PyTorch梯度下降反向傳播
更新時間：2022年03月09日 17:12:49 作者：心?升明月
這篇文章主要介紹了PyTorch反向傳播，反向傳播的目的是計算成本函數C對網絡中任意w或b的偏導數，下文更多詳細內容敘述需要的小伙伴可以參考一下
前言：
反向傳播的目的是計算成本函數C對網絡中任意w或b的偏導數。一旦我們有了這些偏導數，我們將通過一些常數 α的乘積和該數量相對于成本函數的偏導數來更新網絡中的權重和偏差。這是流行的梯度下降算法。而偏導數給出了最大上升的方向。因此，關于反向傳播算法，我們繼續(xù)查看下文。
我們向相反的方向邁出了一小步——最大下降的方向，也就是將我們帶到成本函數的局部最小值的方向
如題：
意思是利用這個二次模型來預測數據，減小損失函數(MSE)的值。
代碼如下：
import torch
import matplotlib.pyplot as plt
import os
os.environ["KMP_DUPLICATE_LIB_OK"] ?= ?"TRUE"
# 數據集
x_data = [1.0,2.0,3.0]
y_data = [2.0,4.0,6.0]
# 權重參數初始值均為1
w = torch.tensor([1.0,1.0,1.0])
w.requires_grad = True ? ?# 需要計算梯度
# 前向傳播
def forward(x):
? ? return w[0]*(x**2)+w[1]*x+w[2]
# 計算損失
def loss(x,y):
? ? y_pred = forward(x)
? ? return (y_pred-y) ** 2
# 訓練模塊
print('predict (before tranining) ',4, forward(4).item())
epoch_list = []
w_list = []
loss_list = []
for epoch in range(1000):
? ? for x,y in zip(x_data,y_data):
? ? ? ? l = loss(x,y)
? ? ? ? l.backward()?? ??? ?# 后向傳播
? ? ? ? print('\tgrad: ',x,y,w.grad.data)
? ? ? ? w.data = w.data - 0.01 * w.grad.data?? ??? ?# 梯度下降
? ? ? ??
? ? ? ? w.grad.data.zero_()?? ?# 梯度清零操作
? ? ? ??
? ? print('progress: ',epoch,l.item())
? ? epoch_list.append(epoch)
? ? w_list.append(w.data)
? ? loss_list.append(l.item())
print('predict (after tranining) ',4, forward(4).item())
# 繪圖
plt.plot(epoch_list,loss_list,'b')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.grid()
plt.show()結果如下：
predict (before tranining) ?4 21.0 ?? ?grad: ?1.0 2.0 tensor([2., 2., 2.]) ?? ?grad: ?2.0 4.0 tensor([22.8800, 11.4400, ?5.7200]) ?? ?grad: ?3.0 6.0 tensor([77.0472, 25.6824, ?8.5608]) progress: ?0 18.321826934814453 ?? ?grad: ?1.0 2.0 tensor([-1.1466, -1.1466, -1.1466]) ?? ?grad: ?2.0 4.0 tensor([-15.5367, ?-7.7683, ?-3.8842]) ?? ?grad: ?3.0 6.0 tensor([-30.4322, -10.1441, ?-3.3814]) progress: ?1 2.858394145965576 ?? ?grad: ?1.0 2.0 tensor([0.3451, 0.3451, 0.3451]) ?? ?grad: ?2.0 4.0 tensor([2.4273, 1.2137, 0.6068]) ?? ?grad: ?3.0 6.0 tensor([19.4499, ?6.4833, ?2.1611]) progress: ?2 1.1675907373428345 ?? ?grad: ?1.0 2.0 tensor([-0.3224, -0.3224, -0.3224]) ?? ?grad: ?2.0 4.0 tensor([-5.8458, -2.9229, -1.4614]) ?? ?grad: ?3.0 6.0 tensor([-3.8829, -1.2943, -0.4314]) progress: ?3 0.04653334245085716 ?? ?grad: ?1.0 2.0 tensor([0.0137, 0.0137, 0.0137]) ?? ?grad: ?2.0 4.0 tensor([-1.9141, -0.9570, -0.4785]) ?? ?grad: ?3.0 6.0 tensor([6.8557, 2.2852, 0.7617]) progress: ?4 0.14506366848945618 ?? ?grad: ?1.0 2.0 tensor([-0.1182, -0.1182, -0.1182]) ?? ?grad: ?2.0 4.0 tensor([-3.6644, -1.8322, -0.9161]) ?? ?grad: ?3.0 6.0 tensor([1.7455, 0.5818, 0.1939]) progress: ?5 0.009403289295732975 ?? ?grad: ?1.0 2.0 tensor([-0.0333, -0.0333, -0.0333]) ?? ?grad: ?2.0 4.0 tensor([-2.7739, -1.3869, -0.6935]) ?? ?grad: ?3.0 6.0 tensor([4.0140, 1.3380, 0.4460]) progress: ?6 0.04972923547029495 ?? ?grad: ?1.0 2.0 tensor([-0.0501, -0.0501, -0.0501]) ?? ?grad: ?2.0 4.0 tensor([-3.1150, -1.5575, -0.7788]) ?? ?grad: ?3.0 6.0 tensor([2.8534, 0.9511, 0.3170]) progress: ?7 0.025129113346338272 ?? ?grad: ?1.0 2.0 tensor([-0.0205, -0.0205, -0.0205]) ?? ?grad: ?2.0 4.0 tensor([-2.8858, -1.4429, -0.7215]) ?? ?grad: ?3.0 6.0 tensor([3.2924, 1.0975, 0.3658]) progress: ?8 0.03345605731010437 ?? ?grad: ?1.0 2.0 tensor([-0.0134, -0.0134, -0.0134]) ?? ?grad: ?2.0 4.0 tensor([-2.9247, -1.4623, -0.7312]) ?? ?grad: ?3.0 6.0 tensor([2.9909, 0.9970, 0.3323]) progress: ?9 0.027609655633568764 ?? ?grad: ?1.0 2.0 tensor([0.0033, 0.0033, 0.0033]) ?? ?grad: ?2.0 4.0 tensor([-2.8414, -1.4207, -0.7103]) ?? ?grad: ?3.0 6.0 tensor([3.0377, 1.0126, 0.3375]) progress: ?10 0.02848036028444767 ?? ?grad: ?1.0 2.0 tensor([0.0148, 0.0148, 0.0148]) ?? ?grad: ?2.0 4.0 tensor([-2.8174, -1.4087, -0.7043]) ?? ?grad: ?3.0 6.0 tensor([2.9260, 0.9753, 0.3251]) progress: ?11 0.02642466314136982 ?? ?grad: ?1.0 2.0 tensor([0.0280, 0.0280, 0.0280]) ?? ?grad: ?2.0 4.0 tensor([-2.7682, -1.3841, -0.6920]) ?? ?grad: ?3.0 6.0 tensor([2.8915, 0.9638, 0.3213]) progress: ?12 0.025804826989769936 ?? ?grad: ?1.0 2.0 tensor([0.0397, 0.0397, 0.0397]) ?? ?grad: ?2.0 4.0 tensor([-2.7330, -1.3665, -0.6832]) ?? ?grad: ?3.0 6.0 tensor([2.8243, 0.9414, 0.3138]) progress: ?13 0.02462013065814972 ?? ?grad: ?1.0 2.0 tensor([0.0514, 0.0514, 0.0514]) ?? ?grad: ?2.0 4.0 tensor([-2.6934, -1.3467, -0.6734]) ?? ?grad: ?3.0 6.0 tensor([2.7756, 0.9252, 0.3084]) progress: ?14 0.023777369409799576 ?? ?grad: ?1.0 2.0 tensor([0.0624, 0.0624, 0.0624]) ?? ?grad: ?2.0 4.0 tensor([-2.6580, -1.3290, -0.6645]) ?? ?grad: ?3.0 6.0 tensor([2.7213, 0.9071, 0.3024]) progress: ?15 0.0228563379496336 ?? ?grad: ?1.0 2.0 tensor([0.0731, 0.0731, 0.0731]) ?? ?grad: ?2.0 4.0 tensor([-2.6227, -1.3113, -0.6557]) ?? ?grad: ?3.0 6.0 tensor([2.6725, 0.8908, 0.2969]) progress: ?16 0.022044027224183083 ?? ?grad: ?1.0 2.0 tensor([0.0833, 0.0833, 0.0833]) ?? ?grad: ?2.0 4.0 tensor([-2.5893, -1.2946, -0.6473]) ?? ?grad: ?3.0 6.0 tensor([2.6240, 0.8747, 0.2916]) progress: ?17 0.02125072106719017 ?? ?grad: ?1.0 2.0 tensor([0.0931, 0.0931, 0.0931]) ?? ?grad: ?2.0 4.0 tensor([-2.5568, -1.2784, -0.6392]) ?? ?grad: ?3.0 6.0 tensor([2.5780, 0.8593, 0.2864]) progress: ?18 0.020513182505965233 ?? ?grad: ?1.0 2.0 tensor([0.1025, 0.1025, 0.1025]) ?? ?grad: ?2.0 4.0 tensor([-2.5258, -1.2629, -0.6314]) ?? ?grad: ?3.0 6.0 tensor([2.5335, 0.8445, 0.2815]) progress: ?19 0.019810274243354797 ?? ?grad: ?1.0 2.0 tensor([0.1116, 0.1116, 0.1116]) ?? ?grad: ?2.0 4.0 tensor([-2.4958, -1.2479, -0.6239]) ?? ?grad: ?3.0 6.0 tensor([2.4908, 0.8303, 0.2768]) progress: ?20 0.019148115068674088 ?? ?grad: ?1.0 2.0 tensor([0.1203, 0.1203, 0.1203]) ?? ?grad: ?2.0 4.0 tensor([-2.4669, -1.2335, -0.6167]) ?? ?grad: ?3.0 6.0 tensor([2.4496, 0.8165, 0.2722]) progress: ?21 0.018520694226026535 ?? ?grad: ?1.0 2.0 tensor([0.1286, 0.1286, 0.1286]) ?? ?grad: ?2.0 4.0 tensor([-2.4392, -1.2196, -0.6098]) ?? ?grad: ?3.0 6.0 tensor([2.4101, 0.8034, 0.2678]) progress: ?22 0.017927465960383415 ?? ?grad: ?1.0 2.0 tensor([0.1367, 0.1367, 0.1367]) ?? ?grad: ?2.0 4.0 tensor([-2.4124, -1.2062, -0.6031]) ?? ?grad: ?3.0 6.0 tensor([2.3720, 0.7907, 0.2636]) progress: ?23 0.01736525259912014 ?? ?grad: ?1.0 2.0 tensor([0.1444, 0.1444, 0.1444]) ?? ?grad: ?2.0 4.0 tensor([-2.3867, -1.1933, -0.5967]) ?? ?grad: ?3.0 6.0 tensor([2.3354, 0.7785, 0.2595]) progress: ?24 0.016833148896694183 ?? ?grad: ?1.0 2.0 tensor([0.1518, 0.1518, 0.1518]) ?? ?grad: ?2.0 4.0 tensor([-2.3619, -1.1810, -0.5905]) ?? ?grad: ?3.0 6.0 tensor([2.3001, 0.7667, 0.2556]) progress: ?25 0.01632905937731266 ?? ?grad: ?1.0 2.0 tensor([0.1589, 0.1589, 0.1589]) ?? ?grad: ?2.0 4.0 tensor([-2.3380, -1.1690, -0.5845]) ?? ?grad: ?3.0 6.0 tensor([2.2662, 0.7554, 0.2518]) progress: ?26 0.01585075818002224 ?? ?grad: ?1.0 2.0 tensor([0.1657, 0.1657, 0.1657]) ?? ?grad: ?2.0 4.0 tensor([-2.3151, -1.1575, -0.5788]) ?? ?grad: ?3.0 6.0 tensor([2.2336, 0.7445, 0.2482]) progress: ?27 0.015397666022181511 ?? ?grad: ?1.0 2.0 tensor([0.1723, 0.1723, 0.1723]) ?? ?grad: ?2.0 4.0 tensor([-2.2929, -1.1465, -0.5732]) ?? ?grad: ?3.0 6.0 tensor([2.2022, 0.7341, 0.2447]) progress: ?28 0.014967591501772404 ?? ?grad: ?1.0 2.0 tensor([0.1786, 0.1786, 0.1786]) ?? ?grad: ?2.0 4.0 tensor([-2.2716, -1.1358, -0.5679]) ?? ?grad: ?3.0 6.0 tensor([2.1719, 0.7240, 0.2413]) progress: ?29 0.014559715054929256 ?? ?grad: ?1.0 2.0 tensor([0.1846, 0.1846, 0.1846]) ?? ?grad: ?2.0 4.0 tensor([-2.2511, -1.1255, -0.5628]) ?? ?grad: ?3.0 6.0 tensor([2.1429, 0.7143, 0.2381]) progress: ?30 0.014172340743243694 ?? ?grad: ?1.0 2.0 tensor([0.1904, 0.1904, 0.1904]) ?? ?grad: ?2.0 4.0 tensor([-2.2313, -1.1157, -0.5578]) ?? ?grad: ?3.0 6.0 tensor([2.1149, 0.7050, 0.2350]) progress: ?31 0.013804304413497448 ?? ?grad: ?1.0 2.0 tensor([0.1960, 0.1960, 0.1960]) ?? ?grad: ?2.0 4.0 tensor([-2.2123, -1.1061, -0.5531]) ?? ?grad: ?3.0 6.0 tensor([2.0879, 0.6960, 0.2320]) progress: ?32 0.013455045409500599 ?? ?grad: ?1.0 2.0 tensor([0.2014, 0.2014, 0.2014]) ?? ?grad: ?2.0 4.0 tensor([-2.1939, -1.0970, -0.5485]) ?? ?grad: ?3.0 6.0 tensor([2.0620, 0.6873, 0.2291]) progress: ?33 0.013122711330652237 ?? ?grad: ?1.0 2.0 tensor([0.2065, 0.2065, 0.2065]) ?? ?grad: ?2.0 4.0 tensor([-2.1763, -1.0881, -0.5441]) ?? ?grad: ?3.0 6.0 tensor([2.0370, 0.6790, 0.2263]) progress: ?34 0.01280694268643856 ?? ?grad: ?1.0 2.0 tensor([0.2114, 0.2114, 0.2114]) ?? ?grad: ?2.0 4.0 tensor([-2.1592, -1.0796, -0.5398]) ?? ?grad: ?3.0 6.0 tensor([2.0130, 0.6710, 0.2237]) progress: ?35 0.012506747618317604 ?? ?grad: ?1.0 2.0 tensor([0.2162, 0.2162, 0.2162]) ?? ?grad: ?2.0 4.0 tensor([-2.1428, -1.0714, -0.5357]) ?? ?grad: ?3.0 6.0 tensor([1.9899, 0.6633, 0.2211]) progress: ?36 0.012220758944749832 ?? ?grad: ?1.0 2.0 tensor([0.2207, 0.2207, 0.2207]) ?? ?grad: ?2.0 4.0 tensor([-2.1270, -1.0635, -0.5317]) ?? ?grad: ?3.0 6.0 tensor([1.9676, 0.6559, 0.2186]) progress: ?37 0.01194891706109047 ?? ?grad: ?1.0 2.0 tensor([0.2251, 0.2251, 0.2251]) ?? ?grad: ?2.0 4.0 tensor([-2.1118, -1.0559, -0.5279]) ?? ?grad: ?3.0 6.0 tensor([1.9462, 0.6487, 0.2162]) progress: ?38 0.011689926497638226 ?? ?grad: ?1.0 2.0 tensor([0.2292, 0.2292, 0.2292]) ?? ?grad: ?2.0 4.0 tensor([-2.0971, -1.0485, -0.5243]) ?? ?grad: ?3.0 6.0 tensor([1.9255, 0.6418, 0.2139]) progress: ?39 0.01144315768033266 ?? ?grad: ?1.0 2.0 tensor([0.2333, 0.2333, 0.2333]) ?? ?grad: ?2.0 4.0 tensor([-2.0829, -1.0414, -0.5207]) ?? ?grad: ?3.0 6.0 tensor([1.9057, 0.6352, 0.2117]) progress: ?40 0.011208509095013142 ?? ?grad: ?1.0 2.0 tensor([0.2371, 0.2371, 0.2371]) ?? ?grad: ?2.0 4.0 tensor([-2.0693, -1.0346, -0.5173]) ?? ?grad: ?3.0 6.0 tensor([1.8865, 0.6288, 0.2096]) progress: ?41 0.0109840864315629 ?? ?grad: ?1.0 2.0 tensor([0.2408, 0.2408, 0.2408]) ?? ?grad: ?2.0 4.0 tensor([-2.0561, -1.0280, -0.5140]) ?? ?grad: ?3.0 6.0 tensor([1.8681, 0.6227, 0.2076]) progress: ?42 0.010770938359200954 ?? ?grad: ?1.0 2.0 tensor([0.2444, 0.2444, 0.2444]) ?? ?grad: ?2.0 4.0 tensor([-2.0434, -1.0217, -0.5108]) ?? ?grad: ?3.0 6.0 tensor([1.8503, 0.6168, 0.2056]) progress: ?43 0.010566935874521732 ?? ?grad: ?1.0 2.0 tensor([0.2478, 0.2478, 0.2478]) ?? ?grad: ?2.0 4.0 tensor([-2.0312, -1.0156, -0.5078]) ?? ?grad: ?3.0 6.0 tensor([1.8332, 0.6111, 0.2037]) progress: ?44 0.010372749529778957 ?? ?grad: ?1.0 2.0 tensor([0.2510, 0.2510, 0.2510]) ?? ?grad: ?2.0 4.0 tensor([-2.0194, -1.0097, -0.5048]) ?? ?grad: ?3.0 6.0 tensor([1.8168, 0.6056, 0.2019]) progress: ?45 0.010187389329075813 ?? ?grad: ?1.0 2.0 tensor([0.2542, 0.2542, 0.2542]) ?? ?grad: ?2.0 4.0 tensor([-2.0080, -1.0040, -0.5020]) ?? ?grad: ?3.0 6.0 tensor([1.8009, 0.6003, 0.2001]) progress: ?46 0.010010283440351486 ?? ?grad: ?1.0 2.0 tensor([0.2572, 0.2572, 0.2572]) ?? ?grad: ?2.0 4.0 tensor([-1.9970, -0.9985, -0.4992]) ?? ?grad: ?3.0 6.0 tensor([1.7856, 0.5952, 0.1984]) progress: ?47 0.00984097272157669 ?? ?grad: ?1.0 2.0 tensor([0.2600, 0.2600, 0.2600]) ?? ?grad: ?2.0 4.0 tensor([-1.9864, -0.9932, -0.4966]) ?? ?grad: ?3.0 6.0 tensor([1.7709, 0.5903, 0.1968]) progress: ?48 0.009679674170911312 ?? ?grad: ?1.0 2.0 tensor([0.2628, 0.2628, 0.2628]) ?? ?grad: ?2.0 4.0 tensor([-1.9762, -0.9881, -0.4940]) ?? ?grad: ?3.0 6.0 tensor([1.7568, 0.5856, 0.1952]) progress: ?49 0.009525291621685028 ?? ?grad: ?1.0 2.0 tensor([0.2655, 0.2655, 0.2655]) ?? ?grad: ?2.0 4.0 tensor([-1.9663, -0.9832, -0.4916]) ?? ?grad: ?3.0 6.0 tensor([1.7431, 0.5810, 0.1937]) progress: ?50 0.00937769003212452 ?? ?grad: ?1.0 2.0 tensor([0.2680, 0.2680, 0.2680]) ?? ?grad: ?2.0 4.0 tensor([-1.9568, -0.9784, -0.4892]) ?? ?grad: ?3.0 6.0 tensor([1.7299, 0.5766, 0.1922]) progress: ?51 0.009236648678779602 ?? ?grad: ?1.0 2.0 tensor([0.2704, 0.2704, 0.2704]) ?? ?grad: ?2.0 4.0 tensor([-1.9476, -0.9738, -0.4869]) ?? ?grad: ?3.0 6.0 tensor([1.7172, 0.5724, 0.1908]) progress: ?52 0.00910158734768629 ?? ?grad: ?1.0 2.0 tensor([0.2728, 0.2728, 0.2728]) ?? ?grad: ?2.0 4.0 tensor([-1.9387, -0.9694, -0.4847]) ?? ?grad: ?3.0 6.0 tensor([1.7050, 0.5683, 0.1894]) progress: ?53 0.00897257961332798 ?? ?grad: ?1.0 2.0 tensor([0.2750, 0.2750, 0.2750]) ?? ?grad: ?2.0 4.0 tensor([-1.9301, -0.9651, -0.4825]) ?? ?grad: ?3.0 6.0 tensor([1.6932, 0.5644, 0.1881]) progress: ?54 0.008848887868225574 ?? ?grad: ?1.0 2.0 tensor([0.2771, 0.2771, 0.2771]) ?? ?grad: ?2.0 4.0 tensor([-1.9219, -0.9609, -0.4805]) ?? ?grad: ?3.0 6.0 tensor([1.6819, 0.5606, 0.1869]) progress: ?55 0.008730598725378513 ?? ?grad: ?1.0 2.0 tensor([0.2792, 0.2792, 0.2792]) ?? ?grad: ?2.0 4.0 tensor([-1.9139, -0.9569, -0.4785]) ?? ?grad: ?3.0 6.0 tensor([1.6709, 0.5570, 0.1857]) progress: ?56 0.00861735362559557 ?? ?grad: ?1.0 2.0 tensor([0.2811, 0.2811, 0.2811]) ?? ?grad: ?2.0 4.0 tensor([-1.9062, -0.9531, -0.4765]) ?? ?grad: ?3.0 6.0 tensor([1.6604, 0.5535, 0.1845]) progress: ?57 0.008508718572556973 ?? ?grad: ?1.0 2.0 tensor([0.2830, 0.2830, 0.2830]) ?? ?grad: ?2.0 4.0 tensor([-1.8987, -0.9493, -0.4747]) ?? ?grad: ?3.0 6.0 tensor([1.6502, 0.5501, 0.1834]) progress: ?58 0.008404706604778767 ?? ?grad: ?1.0 2.0 tensor([0.2848, 0.2848, 0.2848]) ?? ?grad: ?2.0 4.0 tensor([-1.8915, -0.9457, -0.4729]) ?? ?grad: ?3.0 6.0 tensor([1.6404, 0.5468, 0.1823]) progress: ?59 0.008305158466100693 ?? ?grad: ?1.0 2.0 tensor([0.2865, 0.2865, 0.2865]) ?? ?grad: ?2.0 4.0 tensor([-1.8845, -0.9423, -0.4711]) ?? ?grad: ?3.0 6.0 tensor([1.6309, 0.5436, 0.1812]) progress: ?60 0.00820931326597929 ?? ?grad: ?1.0 2.0 tensor([0.2882, 0.2882, 0.2882]) ?? ?grad: ?2.0 4.0 tensor([-1.8778, -0.9389, -0.4694]) ?? ?grad: ?3.0 6.0 tensor([1.6218, 0.5406, 0.1802]) progress: ?61 0.008117804303765297 ?? ?grad: ?1.0 2.0 tensor([0.2898, 0.2898, 0.2898]) ?? ?grad: ?2.0 4.0 tensor([-1.8713, -0.9356, -0.4678]) ?? ?grad: ?3.0 6.0 tensor([1.6130, 0.5377, 0.1792]) progress: ?62 0.008029798977077007 ?? ?grad: ?1.0 2.0 tensor([0.2913, 0.2913, 0.2913]) ?? ?grad: ?2.0 4.0 tensor([-1.8650, -0.9325, -0.4662]) ?? ?grad: ?3.0 6.0 tensor([1.6045, 0.5348, 0.1783]) progress: ?63 0.007945418357849121 ?? ?grad: ?1.0 2.0 tensor([0.2927, 0.2927, 0.2927]) ?? ?grad: ?2.0 4.0 tensor([-1.8589, -0.9294, -0.4647]) ?? ?grad: ?3.0 6.0 tensor([1.5962, 0.5321, 0.1774]) progress: ?64 0.007864190265536308 ?? ?grad: ?1.0 2.0 tensor([0.2941, 0.2941, 0.2941]) ?? ?grad: ?2.0 4.0 tensor([-1.8530, -0.9265, -0.4632]) ?? ?grad: ?3.0 6.0 tensor([1.5884, 0.5295, 0.1765]) progress: ?65 0.007786744274199009 ?? ?grad: ?1.0 2.0 tensor([0.2954, 0.2954, 0.2954]) ?? ?grad: ?2.0 4.0 tensor([-1.8473, -0.9236, -0.4618]) ?? ?grad: ?3.0 6.0 tensor([1.5807, 0.5269, 0.1756]) progress: ?66 0.007711691781878471 ?? ?grad: ?1.0 2.0 tensor([0.2967, 0.2967, 0.2967]) ?? ?grad: ?2.0 4.0 tensor([-1.8417, -0.9209, -0.4604]) ?? ?grad: ?3.0 6.0 tensor([1.5733, 0.5244, 0.1748]) progress: ?67 0.007640169933438301 ?? ?grad: ?1.0 2.0 tensor([0.2979, 0.2979, 0.2979]) ?? ?grad: ?2.0 4.0 tensor([-1.8364, -0.9182, -0.4591]) ?? ?grad: ?3.0 6.0 tensor([1.5662, 0.5221, 0.1740]) progress: ?68 0.007570972666144371 ?? ?grad: ?1.0 2.0 tensor([0.2991, 0.2991, 0.2991]) ?? ?grad: ?2.0 4.0 tensor([-1.8312, -0.9156, -0.4578]) ?? ?grad: ?3.0 6.0 tensor([1.5593, 0.5198, 0.1733]) progress: ?69 0.007504733745008707 ?? ?grad: ?1.0 2.0 tensor([0.3002, 0.3002, 0.3002]) ?? ?grad: ?2.0 4.0 tensor([-1.8262, -0.9131, -0.4566]) ?? ?grad: ?3.0 6.0 tensor([1.5527, 0.5176, 0.1725]) progress: ?70 0.007440924644470215 ?? ?grad: ?1.0 2.0 tensor([0.3012, 0.3012, 0.3012]) ?? ?grad: ?2.0 4.0 tensor([-1.8214, -0.9107, -0.4553]) ?? ?grad: ?3.0 6.0 tensor([1.5463, 0.5154, 0.1718]) progress: ?71 0.007379599846899509 ?? ?grad: ?1.0 2.0 tensor([0.3022, 0.3022, 0.3022]) ?? ?grad: ?2.0 4.0 tensor([-1.8167, -0.9083, -0.4542]) ?? ?grad: ?3.0 6.0 tensor([1.5401, 0.5134, 0.1711]) progress: ?72 0.007320486940443516 ?? ?grad: ?1.0 2.0 tensor([0.3032, 0.3032, 0.3032]) ?? ?grad: ?2.0 4.0 tensor([-1.8121, -0.9060, -0.4530]) ?? ?grad: ?3.0 6.0 tensor([1.5341, 0.5114, 0.1705]) progress: ?73 0.007263725157827139 ?? ?grad: ?1.0 2.0 tensor([0.3041, 0.3041, 0.3041]) ?? ?grad: ?2.0 4.0 tensor([-1.8077, -0.9038, -0.4519]) ?? ?grad: ?3.0 6.0 tensor([1.5283, 0.5094, 0.1698]) progress: ?74 0.007209045812487602 ?? ?grad: ?1.0 2.0 tensor([0.3050, 0.3050, 0.3050]) ?? ?grad: ?2.0 4.0 tensor([-1.8034, -0.9017, -0.4508]) ?? ?grad: ?3.0 6.0 tensor([1.5227, 0.5076, 0.1692]) progress: ?75 0.007156429346650839 ?? ?grad: ?1.0 2.0 tensor([0.3058, 0.3058, 0.3058]) ?? ?grad: ?2.0 4.0 tensor([-1.7992, -0.8996, -0.4498]) ?? ?grad: ?3.0 6.0 tensor([1.5173, 0.5058, 0.1686]) progress: ?76 0.007105532102286816 ?? ?grad: ?1.0 2.0 tensor([0.3066, 0.3066, 0.3066]) ?? ?grad: ?2.0 4.0 tensor([-1.7952, -0.8976, -0.4488]) ?? ?grad: ?3.0 6.0 tensor([1.5121, 0.5040, 0.1680]) progress: ?77 0.00705681974068284 ?? ?grad: ?1.0 2.0 tensor([0.3073, 0.3073, 0.3073]) ?? ?grad: ?2.0 4.0 tensor([-1.7913, -0.8956, -0.4478]) ?? ?grad: ?3.0 6.0 tensor([1.5070, 0.5023, 0.1674]) progress: ?78 0.007009552326053381 ?? ?grad: ?1.0 2.0 tensor([0.3081, 0.3081, 0.3081]) ?? ?grad: ?2.0 4.0 tensor([-1.7875, -0.8937, -0.4469]) ?? ?grad: ?3.0 6.0 tensor([1.5021, 0.5007, 0.1669]) progress: ?79 0.006964194122701883 ?? ?grad: ?1.0 2.0 tensor([0.3087, 0.3087, 0.3087]) ?? ?grad: ?2.0 4.0 tensor([-1.7838, -0.8919, -0.4459]) ?? ?grad: ?3.0 6.0 tensor([1.4974, 0.4991, 0.1664]) progress: ?80 0.006920332089066505 ?? ?grad: ?1.0 2.0 tensor([0.3094, 0.3094, 0.3094]) ?? ?grad: ?2.0 4.0 tensor([-1.7802, -0.8901, -0.4450]) ?? ?grad: ?3.0 6.0 tensor([1.4928, 0.4976, 0.1659]) progress: ?81 0.006878111511468887 ?? ?grad: ?1.0 2.0 tensor([0.3100, 0.3100, 0.3100]) ?? ?grad: ?2.0 4.0 tensor([-1.7767, -0.8883, -0.4442]) ?? ?grad: ?3.0 6.0 tensor([1.4884, 0.4961, 0.1654]) progress: ?82 0.006837360095232725 ?? ?grad: ?1.0 2.0 tensor([0.3106, 0.3106, 0.3106]) ?? ?grad: ?2.0 4.0 tensor([-1.7733, -0.8867, -0.4433]) ?? ?grad: ?3.0 6.0 tensor([1.4841, 0.4947, 0.1649]) progress: ?83 0.006797831039875746 ?? ?grad: ?1.0 2.0 tensor([0.3111, 0.3111, 0.3111]) ?? ?grad: ?2.0 4.0 tensor([-1.7700, -0.8850, -0.4425]) ?? ?grad: ?3.0 6.0 tensor([1.4800, 0.4933, 0.1644]) progress: ?84 0.006760062649846077 ?? ?grad: ?1.0 2.0 tensor([0.3117, 0.3117, 0.3117]) ?? ?grad: ?2.0 4.0 tensor([-1.7668, -0.8834, -0.4417]) ?? ?grad: ?3.0 6.0 tensor([1.4759, 0.4920, 0.1640]) progress: ?85 0.006723103579133749 ?? ?grad: ?1.0 2.0 tensor([0.3122, 0.3122, 0.3122]) ?? ?grad: ?2.0 4.0 tensor([-1.7637, -0.8818, -0.4409]) ?? ?grad: ?3.0 6.0 tensor([1.4720, 0.4907, 0.1636]) progress: ?86 0.00668772729113698 ?? ?grad: ?1.0 2.0 tensor([0.3127, 0.3127, 0.3127]) ?? ?grad: ?2.0 4.0 tensor([-1.7607, -0.8803, -0.4402]) ?? ?grad: ?3.0 6.0 tensor([1.4682, 0.4894, 0.1631]) progress: ?87 0.006653300020843744 ?? ?grad: ?1.0 2.0 tensor([0.3131, 0.3131, 0.3131]) ?? ?grad: ?2.0 4.0 tensor([-1.7577, -0.8789, -0.4394]) ?? ?grad: ?3.0 6.0 tensor([1.4646, 0.4882, 0.1627]) progress: ?88 0.0066203586757183075 ?? ?grad: ?1.0 2.0 tensor([0.3135, 0.3135, 0.3135]) ?? ?grad: ?2.0 4.0 tensor([-1.7548, -0.8774, -0.4387]) ?? ?grad: ?3.0 6.0 tensor([1.4610, 0.4870, 0.1623]) progress: ?89 0.0065881176851689816 ?? ?grad: ?1.0 2.0 tensor([0.3139, 0.3139, 0.3139]) ?? ?grad: ?2.0 4.0 tensor([-1.7520, -0.8760, -0.4380]) ?? ?grad: ?3.0 6.0 tensor([1.4576, 0.4859, 0.1620]) progress: ?90 0.0065572685562074184 ?? ?grad: ?1.0 2.0 tensor([0.3143, 0.3143, 0.3143]) ?? ?grad: ?2.0 4.0 tensor([-1.7493, -0.8747, -0.4373]) ?? ?grad: ?3.0 6.0 tensor([1.4542, 0.4847, 0.1616]) progress: ?91 0.0065271081402897835 ?? ?grad: ?1.0 2.0 tensor([0.3147, 0.3147, 0.3147]) ?? ?grad: ?2.0 4.0 tensor([-1.7466, -0.8733, -0.4367]) ?? ?grad: ?3.0 6.0 tensor([1.4510, 0.4837, 0.1612]) progress: ?92 0.00649801641702652 ?? ?grad: ?1.0 2.0 tensor([0.3150, 0.3150, 0.3150]) ?? ?grad: ?2.0 4.0 tensor([-1.7441, -0.8720, -0.4360]) ?? ?grad: ?3.0 6.0 tensor([1.4478, 0.4826, 0.1609]) progress: ?93 0.0064699104987084866 ?? ?grad: ?1.0 2.0 tensor([0.3153, 0.3153, 0.3153]) ?? ?grad: ?2.0 4.0 tensor([-1.7415, -0.8708, -0.4354]) ?? ?grad: ?3.0 6.0 tensor([1.4448, 0.4816, 0.1605]) progress: ?94 0.006442630663514137 ?? ?grad: ?1.0 2.0 tensor([0.3156, 0.3156, 0.3156]) ?? ?grad: ?2.0 4.0 tensor([-1.7391, -0.8695, -0.4348]) ?? ?grad: ?3.0 6.0 tensor([1.4418, 0.4806, 0.1602]) progress: ?95 0.006416172254830599 ?? ?grad: ?1.0 2.0 tensor([0.3159, 0.3159, 0.3159]) ?? ?grad: ?2.0 4.0 tensor([-1.7366, -0.8683, -0.4342]) ?? ?grad: ?3.0 6.0 tensor([1.4389, 0.4796, 0.1599]) progress: ?96 0.006390606984496117 ?? ?grad: ?1.0 2.0 tensor([0.3161, 0.3161, 0.3161]) ?? ?grad: ?2.0 4.0 tensor([-1.7343, -0.8671, -0.4336]) ?? ?grad: ?3.0 6.0 tensor([1.4361, 0.4787, 0.1596]) progress: ?97 0.0063657015562057495 ?? ?grad: ?1.0 2.0 tensor([0.3164, 0.3164, 0.3164]) ?? ?grad: ?2.0 4.0 tensor([-1.7320, -0.8660, -0.4330]) ?? ?grad: ?3.0 6.0 tensor([1.4334, 0.4778, 0.1593]) progress: ?98 0.0063416799530386925 ?? ?grad: ?1.0 2.0 tensor([0.3166, 0.3166, 0.3166]) ?? ?grad: ?2.0 4.0 tensor([-1.7297, -0.8649, -0.4324]) ?? ?grad: ?3.0 6.0 tensor([1.4308, 0.4769, 0.1590]) progress: ?99 0.00631808303296566 predict (after tranining) ?4 8.544171333312988
損失值隨著迭代次數的增加呈遞減趨勢，如下圖所示：
可以看出：x=4時的預測值約為8.5，與真實值8有所差距，可通過提高迭代次數或者調整學習率、初始參數等方法來減小差距。
參考文獻：
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