085,"__hash__":4086},"summaries\u002Fsummaries\u002F79f82c07ea7441fe-trl-code-guide-sft-to-grpo-llm-alignment-on-t4-gpu-summary.md","TRL Code Guide: SFT to GRPO LLM Alignment on T4 GPU",{"provider":7,"model":3993,"input_tokens":3994,"output_tokens":3995,"processing_time_ms":3996,"cost_usd":3997},"x-ai\u002Fgrok-4.1-fast",9458,2615,35753,0.00269195,{"type":14,"value":3999,"toc":4048},[4000,4004,4012,4016,4026,4030,4036,4040],[17,4001,4003],{"id":4002},"lora-and-trl-setup-enables-post-training-on-limited-hardware","LoRA and TRL Setup Enables Post-Training on Limited Hardware",[22,4005,4006,4007,4011],{},"Use LoRA (r=8, alpha=16, dropout=0.05, targets=",[4008,4009,4010],"span",{},"'q_proj','k_proj','v_proj','o_proj'",") with TRL trainers to adapt Qwen\u002FQwen2.5-0.5B-Instruct on T4 GPU (16GB). Common args across stages: num_train_epochs=1, gradient_checkpointing=True, bf16 if supported else fp16, logging_steps=10, report_to=\"none\", save_strategy=\"no\". Install stack: torchao>=0.16, trl>=0.20, transformers>=4.45, peft>=0.13, bitsandbytes. Helpers like chat_generate apply chat template, generate with temp=0.7\u002Ftop_p=0.9. Cleanup VRAM with gc.collect() + torch.cuda.empty_cache() between stages to fit in Colab.",[17,4013,4015],{"id":4014},"sft-and-rm-build-imitation-and-reward-signals","SFT and RM Build Imitation and Reward Signals",[22,4017,4018,4019,4022,4023,4025],{},"For Supervised Fine-Tuning, load trl-lib\u002FCapybara (train",[4008,4020,4021],{},":300","), use SFTConfig(per_device_train_batch_size=2, gradient_accumulation_steps=4, learning_rate=2e-4, max_length=768). Trainer imitates high-quality chat responses; post-train inference on \"Explain bias-variance tradeoff in two sentences\" yields coherent output. Reward Modeling on trl-lib\u002Fultrafeedback_binarized (train",[4008,4024,4021],{},") uses RewardConfig(batch_size=2, accum_steps=2, lr=1e-4, max_length=512), LoRA task_type=\"SEQ_CLS\". Trains to score chosen vs. rejected pairs, producing a preference-based reward without explicit RL.",[17,4027,4029],{"id":4028},"dpo-skips-rm-for-direct-preference-alignment","DPO Skips RM for Direct Preference Alignment",[22,4031,4032,4033,4035],{},"DPOTrainer on same ultrafeedback_binarized",[4008,4034,4021],{}," simplifies via implicit rewards: DPOConfig(batch_size=1, accum_steps=4, lr=5e-6, beta=0.1, max_length=512, max_prompt_length=256). Beta controls KL-divergence from reference policy, preventing mode collapse. Optimizes policy to prefer chosen over rejected responses directly, reducing steps vs. traditional RM+PPO.",[17,4037,4039],{"id":4038},"grpo-uses-custom-rewards-to-sharpen-reasoning","GRPO Uses Custom Rewards to Sharpen Reasoning",[22,4041,4042,4043,4047],{},"GRPOTrainer generates num_generations=4 completions per prompt (max_prompt_length=128, max_completion_length=96, max_steps=15), ranks via reward_funcs. Custom dataset: 200 synthetic math problems (e.g., \"Solve 17 + 28 =\", gold=eval). Rewards: correctness_reward (1.0 if last extracted number matches gold else 0), brevity_reward (max(0,1-len(c)\u002F200)",[4044,4045,4046],"em",{},"0.2). GRPOConfig(lr=1e-5, batch=2, accum=2). Inference on \"17+28?\", \"9","7?\", \"100-47?\" produces accurate, concise answers like final numbers, improving verifiable task performance over base.",{"title":63,"searchDepth":64,"depth":64,"links":4049},[4050,4051,4052,4053],{"id":4002,"depth":64,"text":4003},{"id":4014,"depth":64,"text":4015},{"id":4028,"depth":64,"text":4029},{"id":4038,"depth":64,"text":4039},[70],{"content_references":4056,"triage":4072},[4057,4060,4063,4065,4067],{"type":77,"title":4058,"url":4059,"context":80},"TRL","https:\u002F\u002Fgithub.com\u002Fhuggingface\u002Ftrl",{"type":4061,"title":4062,"context":80},"dataset","trl-lib\u002FCapybara",{"type":4061,"title":4064,"context":80},"trl-lib\u002Fultrafeedback_binarized",{"type":77,"title":4066,"context":80},"Qwen\u002FQwen2.5-0.5B-Instruct",{"type":4068,"title":4069,"url":4070,"context":4071},"other","trl_llm_post_training_sft_dpo_grpo_marktechpost.py","https:\u002F\u002Fgithub.com\u002FMarktechpost\u002FAI-Agents-Projects-Tutorials\u002Fblob\u002Fmain\u002FLLM%20Projects\u002Ftrl_llm_post_training_sft_dpo_grpo_marktechpost.py","recommended",{"relevance":85,"novelty":86,"quality":86,"actionability":85,"composite":4073,"reasoning":4074},4.55,"Category: AI & LLMs. The article provides a detailed guide on using TRL and LoRA for LLM post-training, addressing practical applications for developers looking to implement AI features. It includes specific configurations and techniques that can be directly applied in production, making it highly actionable.","\u002Fsummaries\u002F79f82c07ea7441fe-trl-code-guide-sft-to-grpo-llm-alignment-on-t4-gpu-summary","2026-05-01 20:52:08","2026-05-03 17:01:49",{"title":3991,"description":63},{"loc":4075},"79f82c07ea7441fe","https:\u002F\u002Fwww.marktechpost.com\u002F2026\u002F05\u002F01\u002Fa-coding-guide-on-llm-post-training-with-trl-from-supervised-fine-tuning-to-dpo-and-grpo-reasoning\u002F","summaries\u002F79f82c07ea7441fe-trl-code-guide-sft-to-grpo-llm-alignment-on-t4-gpu-summary",[102,104,103],"Train Qwen2.5-0.5B via SFT, RM, DPO, GRPO using TRL+LoRA on Colab T4: configs include r=8 LoRA, 300-sample datasets, epochs=1, small batches\u002Faccum for memory efficiency, custom math rewards boost reasoning.",[],"py8Fe1-Noi99CHywKy61Q363dqRBmUxl6tZ9TDJOp3E",{"id":4088,"title":4089,"ai":4090,"body":4095,"categories":4163,"created_at":71,"date_modified":71,"description":63,"extension":72,"faq":71,"featured":73,"kicker_label":71,"meta":4164,"navigation":90,"path":4176,"published_at":4177,"question":71,"scraped_at":4178,"seo":4179,"sitemap":4180,"source_id":4181,"source_name":97,"source_type":98,"source_url":4182,"stem":4183,"tags":4184,"thumbnail_url":71,"tldr":4186,"tweet":71,"unknown_tags":4187,"__hash__":4188},"summaries\u002Fsummaries\u002Fbeb19294561867ca-benchmarking-llm-compression-fp8-gptq-and-smoothqu-summary.md","Benchmarking LLM Compression: FP8, GPTQ, and SmoothQuant",{"provider":7,"model":8,"input_tokens":4091,"output_tokens":4092,"processing_time_ms":4093,"cost_usd":4094},10756,674,2766,0.0037,{"type":14,"value":4096,"toc":4159},[4097,4101,4109,4129,4133,4136,4156],[17,4098,4100],{"id":4099},"quantization-strategies-for-llm-efficiency","Quantization Strategies for LLM Efficiency",[22,4102,4103,4104,4108],{},"Post-training quantization (PTQ) is essential for deploying LLMs in resource-constrained environments. This tutorial demonstrates three distinct approaches using the ",[4105,4106,4107],"code",{},"llmcompressor"," library to reduce model footprint and improve inference speed while maintaining output quality:",[33,4110,4111,4117,4123],{},[36,4112,4113,4116],{},[39,4114,4115],{},"FP8 Dynamic Quantization:"," A data-free approach that compresses linear layers into 8-bit precision while keeping the language modeling head in higher precision. It is the fastest to implement and provides a baseline for efficiency gains.",[36,4118,4119,4122],{},[39,4120,4121],{},"GPTQ W4A16:"," A more aggressive compression method that reduces weights to 4-bit while maintaining 16-bit activation precision. This requires a calibration dataset (in this case, 256 samples from UltraChat) to minimize reconstruction error, resulting in significantly smaller model sizes.",[36,4124,4125,4128],{},[39,4126,4127],{},"SmoothQuant + GPTQ W8A8:"," An advanced pipeline that addresses activation outliers using SmoothQuant (smoothing strength 0.8) before applying 8-bit quantization. This combination balances accuracy recovery with the performance benefits of 8-bit operations.",[17,4130,4132],{"id":4131},"benchmarking-and-deployment-workflow","Benchmarking and Deployment Workflow",[22,4134,4135],{},"To evaluate these methods, the implementation establishes a standardized benchmarking suite that measures:",[33,4137,4138,4144,4150],{},[36,4139,4140,4143],{},[39,4141,4142],{},"Disk Size:"," Total storage footprint in GB.",[36,4145,4146,4149],{},[39,4147,4148],{},"Perplexity (PPL):"," Evaluated on the WikiText-2 dataset to ensure compression hasn't degraded model reasoning.",[36,4151,4152,4155],{},[39,4153,4154],{},"Generation Latency & Throughput:"," Measured in seconds and tokens per second (tok\u002Fs) using a consistent prompt.",[22,4157,4158],{},"The workflow emphasizes a \"save-and-test\" cycle, where each compressed model is saved as a reusable artifact. By comparing the FP16 baseline against these quantized variants, developers can make informed trade-offs between model size and inference performance, creating a repeatable pipeline for production-ready model deployment.",{"title":63,"searchDepth":64,"depth":64,"links":4160},[4161,4162],{"id":4099,"depth":64,"text":4100},{"id":4131,"depth":64,"text":4132},[70],{"content_references":4165,"triage":4174},[4166,4168,4172],{"type":77,"title":4107,"url":4167,"context":4071},"https:\u002F\u002Fgithub.com\u002Fvllm-project\u002Fllm-compressor",{"type":4061,"title":4169,"url":4170,"context":4171},"UltraChat 200k","https:\u002F\u002Fhuggingface.co\u002Fdatasets\u002FHuggingFaceH4\u002Fultrachat_200k","cited",{"type":4061,"title":4173,"context":4171},"WikiText-2",{"relevance":85,"novelty":86,"quality":86,"actionability":85,"composite":4073,"reasoning":4175},"Category: AI & LLMs. The article provides a detailed practical guide on compressing LLMs, addressing a core topic of AI engineering with actionable insights on quantization strategies. It includes specific methods and a benchmarking workflow that developers can implement directly in their projects.","\u002Fsummaries\u002Fbeb19294561867ca-benchmarking-llm-compression-fp8-gptq-and-smoothqu-summary","2026-05-17 18:19:09","2026-05-17 18:48:19",{"title":4089,"description":63},{"loc":4176},"beb19294561867ca","https:\u002F\u002Fwww.marktechpost.com\u002F2026\u002F05\u002F17\u002Fa-coding-implementation-to-compress-and-benchmark-instruction-tuned-llms-with-fp8-gptq-and-smoothquant-quantization-using-llmcompressor\u002F","summaries\u002Fbeb19294561867ca-benchmarking-llm-compression-fp8-gptq-and-smoothqu-summary",[102,4185,104,103],"ai-tools","A practical guide to compressing instruction-tuned LLMs using llmcompressor, comparing FP8 dynamic, GPTQ W4A16, and SmoothQuant W8A8 quantization strategies across size, latency, and perplexity.",[],"30L_xT8fTg-Uhmof_yAXXdldKTf6tCZLD87bHm4DkII",{"id":4190,"title":4191,"ai":4192,"body":4197,"categories":4248,"created_at":71,"date_modified":71,"description":63,"extension":72,"faq":71,"featured":73,"kicker_label":71,"meta":4249,"navigation":90,"path":4258,"published_at":4259,"question":71,"scraped_at":4260,"seo":4261,"sitemap":4262,"source_id":4263,"source_name":4264,"source_type":98,"source_url":4265,"stem":4266,"tags":4267,"thumbnail_url":71,"tldr":4269,"tweet":71,"unknown_tags":4270,"__hash__":4271},"summaries\u002Fsummaries\u002Fadd9ec06f3d8b78d-decoder-only-transformers-drive-gpt-scaling-summary.md","Decoder-Only Transformers Drive GPT Scaling",{"provider":7,"model":3993,"input_tokens":4193,"output_tokens":4194,"processing_time_ms":4195,"cost_usd":4196},8457,1685,17671,0.00202705,{"type":14,"value":4198,"toc":4242},[4199,4203,4206,4209,4213,4216,4219,4223,4226,4229,4233,4236,4239],[17,4200,4202],{"id":4201},"self-attention-enables-parallel-long-range-dependencies","Self-Attention Enables Parallel Long-Range Dependencies",[22,4204,4205],{},"Transformers replace RNNs' sequential processing, which suffers vanishing gradients beyond 50-100 words, with self-attention that computes direct relationships between all token pairs simultaneously. For a token like \"it\" in \"The cat sat on the mat and looked at the fishbowl because it was hungry,\" every prior word votes on relevance via query-key dot products scaled by embed_size^{-0.5}, softmax-normalized, and applied to values. This parallelization trains across thousands of GPUs.",[22,4207,4208],{},"GPT's decoder-only design strips away the encoder, applying a causal mask to block future tokens, forcing rich representations solely from predicting the next token. GPT-1 (117M params, 12 layers) showed modest NLP scores, but GPT-2 (1.5B params) gained zero-shot abilities like summarization via prompting. GPT-3 (175B params, 96 layers) added in-context learning from prompt examples without fine-tuning. Deeper layers progress from syntax (early) to reasoning and world models (late). This simplicity scales better than encoder-decoder setups, avoiding cross-attention overhead.",[17,4210,4212],{"id":4211},"moe-and-test-time-compute-scale-beyond-dense-models","MoE and Test-Time Compute Scale Beyond Dense Models",[22,4214,4215],{},"Dense models activate all parameters per token, making trillions unaffordable. Mixture of Experts (MoE) routes each token to 2-8 specialized experts out of 128+, activating ~5% of weights—e.g., DeepSeek-V3 uses 37B active out of 671B total, trained for $5.6M on 2,048 H800 GPUs, matching GPT-4. Multi-Head Latent Attention (MLA) compresses KV cache to cut memory bandwidth. Tradeoffs include expert collapse (router overloads few experts) and full-model memory needs despite sparse activation.",[22,4217,4218],{},"o1 introduced test-time compute: generate internal reasoning chains (30s for hard problems), backtrack dead ends, and refine via RL on verifiable rewards like math solutions. This outperforms larger instant-response models, decoupling ability from size. GPT-5 routes simple queries fast (System 1) and complex ones deeply (System 2). Open models like DeepSeek-R1 replicate this.",[17,4220,4222],{"id":4221},"multimodal-fusion-and-real-world-impacts","Multimodal Fusion and Real-World Impacts",[22,4224,4225],{},"Early fusion embeds vision tokens from Vision Transformers (e.g., MetaCLIP) into the same space as text, enabling unified attention across modalities—no separate captioning. Models like LLaMA 4, Qwen-VL handle charts, 3D spatial reasoning (GLM-4.5V's rotated positional encoding). This yields native cross-modal reasoning, e.g., diagnosing X-rays directly.",[22,4227,4228],{},"Applications: Harvey AI (RAG + fine-tuned GPT-4) cuts legal review 40-60%; GPT-4.1 hits 54.6% on SWE-bench (21.4pp over GPT-4o), ingesting 1M-token codebases; 75% medical accuracy accelerates drug discovery. Open weights (LLaMA, DeepSeek) ensure data sovereignty.",[17,4230,4232],{"id":4231},"implement-mini-gpt-from-scratch-in-pytorch","Implement Mini-GPT from Scratch in PyTorch",[22,4234,4235],{},"Build a character-level GPT: Tokenizer maps unique chars to indices (vocab_size ~50). SelfAttention computes QKV projections, scores = (Q @ K.T) * scale, weights = softmax(scores), out = weights @ V. TransformerBlock adds residual attention + FFN (4x expand, ReLU), LayerNorm post each.",[22,4237,4238],{},"MiniGPT stacks NUM_LAYERS=2 blocks on token + positional embeddings (BLOCK_SIZE=32), outputs logits via linear to vocab_size. Train on dataset.txt: batch BATCH_SIZE=16 sequences, predict next token with CrossEntropyLoss, Adam at 3e-4, 20 EPOCHS. Generation: sample from last-token softmax via multinomial, append up to 100 tokens from context like \"AI is\".",[22,4240,4241],{},"Project structure: data\u002Fdataset.txt, model\u002F{tokenizer,attention,transformer,gpt}.py, train.py saves model.pth, generate.py loads\u002Finfers. Config: EMBED_SIZE=64, NUM_HEADS=4 (implied in attention). This replicates core logic scalably.",{"title":63,"searchDepth":64,"depth":64,"links":4243},[4244,4245,4246,4247],{"id":4201,"depth":64,"text":4202},{"id":4211,"depth":64,"text":4212},{"id":4221,"depth":64,"text":4222},{"id":4231,"depth":64,"text":4232},[70],{"content_references":4250,"triage":4255},[4251],{"type":4252,"title":4253,"author":4254,"context":4171},"paper","Attention Is All You Need","Ashish Vaswani’s team",{"relevance":86,"novelty":87,"quality":86,"actionability":64,"composite":4256,"reasoning":4257},3.4,"Category: AI & LLMs. The article provides a detailed explanation of the architecture behind GPT models, which is relevant for developers looking to integrate AI features. However, while it offers insights into model design, it lacks practical applications or frameworks that the audience can directly implement.","\u002Fsummaries\u002Fadd9ec06f3d8b78d-decoder-only-transformers-drive-gpt-scaling-summary","2026-04-18 19:32:29","2026-04-19 01:22:04",{"title":4191,"description":63},{"loc":4258},"add9ec06f3d8b78d","Python in Plain English","https:\u002F\u002Fpython.plainenglish.io\u002Fthe-architecture-behind-gpt-models-de61992c088a?source=rss----78073def27b8---4","summaries\u002Fadd9ec06f3d8b78d-decoder-only-transformers-drive-gpt-scaling-summary",[102,104,103,4268],"coding","GPT models use decoder-only transformers with causal masking for next-token prediction, enabling emergent zero-shot and in-context learning when scaled massively, now enhanced by MoE for efficiency and reasoning chains.",[],"FYS789V3fqVrHXGVHROYyiskRFH6nT84_QPvh_I63p0",{"id":4273,"title":4274,"ai":4275,"body":4280,"categories":4308,"created_at":71,"date_modified":71,"description":63,"extension":72,"faq":71,"featured":73,"kicker_label":71,"meta":4309,"navigation":90,"path":4310,"published_at":4311,"question":71,"scraped_at":71,"seo":4312,"sitemap":4313,"source_id":4314,"source_name":4315,"source_type":98,"source_url":4316,"stem":4317,"tags":4318,"thumbnail_url":71,"tldr":4320,"tweet":71,"unknown_tags":4321,"__hash__":4322},"summaries\u002Fsummaries\u002Fkarpathy-s-pure-python-ai-from-scratch-summary.md","Karpathy's Pure Python AI From Scratch",{"provider":7,"model":3993,"input_tokens":4276,"output_tokens":4277,"processing_time_ms":4278,"cost_usd":4279},4820,1448,12742,0.0012176,{"type":14,"value":4281,"toc":4303},[4282,4286,4289,4293,4296,4300],[17,4283,4285],{"id":4284},"minimal-code-for-core-ai-models","Minimal Code for Core AI Models",[22,4287,4288],{},"Train and run a full GPT in just 200 lines of dependency-free Python, covering tokenization, model architecture, training loop, and sampling—proving LLMs are accessible without frameworks. Similarly, implement deep RL to master Atari Pong from raw pixels using policy gradients, weighing pros (sample efficiency) against cons (high variance). Character-level RNNs generate poetry, LaTeX, and code; analyze gradients to spot future directions like better optimization. Fool ImageNet classifiers with tiny perturbations, showing even linear models (not just convnets) break easily, challenging robustness claims.",[17,4290,4292],{"id":4291},"historical-benchmarks-and-progress","Historical Benchmarks and Progress",[22,4294,4295],{},"Revisit LeCun's 1989 backprop-trained neural net—the first real-world end-to-end DL app—then upgrade it with 33 years of advances (e.g., modern optimizers, architectures) to quantify progress; preview how 2022 DL will age by 2055. Humans hit 6.7% error@5 on ImageNet vs. top convnets, but manual CIFAR-10 labeling reveals human baselines aren't unbeatable. Early CV state (2012) lags far behind human vision, tempering AI hype.",[17,4297,4299],{"id":4298},"practical-training-and-experiments","Practical Training and Experiments",[22,4301,4302],{},"Follow a battle-tested recipe for neural nets: batch size 0.2-10% of GPU memory, weak regularization first, then strengthen; cosine anneal LR over 1M steps. Scrape 2M selfies to train convnets classifying good\u002Fbad #selfies, visualizing what networks 'think'. Track productivity via window\u002Fkeystroke logging on Ubuntu\u002FOSX, generating HTML viz for insights. Biohacking basics: tweak energy metabolism via experiments. PhD survival: navigate academia with tips on focus, advising.",{"title":63,"searchDepth":64,"depth":64,"links":4304},[4305,4306,4307],{"id":4284,"depth":64,"text":4285},{"id":4291,"depth":64,"text":4292},{"id":4298,"depth":64,"text":4299},[70],{},"\u002Fsummaries\u002Fkarpathy-s-pure-python-ai-from-scratch-summary","2026-04-08 21:21:19",{"title":4274,"description":63},{"loc":4310},"2ff230eac68aac35","Andrej Karpathy Blog","https:\u002F\u002Funknown","summaries\u002Fkarpathy-s-pure-python-ai-from-scratch-summary",[104,102,4319,103],"deep-learning","Andrej Karpathy distills neural nets, LLMs, RL, and Bitcoin into 200-500 line pure Python scripts—no deps needed—to teach core mechanics hands-on.",[],"SiA702o4JPFym6Ze2kqREo-Ap1fC_lo4d1oWU5fAQzM"]