The Softmax Jacobian

How a network computes, why gradients vanish, and what makes depth trainable

Softmax has a property no elementwise activation has: its outputs are tied to each other. Every probability is divided by the same total, so raising one logit does not only raise its own probability. It lowers all the others, because the shares have to keep adding to 1.

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โ–ถ The Softmax Jacobian
โ† Where Backprop Starts: the Derivative of the LossBackprop Through a Layer Block: the Activation's Half โ†’