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I have trouble understanding how to implement derivative of softmax function. Here is what I tried:

def Softmax(x):
    e_x = np.exp(x - np.max(x))
    return e_x / e_x.sum()

def d_Softmax(X):
    x=Softmax(X)
    s=x.reshape(-1,1)
    return (np.diagflat(s) - np.dot(s, s.T))

I am not sure if it works as it should. The normal softmax function, when taking $m \times n$ matrix as input, outputs a matrix of the same shape. The derivative, however, seems to output a matrix of shape $mn \times mn$.

I am trying to implement backpropagation of a simple 3-layer neural network on my own, but no other matrix has the shape aligned with the derivative that the softmax returns, so I don't know what it should be multiplied with.

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