MXNet - 将标量乘以数组导致零
MXNet - multiplying scalar to an array leads to zero
我正在尝试实现 mxnet in this page 的教程，计算体面梯度：
def SGD(params, lr):
for param in params:
param[:] = param - lr * param.grad
我注意到当 lr<1 时，标量与数组相乘
lr * param.grad
变成一个零矩阵，大小为param.grad
我不知道为什么会这样。任何人都可以帮助我理解这一点吗？
非常感谢
我在 PyCharm 本地 运行 该笔记本中的代码，并附加了一个调试器以尝试重现您所看到的内容。
def SGD(params, lr):
for param in params:
t = lr * param.grad
param[:] = param - t
当我在上面的代码中放置断点并检查 t 时，调试器显示全为零。但是当我 运行 代码时，一切 运行 都很好。那很奇怪。因此，我修改了代码以在每次迭代中打印每个像素的所有梯度的总和。
def SGD(params, lr):
for param in params:
t = lr * param.grad
print(nd.sum(param.grad, axis=-1))
param[:] = param - t
我得到了 this 输出。一次迭代的输出如下所示：
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -6.23335197e-08
2.91620381e-08 2.32830644e-10 1.11467671e-08 -7.45058060e-09
2.09547579e-09 -3.11993062e-08 3.44589353e-08 -7.45058060e-09
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
1.73723835e-09 -1.45343968e-08 1.51213424e-08 -4.47034836e-08
-1.19209290e-07 -8.10250640e-08 8.66129994e-08 3.77185643e-08
8.47503543e-08 8.66129994e-08 8.70786607e-08 5.35510480e-09
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 5.47231149e-09 -4.99075004e-10 -4.99075004e-10
6.05359674e-09 -9.66247171e-09 1.83936208e-08 -7.50416707e-09
1.12872200e-07 9.31513569e-08 2.45261617e-07 -1.86264515e-07
-5.28991222e-07 -2.68220901e-07 -1.22934580e-07 0.00000000e+00
2.08616257e-07 1.89989805e-07 4.33064997e-08 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 -2.75546541e-09 2.39708999e-08 -2.04163371e-08
6.70552254e-08 6.14672899e-08 4.40049917e-08 8.94069672e-08
8.94069672e-08 2.98023224e-07 1.19209290e-07 -5.96046448e-08
-2.38418579e-07 -4.76837158e-07 -4.76837158e-07 -2.38418579e-07
1.78813934e-07 4.13507223e-07 2.83122063e-07 3.09199095e-07
1.34285074e-07 6.17840215e-08 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 -2.19943086e-09 1.58324838e-08 6.26314431e-08
4.47034836e-08 5.96046448e-08 2.38418579e-07 4.76837158e-07
2.38418579e-07 4.76837158e-07 5.66244125e-07 1.49011612e-07
-4.17232513e-07 -2.38418579e-07 -3.57627869e-07 0.00000000e+00
0.00000000e+00 1.22934580e-07 1.97440386e-07 2.73808837e-07
4.55183908e-08 1.16733858e-08 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 7.33416528e-09 4.35829861e-08
4.36230039e-08 3.72456270e-08 1.67638063e-08 5.96046448e-08
1.49011612e-07 2.38418579e-07 -1.19209290e-07 -2.38418579e-07
-1.78813934e-07 2.38418579e-07 6.25848770e-07 3.57627869e-07
2.98023224e-08 -4.17232513e-07 -3.57627869e-07 -5.96046448e-08
-1.04308128e-07 1.19209290e-07 1.08033419e-07 -6.14672899e-08
-1.40164047e-07 -1.22236088e-07 -1.07334927e-07 0.00000000e+00
0.00000000e+00 0.00000000e+00 -2.17623892e-08 6.13508746e-08
7.71033228e-08 4.65661287e-09 0.00000000e+00 -5.96046448e-08
0.00000000e+00 2.38418579e-07 1.19209290e-07 3.57627869e-07
4.76837158e-07 1.19209290e-07 -2.38418579e-07 -1.78813934e-07
-4.76837158e-07 0.00000000e+00 1.78813934e-07 1.19209290e-07
5.06639481e-07 1.78813934e-07 -1.19209290e-07 -1.19209290e-07
-1.19209290e-07 0.00000000e+00 -1.34168658e-08 0.00000000e+00
0.00000000e+00 0.00000000e+00 4.71118256e-10 2.32830644e-09
2.53785402e-08 -2.83122063e-07 1.19209290e-07 1.19209290e-07
2.98023224e-07 0.00000000e+00 2.38418579e-07 3.20374966e-07
0.00000000e+00 3.57627869e-07 -2.38418579e-07 2.38418579e-07
-9.53674316e-07 -7.15255737e-07 1.19209290e-07 3.57627869e-07
4.17232513e-07 -7.45058060e-08 -5.96046448e-08 -1.19209290e-07
1.49011612e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -2.59024091e-09
-5.21540642e-08 -7.45058060e-09 -1.78813934e-07 5.96046448e-08
1.78813934e-07 1.19209290e-07 4.76837158e-07 2.98023224e-07
-5.96046448e-08 2.38418579e-07 3.57627869e-07 5.96046448e-08
-4.76837158e-07 1.78813934e-07 4.17232513e-07 -1.19209290e-07
2.98023224e-07 5.96046448e-08 2.04890966e-08 -1.30385160e-08
-4.83123586e-09 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 3.23634595e-08
-5.58793545e-08 -1.34110451e-07 -1.49011612e-08 -5.96046448e-08
1.49011612e-07 1.49011612e-08 1.78813934e-07 0.00000000e+00
0.00000000e+00 8.94069672e-08 5.96046448e-08 -1.19209290e-07
-3.57627869e-07 0.00000000e+00 4.76837158e-07 -2.38418579e-07
0.00000000e+00 1.02445483e-07 1.46217644e-07 -1.32713467e-08
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
-2.79396772e-08 -1.56462193e-07 -1.93715096e-07 1.82539225e-07
3.68803740e-07 4.32133675e-07 5.96046448e-08 -1.19209290e-07
0.00000000e+00 2.98023224e-07 -1.19209290e-07 -5.06639481e-07
1.19209290e-07 4.76837158e-07 8.94069672e-08 0.00000000e+00
0.00000000e+00 5.96046448e-08 8.61473382e-08 4.39467840e-08
4.85442797e-11 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
-2.79396772e-08 -1.86264515e-07 -1.93715096e-07 2.98023224e-08
3.57627869e-07 3.57627869e-07 -2.38418579e-07 -1.19209290e-07
-2.38418579e-07 -1.78813934e-07 -1.78813934e-07 0.00000000e+00
-4.02331352e-07 -2.23517418e-08 2.08616257e-07 -2.98023224e-08
2.38418579e-07 2.08616257e-07 2.37952918e-07 7.72388375e-08
3.80787242e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
-7.45058060e-08 -2.98023224e-08 1.11758709e-07 1.78813934e-07
4.76837158e-07 3.57627869e-07 -1.19209290e-07 0.00000000e+00
-3.57627869e-07 2.38418579e-07 -1.19209290e-07 5.96046448e-08
1.19209290e-07 1.49011612e-07 8.94069672e-08 1.78813934e-07
4.17232513e-07 4.47034836e-07 4.47034836e-07 8.42846930e-08
-3.70637281e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
-1.04308128e-07 0.00000000e+00 3.35276127e-07 2.68220901e-07
7.74860382e-07 7.15255737e-07 2.38418579e-07 1.19209290e-07
-2.38418579e-07 -3.57627869e-07 -3.57627869e-07 -8.94069672e-08
3.87430191e-07 3.57627869e-07 3.57627869e-07 5.96046448e-08
2.98023224e-07 4.76837158e-07 5.36441803e-07 4.84287739e-08
4.59044713e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -9.77270531e-09
-1.19209290e-07 7.45058060e-09 0.00000000e+00 3.57627869e-07
2.38418579e-07 5.96046448e-07 3.57627869e-07 9.53674316e-07
4.76837158e-07 1.19209290e-07 -2.38418579e-07 1.19209290e-07
-2.98023224e-07 -1.19209290e-07 -5.96046448e-08 -3.57627869e-07
1.78813934e-07 4.47034836e-07 3.87430191e-07 1.08033419e-07
3.81596692e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -4.18361026e-08
-5.63450158e-08 -4.84287739e-08 5.96046448e-08 2.38418579e-07
4.76837158e-07 3.57627869e-07 5.96046448e-07 1.78813934e-07
-1.19209290e-07 -1.19209290e-07 -2.68220901e-07 0.00000000e+00
0.00000000e+00 2.38418579e-07 -5.96046448e-07 -3.87430191e-07
1.19209290e-07 3.57627869e-07 3.87430191e-07 1.24797225e-07
6.91925379e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -4.36812968e-08
-5.60366971e-08 -8.84756446e-08 1.19209290e-07 -1.19209290e-07
3.57627869e-07 5.96046448e-08 0.00000000e+00 0.00000000e+00
-5.96046448e-07 1.19209290e-07 -2.98023224e-08 1.78813934e-07
-2.38418579e-07 -2.38418579e-07 3.57627869e-07 -3.57627869e-07
2.38418579e-07 2.38418579e-07 3.42726707e-07 1.14087015e-07
2.49773286e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -1.28651578e-09
-1.01268569e-07 -1.50499545e-07 -4.47034836e-08 0.00000000e+00
5.96046448e-08 3.57627869e-07 1.19209290e-07 -3.57627869e-07
-3.57627869e-07 2.98023224e-07 3.12924385e-07 5.96046448e-08
0.00000000e+00 -3.57627869e-07 -4.76837158e-07 5.96046448e-08
2.98023224e-07 2.98023224e-07 1.78813934e-07 7.29633030e-08
1.60424936e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
-7.72104300e-08 -3.55039447e-08 2.83529516e-07 2.63098627e-08
3.25031579e-07 7.45058060e-09 1.19209290e-07 -5.96046448e-08
-3.27825546e-07 6.70552254e-08 3.12924385e-07 4.17232513e-07
-3.57627869e-07 -4.76837158e-07 -1.19209290e-07 1.78813934e-07
2.98023224e-07 1.71363354e-07 6.27478585e-08 1.92048901e-08
-3.83870313e-09 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
-6.35419752e-08 -5.20981303e-08 2.64481059e-08 6.12053555e-08
2.30735168e-07 -2.51457095e-08 -2.98023224e-07 -3.57627869e-07
1.78813934e-07 6.55651093e-07 2.38418579e-07 -5.96046448e-08
-3.57627869e-07 3.57627869e-07 1.19209290e-07 1.78813934e-07
1.49011612e-07 8.19563866e-08 4.22005542e-08 2.06365929e-08
2.06365929e-08 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
2.09386428e-08 5.31318420e-08 -5.19480636e-09 -1.55114321e-07
7.33416528e-08 -2.98023224e-08 -2.98023224e-08 -2.98023224e-07
4.76837158e-07 2.38418579e-07 5.96046448e-08 3.57627869e-07
1.19209290e-07 0.00000000e+00 2.38418579e-07 1.04308128e-07
3.91155481e-08 4.49217623e-08 2.17316245e-08 2.06365929e-08
2.23254459e-09 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
1.64938871e-08 6.39862421e-08 5.16827185e-08 1.46355887e-07
-1.34110451e-07 -5.96046448e-08 2.38418579e-07 7.74860382e-07
9.53674316e-07 1.19209290e-07 0.00000000e+00 3.57627869e-07
2.38418579e-07 0.00000000e+00 1.19209290e-07 1.44354999e-08
2.26427801e-08 1.19798682e-09 -4.99121011e-09 -4.99121011e-09
-2.63172950e-09 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 3.20321369e-08 5.63813956e-08 8.19563866e-08
0.00000000e+00 -1.19209290e-07 1.19209290e-07 1.19209290e-07
1.19209290e-07 -1.19209290e-07 0.00000000e+00 0.00000000e+00
5.96046448e-08 -7.45058060e-09 4.09781933e-08 1.63381628e-08
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 -7.45058060e-08 -5.96046448e-08
-1.78813934e-07 5.96046448e-08 -2.88709998e-08 -3.35276127e-08
6.28060661e-08 2.98023224e-08 1.19209290e-07 5.96046448e-08
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 -1.19209290e-07 -1.19209290e-07
0.00000000e+00 -1.49011612e-08 -2.67755240e-08 -1.49157131e-09
7.06131686e-09 6.01576176e-08 -2.69501470e-08 1.49011612e-08
0.00000000e+00 0.00000000e+00 -7.45058060e-09 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]
<NDArray 784 @cpu(0)>
请注意，前几十个像素的权重梯度始终为零。由于调试器仅显示 ndarray 上的前几个值，因此您看到的只是零。
前几十个像素的权重梯度很可能为零，因为这些像素不包含任何可用于对图像中的数字进行分类的信息。请注意，MNIST 图像以图像为中心。沿边界的像素仅为 0.
希望对您有所帮助。
我正在尝试实现 mxnet in this page 的教程，计算体面梯度：
def SGD(params, lr):
for param in params:
param[:] = param - lr * param.grad
我注意到当 lr<1 时，标量与数组相乘
lr * param.grad
变成一个零矩阵，大小为param.grad
我不知道为什么会这样。任何人都可以帮助我理解这一点吗？
非常感谢
我在 PyCharm 本地 运行 该笔记本中的代码，并附加了一个调试器以尝试重现您所看到的内容。
def SGD(params, lr):
for param in params:
t = lr * param.grad
param[:] = param - t
当我在上面的代码中放置断点并检查 t 时，调试器显示全为零。但是当我 运行 代码时，一切 运行 都很好。那很奇怪。因此，我修改了代码以在每次迭代中打印每个像素的所有梯度的总和。
def SGD(params, lr):
for param in params:
t = lr * param.grad
print(nd.sum(param.grad, axis=-1))
param[:] = param - t
我得到了 this 输出。一次迭代的输出如下所示：
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 -6.23335197e-08
2.91620381e-08 2.32830644e-10 1.11467671e-08 -7.45058060e-09
2.09547579e-09 -3.11993062e-08 3.44589353e-08 -7.45058060e-09
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
1.73723835e-09 -1.45343968e-08 1.51213424e-08 -4.47034836e-08
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<NDArray 784 @cpu(0)>
请注意，前几十个像素的权重梯度始终为零。由于调试器仅显示 ndarray 上的前几个值，因此您看到的只是零。
前几十个像素的权重梯度很可能为零，因为这些像素不包含任何可用于对图像中的数字进行分类的信息。请注意，MNIST 图像以图像为中心。沿边界的像素仅为 0.
希望对您有所帮助。