如何向量化多维矩阵的 Softmax 概率

Question

我正在尝试完成 Stanford cs244n class 的 assignment 1。问题 1b 强烈建议对 Softmax 函数进行优化。我设法得到了N维向量的Softmax。我还得到了 MxN 维矩阵的 Softmax，但在列中使用了 for 循环。我有以下代码：

def softmax(x):
    orig_shape = x.shape

    # Matrix
    if len(x.shape) > 1:
        softmax = np.zeros(orig_shape)
        for i,col in enumerate(x):
            softmax[i] = np.exp(col - np.max(col))/np.sum(np.exp(col - np.max(col)))
    # Vector
    else:
        softmax = np.exp(x - np.max(x))/np.sum(np.exp(x - np.max(x)))
    return softmax

我可以实现更优化的 Matrix 实现吗？

Answer 1

您可以尝试使用 np.apply_along_axis，您必须在其中指定执行代码的轴（在您的情况下为 axis=1）。这是一个工作示例：

In [1]: import numpy as np

In [2]: def softmax(x):
   ...:     orig_shape = x.shape
    ...: 
   ...:     # Matrix
   ...:     if len(x.shape) > 1:
   ...:         softmax = np.zeros(orig_shape)
   ...:         for i,col in enumerate(x):
   ...:             softmax[i] = np.exp(col - np.max(col))/np.sum(np.exp(col - np.max(col)))
   ...:     # Vector
   ...:     else:
   ...:         softmax = np.exp(x - np.max(x))/np.sum(np.exp(x - np.max(x)))
   ...:     return softmax
   ...: 

In [3]: def softmax_vectorize(x):
   ...:     return np.exp(x - np.max(x))/np.sum(np.exp(x - np.max(x)))
   ...: 

In [4]: X = np.array([[1, 0, 0, 4, 5, 0, 7],
   ...:            [1, 0, 0, 4, 5, 0, 7],
   ...:            [1, 0, 0, 4, 5, 0, 7]])

In [5]: print softmax(X)
[[  2.08239574e-03   7.66070581e-04   7.66070581e-04   4.18260365e-02
    1.13694955e-01   7.66070581e-04   8.40098401e-01]
 [  2.08239574e-03   7.66070581e-04   7.66070581e-04   4.18260365e-02
    1.13694955e-01   7.66070581e-04   8.40098401e-01]
 [  2.08239574e-03   7.66070581e-04   7.66070581e-04   4.18260365e-02
    1.13694955e-01   7.66070581e-04   8.40098401e-01]]

In [6]: print np.apply_along_axis(softmax_vecorize, axis=1, arr=X)
[[  2.08239574e-03   7.66070581e-04   7.66070581e-04   4.18260365e-02
    1.13694955e-01   7.66070581e-04   8.40098401e-01]
 [  2.08239574e-03   7.66070581e-04   7.66070581e-04   4.18260365e-02
    1.13694955e-01   7.66070581e-04   8.40098401e-01]
 [  2.08239574e-03   7.66070581e-04   7.66070581e-04   4.18260365e-02
    1.13694955e-01   7.66070581e-04   8.40098401e-01]]

Answer 2

使用 NumPy broadcasting on relevant ufuncs 并且涵盖通用维数的 ndarrays -

exp_max = np.exp(x - np.max(x,axis=-1,keepdims=True))
out = exp_max/np.sum(exp_max,axis=-1,keepdims=True)

如何向量化多维矩阵的 Softmax 概率

How to vectorize Softmax probability of a multi dimensional matrix

python

performance

numpy

vectorization

softmax