I was reading a paper about neural network technique. In this paper, one have an initial vector $V_i$ of parameters here let's says $[a_1, a_2, a_3]$, with initial probabilities $[p_1, p_2, p_3]$ (obtained by passing $V_i$ throught a softmax function).
This inital vector is changed during the backpropagation, so we get a new vector $[a_1', a_2', a_3']$ with new probabilities $[p_1', p_2', p_3']$.
According to the paper only two value need to be modified, so the probabilities of the others need to stay the same. (cf. "we need to rescale the value of these two updated architecture parameters by multiplying a ratio to keep the path weights of unsampled paths unchanged."). Here let's says $a_3$ have not been sampled so after rescaling $p_3'$ should equals $p_3$. So one need to rescale $[a_1', a_2']$ to handle this constraint, and so $p_1'$ and $p_2'$ can change.
But I can't understand how is it possible, I tried to use the reverse softmax but my results are not conclusive, have you any intuition ?
Thank you for your time.