Rolling Average vs Softmax & Cross Entropy

If each Guess Factor bin is considered an output unit before Softmax (logit), and loss is Cross Entropy, then the gradient of each logit is then:

q_i - 1, if bin is hit

q_i, otherwise

If gradient is not applied on logit as normal, but instead applied on q_i itself, then:

q_i := q_i - eta * (q_i - 1) = (1 - eta) * q_i + eta * 1, if bin i hit

q_i := q_i - eta * q_i = (1 - eta) * q_i + eta * 0, otherwise

Which is essentially rolling average, where eta (learning rate) equals to the alpha (decay rate) in exponential moving average.