Why Do Neural Networks Love the Softmax?

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Neural Networks see something special in the softmax function.

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SOURCE NOTES

I decided to make this video when inspecting jacobians/gradients starting from the end of a small network. Right near the softmax, the jacobian looked simple enough that I suspected interesting math behind it. And there was. I came across several excellent blogs on the Softmax's jacobian and its interaction with the negative log likelihood. Source [1] was the primary source, since it was quite well explained and used condensed notation. [2] was useful for understanding the broader context and [3] was a separate, thorough perspective.

SOURCES

[1] M. Peterson, "Softmax with cross-entropy," https://mattpetersen.github.io/softma..., 2017

[2] I. Goodfellow, Y. Bengio, A. Courville, Deep Learning, MIT Press, 2016, section 6.2.2.3

[3] M. Lester James, "Understanding softmax and the negative log-likelihood," https://ljvmiranda921.github.io/noteb..., 2017

TIME CODES
0:00 Everyone uses the softmax
0:23 A Standard Explanation
3:20 But Why the Exponential Function?
3:57 The Broader Context
6:05 Two Choices Together
6:51 The Gradient
10:07 Other Reasons

• #education
• #softmax
• #neural_network